![Introduction and Problem Statement 3
that the achievement of system-level requirements by far exceed the achievable relia-
bility of individual components [MUR 03]. The deep intrication of components and
sub-systems, which come from different technologies, and which are subject to vari-
ous constraints, calls for a joint design to solve potentially conflicting constraints early
on. The fact that control has the ability to cope with uncertainty and disturbances, due
to closed loops based on sensing the current system’s state, makes it a basic method-
ology to be used in such complex systems design.
Besides reaching the specified performance in normal situations, reliability and
safety-related problems are of a constant concern for system designers. A general
and integrated concept is dependability, which is the system property that includes
various attributes such as availability, reliability, safety, confidentiality, integrity, and
maintainability [LAP 92]. Being confronted with faults, errors and failures, a system’s
dependability can be achieved in different ways, i.e. fault prevention, fault tolerance,
fault removal and fault forecasting [AVI 00]. While these concepts have been formal-
ized for systems in a broad sense, it appears that the existing control toolbox already
provides concepts, e.g. robust and fault tolerant control, which are likely to achieve
control system dependability. A better integration of advanced control, computing
power and redundancy based on resource distribution is expected to further enhance
this capability.
Except in the case of failures due to hardware or software components, most pro-
cesses usually run with nominal behavior: however, even in the nominal modes, nei-
ther the process nor the execution resource parameters are ever perfectly known or
modeled. A very conservative viewpoint consists of allocating system resources to sat-
isfy the worst case, but this results in the execution resources being over-provisioned
and thus wasted. From the control viewpoint, specific deficiencies to be considered
include poorly predictable timing deviations, delays, and data loss.
Control usually deals with modeling uncertainty, dynamic adaptation, and distur-
bance attenuation. More precisely, as shown with recent results obtained on NCS
[BAI 07], control loops are often robust and can tolerate computing and networking
performance induced disturbances, up to a certain extent. Therefore, timing devia-
tions such as jitter or data loss, as long as they remain inside the bounds which are
compliant with the control specification, may be considered as features of the nom-
inal system, not exceptions. Relying on control robustness allows for provisioning
the execution resources according to average needs rather than for worst cases, and to
consider system reconfiguration only when the failures exceed the capabilities of the
running controller tolerance.
An NCS is made up of a heterogenous collection of physical devices, falling
within the realm of continuous time, and information sub-systems basically working
with discrete timescales. During an NCS design process, many conflicting constraints](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-20-320.jpg)
![4 Networked Control Systems Co-design
must be simultaneously solved before reaching a satisfactory and implementable so-
lution. For example, trade-offs must be negotiated between processing and network-
ing speed, control tracking performance, robustness, redundancy and reconfigurabil-
ity, energy consumption, and overall cost effectiveness. These conventional design
process problems from the different domains in succession prevent any coherent and
effective integration of methodologies, technologies or associated constraints.
Traditionally control usually deals with a single process and a single computer,
and it is often assumed that the limitations of communication links and computing
resources do not significantly affect performance, or they are taken into account in a
limited way. Existing tools dealing with modeling and identification, robust control,
fault diagnosis and isolation, fault tolerant control and flexible real-time scheduling
need to be enhanced, adapted and extended to cope with the networked characteristics
of the control system.
Finally, the concept of a co-design system approach has emerged to allow
progress in the integration of control, control, and communications in the NCS design
[MUR 03] and to develop implementation-aware control system co-design approaches
[BAI 07].
According to the systems scientist and philosopher, C.W. Churchman, “the system
approach begins when first you view the world through the eyes of another” [CHU 79].
The basic aspect of co-design applied to NCS is that the design of controllers and the
design of the execution resources, i.e. the real-time computing and communication
sub-systems, are integrated right from the early design steps to jointly solve the con-
straints arising from all sides.
Control design: from continuous time to networked implementation
In the early age of control, analog computers were used to work out the control
signals, firstly from mechanical devices, and then from electronic amplifiers and in-
tegrators: both the plant and the controller remained in the realm of continuous time,
while frequency analysis and Laplace transform were the main tools at hand. The
main drawbacks of analog computing come from limited accuracy and bandwidth,
drift and noise, and from limited capabilities to handle nonlinearities. Pure and known
delays could, however, be handled at control synthesis time by using the well-known
Smith predictor.
Then, due to the increasing power and availability of cheap numerical processors,
digital controllers gradually took over the analogue technology. However, controlling
a continuous plant with a discrete digital system inevitably introduces timing distor-
tions. In particular, it becomes necessary to sample and convert the sensors measure-
ments to binary data, and conversely to convert them back to physically related values
I.2.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-21-320.jpg)
![Introduction and Problem Statement 5
and hold the control signals to actuators. The sampling theory and the z transform
became the standard tools for digital control systems analysis and design. A smart
property of the z transform is that it keeps the linearity of the system through the
sampling process. As the underlying assumption behind the z transform is equidistant
sampling, periodic sampling became the standard for the design and implementation
of digital controllers.
Note that, at the infancy of digital control, where computing power was weak and
memory was expensive, it was important to minimize the controllers’ complexity and
needed operating power. It is not obvious that the periodic sampling assumption is
always the best choice: for example, [DOR 62] show that adaptive sampling, where
the sampling frequency is changed according to the value of the derivative of the error
signal, can be more effective than equidistant sampling in terms of the number of com-
puted samples (but possibly not in terms of disturbance rejection [SMI 71]). [HSI 72]
and [HSI 74] provide a summary of these efforts. However, due to the constantly
increasing power and decreasing costs of computing, interest in sampling adaptabil-
ity and the related computing power savings has progressively vanished, while the
linearity preservation property of equidistant sampling has helped it to remain the in-
disputable standard for years.
From the computing side, real-time scheduling modeling and analysis were intro-
duced in the illustrious seminal paper [LIU 73]. This first schedulability analysis was
based on restrictive assumptions, one of them being the periodicity of all the real-time
tasks in the system. Even if more general assumptions have been progressively in-
troduced to cope with more realistic problems and tasks sets [AUD 95; SHA 04], the
periodicity assumption remains very popular, e.g. see today’s success of rate mono-
tonic analysis (RMA) based tools in industry, e.g. [SHA 90; DOY 94; HEC 94]. The
combination of these popular modeling and analysis methods and tools has likely rein-
forced the understanding that control systems are basically periodic and hard real-time
systems.
More recently, again due to the progress in electronic devices technology, it has
become possible to distribute control loops over networks. Networking allows for
the dissemination of sensors, actuators, and controllers on different physical nodes.
Moreover, the topology of the network can be time varying, thus allowing the control
devices to be mobile: hence, the whole control system can be highly adaptive in a
dynamic environment. In particular, wireless communications allow for a cheap de-
ployment of sensor networks and remotely controlled devices. However, networking
also induces disturbances in control loops, such as variable and potentially long de-
lays, data corruption, message desequencing and occasional data loss. These timing
uncertainties and disturbances are in addition to those coming from the digital imple-
mentation of the controllers in the network nodes.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-22-320.jpg)
![6 Networked Control Systems Co-design
Timing parameter assignment
Digital control systems can be implemented as a set of tasks running on top of a
commercial off-the-shelf real-time operating system (RTOS) using fixed-priority and
pre-emption. The performance of a control loop, e.g. measured by the tracking error,
and even more importantly its stability, strongly relies on the values of the sampling
rates and sensor-to-actuator latencies (the latency considered for control purposes is
the delay between the instant when a measure qn is taken at a sensor and the instant
when the control signal U(qn ) is received by the actuators [ÅST 97]. Therefore, it
is essential that the implementation of the controller respects an adequate timing be-
havior to meet the expected performance. However, implementation constraints such
as multi-rate sampling, pre-emption, synchronization, and various sources of delays
make the run-time behavior of the controller very difficult to accurately predict. Deal-
ing with closed-loop controllers may take advantage of the robustness and adaptivity
of such systems to design and implement flexible and adaptive real-time control archi-
tectures.
Closed-loop digital control systems use a computer to sample sensors, calculate
a control law and send control signals to the actuators of a physical process. The
control algorithm can be either designed in continuous time and then discretized or
directly synthesized in discrete time, taking into account a model of the plant sampled
by a zero-order holder. A control theory for linear systems sampled at fixed rates was
established a long time ago [ÅST 97].
Assigning an adequate value for the sampling rate is a decisive duty, as this value
has a direct impact on the control performance and stability. While an absolute lower
limit for the sampling rate is given by Shannon’s theorem, in practice, rules of thumb
are used to give a useful range of control frequencies according to the process dy-
namics and the desired closed loop bandwidth. Among others, such a rule of thumb is
given in [ÅST 97] as ωc h ≈ 0.15 . . . 0.5, where ωc is the desired closed-loop pulsation
and h is the sampling period. Note that such rules only give preliminary information
about the sampling rate to be actually implemented, and sampling rate selection needs
to be further refined by simulations and experiments. In particular, it appears that
the actual sampling rate to be used with some nonlinear systems, as those described
in sections 1.4.2.3, 2.4.4, and in Chapter 7, must be far faster to achieve closed-loop
stability. However, most often, it can be stated that the lower the control period and
latencies are, the better the control performance is, e.g. measured by the tracking error
or disturbance rejection. This assumption can be reinforced by providing a suitable
control structure and parameter tuning, as shown in section 2.3 with the discussion on
weakly hard real-time constraints and accelerable control tasks.
While timing uncertainties have an impact on the control performance, the actual
scheduling parameters are difficult to model accurately or constrain within precisely
known bounds. Thus, it is worth examining the sensitivity of control systems w.r.t.
I.3.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-23-320.jpg)
![Introduction and Problem Statement 7
Sampling rate
Performance degradation
Best performance
Continuous
control
Acceptable
performance
zone
Unacceptable
performance
zone
Instability
Digital
control
Networked
control
A B C
PA PB PC
control vs. sampling rate
timing fluctuations. The accepted wisdom is that the lower the control period is, the
better the control performance is. However, the underlying implementation system is
a limited resource and cannot accommodate arbitrarily high sampling rates; thus, there
must be a trade-off between the control performance and the execution resource uti-
lization. This is particularly true for distributed embedded system design with limited
resources due to weight, cost and energy consumption constraints. In [MOY 07] and
ing a good sampling period which gives a trade-off between control performance and
the related network load.
sampling rate range from PB to PC . Increasing the sampling rate beyond PC will
increase the network load and lead to longer network-induced delays. This results
in a control performance degradation. Note that for a given control application, the
affordable network bandwidth can also vary accordingly. This can provide a network
QoS designer with a larger solution space for designing the QoS mechanisms with
more flexibility.
The hard real-time assumption must be softened to better cope with the reality of
closed-loop control, for instance, changing the hard timing constraints for “weakly-
hard” constraints [BER 01]. For example, hard deadlines may be replaced by statisti-
cal models, e.g. to specify the jitter characteristics compliant with the requested con-
trol performance. They may also be changed for deadline miss or data-loss patterns,
e.g. to specify the number of deadline misses allowed over a specified time window
Figure I.2. Performance comparison of continuous control, digital control, and networked
[LIA 02], the illustrative chart in Figure I.2 is given to show the importance of choos-
From Figure I.2, it can be seen that the control performance is acceptable for a](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-24-320.jpg)
![8 Networked Control Systems Co-design
according to the so-called (m, k)-firm model [HAM 95]. More precisely, a task meets
the (m, k)-firm constraint if at least m among any k consecutive task instances meet
their deadline. Note that to be fully exploited, weakly hard constraints should be as-
sociated with a decisional process: tasks missing their deadline can, for example, be
delayed, aborted or skipped according to their impact on the control law behavior, e.g.
as analyzed in [CER 05].
Finding the values of such weakly hard constraints for a given control law is cur-
rently out of the scope of current control theory, in general. However, the intrinsic
robustness of closed-loop controllers allows for relying on softened timing constraint
specification and flexible scheduling design, leading to an adaptive system with grace-
ful performance degradation during system overloads. Chapter 5 gives an example of
finding the values of m and k when the (m, k)-firm constraint is applied to the control-
loop task execution requirement.
Control and task/message scheduling
From the implementation point of view, real-time systems are often modeled as
a set of periodic tasks assigned to one or several processors. In distributed real-time
systems, messages are exchanged among related tasks through a network. To ensure
the execution of tasks on a processor, the worst-case response time analysis technique
is often used to analyze fixed-priority real-time systems. Well-known scheduling poli-
cies, such as rate monotonic for fixed priorities and EDF for dynamic priorities, assign
priorities according to timing parameters, respectively, sampling periods and dead-
lines. They are said to be “optimal” as they maximize the number of task sets which
can be scheduled with respect to deadlines, under some restrictive assumptions. Un-
fortunately, they are not optimized for control purposes. They hardly take into account
precedence and synchronization constraints, which naturally appear in a control algo-
rithm. The relative urgency or criticality of the control tasks can be unrelated with
the timing parameters. Thus, the timing requirements of control systems w.r.t. the
performance specification do not fit well into scheduling policies based purely on
schedulability achievement.
It has been shown through experiments, e.g. [CER 03], that a blind use of such
traditional scheduling policy can lead to an inefficient controller implementation; on
the other hand, a scheduling policy based on an application’s requirements, associ-
ated with a smart partition of the control algorithm into real-time modules may give
better results. It may be that improving some computing related feature is in con-
tradiction with another one targeted to improve the control behavior. For example,
the case studies examined in [BUT 07] show that an effective method to minimize
the output control jitter consists of systematically delaying the output delivery at the
I.4.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-25-320.jpg)
![Introduction and Problem Statement 9
end of the control period: however, this method also introduces a systematic one pe-
riod input/output latency, and therefore most often provides the worst possible control
performance among the set of considered strategies.
Another example of unsuitability between computing and control requirements
arises when using priority inheritance or priority ceiling protocols to bypass priority
inversion due to mutual exclusion, e.g. to ensure the integrity of shared data. While
they are designed to avoid deadlocks and minimize priority inversion lengths, such
protocols jeopardize the initial schedule at run time, although it was carefully designed
with latencies and control requirements in mind. As a consequence, latencies along
some control paths can be largely increased, leading to a poor control performance or
even instability.
In a distributed system design, not only should the task set schedulability be en-
sured, but also message transmission through the network, since sensor to actuator
latencies heavily depend on transmission delay. Also, the schedulability tests must
consider tasks and messages as a whole, since a message is produced by a task exe-
cution and it may be needed to trigger another task execution. In [TIN 94], a holistic
approach is proposed. It consists of applying the worst-case response time analysis
technique to evaluating the end-to-end response time of a set of tasks distributed over
a controller area network (CAN). Periodic messages over CAN are scheduled under
a non pre-emptive, fixed priority policy. Their release jitters are caused by local task
scheduling. The worst case is considered where all messages are assumed to be re-
leased at the same time. This approach can effectively be used to validate distributed
control applications, but suffers from the resource over-provisioning problem because
of the obligation to consider the worst-case. The inherent robustness of the closed-
loop control application is not exploited.
Finally, off-line schedulability analysis relies on correctly estimating the tasks’
worst-case execution time (WCET). Even in embedded systems the processors use
caches and pipelines to improve the average computing speed, but this decreases the
timing predictability. When a network is included, additional timing uncertainty is
emphasized. Depending on the network protocols, the network-induced delay and
data loss can be very different. For instance, let us just take as an example the two
widely used industrial networks CAN and switched Ethernet.
A CAN uses a global priority-based medium access control protocol. High priority
messages have lower transmission latencies while low priority ones can suffer from
longer transmission delays [LIA 01]. An Ethernet switch can also deal with messages
using quite different scheduling policies (e.g. FIFO, WRR, fixed priority), resulting in
very different transmission delays. For real-time computing and networking design-
ers, the new challenge is how to design the quality of service (QoS) mechanisms in
scheduling both tasks in multitasking computing and messages managed by network
protocols, e.g. message scheduling at the MAC level, routing, etc. to meet specified](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-26-320.jpg)
![10 Networked Control Systems Co-design
control-loop requirements. In fact, traditional QoS approaches assume that there is
a deadline for each application, and a static resource allocation principle based on
the worst-case situation is often used to provide delay/deadline guarantees. This ap-
proach also leads to a resource over-provisioning problem since a worst-case scenario
is considered.
Another source of uncertainty may come from some parts of the estimation and
control algorithms themselves. For example, the duration of a vision process highly
depends on incoming data from a dynamic scene. Also, some algorithms are iterative,
with a poorly predictable convergence rate, so the time before reaching a predefined
threshold is unknown (and must be bounded by a timeout associated with a recovery
process). In a dynamic environment, some of the less important control activities
can be suspended or resumed in the case of transient overload, or alternative control
algorithms with different costs can be scheduled according to various control modes,
leading to large variations in the computing load.
Thus, real-time control design based on worst-case execution time, maximum ex-
pected delay, and strict deadlines inevitably lead to a low average usage of the com-
puting resources and to a poor adaptability w.r.t. a complex execution environment.
All these drawbacks call for a better integration of control objectives with comput-
ing and communication capabilities through a co-design approach taking into account
both actual application requirements and the implementation system characteristics.
Diagnosis and fault tolerance in NCS
Due to an increasing complexity of dynamic systems, as well as the need for
reliability, safety and efficient operation, model-based fault diagnosis has became
an important subject in modern control theory and practice, e.g. [WIL 76; FRA 90;
GER 98]. Different techniques of model-based methods include observer based-,
parity relation- and parameter estimation approaches [CHE 99; MAN 00; ZHA 03].
When sampling and control data are transmitted over the network, many network-
induced effects such as time delays and packet losses will naturally arise. Owing to
the network-induced effects, the theories for traditional point-to-point systems should
be revisited when dealing with NCSs. Different studies have shown the importance
of taking into account characteristics of networks in the design of a fault diagnosis
system [DIN 06; LLA 06]. The main idea of these approaches is to minimize the false
alarms caused by transmission delays. In this case, a network-induced delay is consid-
ered when designing the FDI filter. On the other hand, FDI algorithms require specific
information on the process, thus the implementation of such algorithms increases the
network load and consequently, affects its QoS. The number of signals to be transmit-
ted may be reduced by allowing only a part of sensors and actuators to have access to
the network. In this case, less information is available for FDI at each sampling time.
I.5.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-27-320.jpg)
![Introduction and Problem Statement 11
In [ZHA 05], observability conditions are established for the reduced communication
pattern.
Based on the fault diagnosis algorithm for NCSs, fault-tolerant control of NCSs
can be obtained. The existing methods of fault-tolerant control techniques against
actuator faults can be categorized into two groups: passive [SEO 96; CHE 04] and
active approaches [ZHA 02; ZHA 06]. [ZHE 03] proposed a passive controller for
NCSs considering random time delays. Although the passive controllers are easy to
implement, their performances are relatively conservative. The reason is that this class
of controllers, based on the alleged set of component failures and with a fixed struc-
ture and parameters, is used to deal with all the different failure scenarios possible. If
a failure occurs out of those considered in the design, the stability and performance
of the closed-loop system is unanticipated. Such potential limitations of passive ap-
proaches are behind the motivation for the research on active FTC (AFTC). AFTC
procedures require an on-line and real-time fault diagnosis process and a controller
reconfiguration mechanism. Because AFTC approaches propose a kind of flexibility
to select different controllers according to different component failures, better perfor-
mance of the closed loop system is expected. However, the above case holds only if
the fault diagnosis process provides a correct, or synchronous, decision.
Some preliminary results have been obtained on AFTC which tend to make the
reconfiguration mechanism immune from imperfect fault diagnosis decisions, as in
[MAH 03] and [WU 97]. [MAK 04] further discussed the above issue by using the
guaranteed cost control approach and on-line controller switching in such a way that
the closed-loop system was stable at all times. However, [MAK 04] did not consider
the plant controlled over the network.
Co-design approaches
NCS encompasses the control-loop application and the implementation system
(CPU and the networks managed by operating systems and protocols). Research work
on NCS mainly focuses on the robust control-loop design which takes into account
the implementation-induced delays and data loss. Network delays are assumed to
be either constant (can be realized by input data buffering) or randomly distributed,
following a well-known probability distribution. Data losses are assumed to follow
a Bernoulli process [ANT 07a; ZAM 08]. From these works, it appears that the as-
sumptions on network delay or data loss patterns seldom consider the actual network
characteristics nor the possible QoS mechanisms which are specific for each type of
network. In fact, using a prioritized bus like CAN, a switched Ethernet or a wireless
sensor network will result in fundamentally different QoS characteristics. This point is
of primary importance especially when the network is shared by several control loops
and other applications whose exact characteristics are often unknown at the control
loop design step. In this case, the traffic scheduling has a great impact on both delay
I.6.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-28-320.jpg)
![12 Networked Control Systems Co-design
variations and packet loss, which in turn impacts the control quality (stability and per-
formance) of the control loops. One solution to this problem relies on a tight coupling
between the control specification and the implementation system at design time.
Generally speaking, two ways to achieve an efficient NCS design can be distin-
guished. One way that is currently being explored by the control theorists can be
called “implementation-aware control law design.” The idea is to make on-line adap-
tations to the control loops parameters by adjusting, for example, the control loop
sampling period using a LQ approach in [EKE 00; CER 03], sample-time and/or de-
lay dependent gain scheduling in [MAR 04] and [SAL 05], a robust H∞ design in
[SIM 05], a hybrid rate adaptation in [ANT 07b], or both the actuation intervals and
control gains using model predictive control and hybrid modeling as in [Ben 06], or
LQ control associated with a (m, k)-firm policy as in [JIA 07] and [FEL 08].
Another is the so-called “control-aware QoS adaptation,” which is being explored
by the network QoS designers. The idea is to re-allocate the implementation system
resources on-line to maintain or increase the QoS level required by the control appli-
cation. In [JUA 07], a hybrid CAN message priority allocation scheme is proposed.
When there is an urgent transmission need, a dynamic priority field can be used to give
it even higher priority. This work exhibits a link between the hybrid priority scheme
and the control loop performance. In [DIO 07], the dynamic allocation of bandwidth
sharing in Ethernet switches with weighted round-robin (WRR) scheduler based on
both observed delay and the variation in the control quality (i.e. the difference be-
tween the reference and the process state) is presented. For this purpose, bandwidth
sharing (i.e. the weight assigned to each data flow or Ethernet switch port) is defined
as a function of the sensor to actuator delay and the current quality of control (QoC)
level.
Of course, a combination of both approaches will contribute to a more efficient
NCS design. Another very important aspect is the diagnosis and fault tolerance in
NCS. This aspect is to be integrated in the co-design approach for achieving efficient
and dependable NCS design.
Outline of the book
This book intends to provide an introduction to the problems that arise in NCS
design and to present the different co-design approaches.
The first chapter provides preliminary concepts, together with state of the art tech-
niques and existing solutions to implement distributed process control and diagno-
sis. In particular, control-aware static computing and network resource allocation
schemes are first reviewed. Then, the real-time adaptive resource allocation approach
I.7.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-29-320.jpg)
![14 Networked Control Systems Co-design
scheduling co-design schemes, coupling control performance, and scheduling param-
eters more tightly, through the means of a few case studies. In section 4.2 the varying
sampling control laws are used as building blocks for such co-design schemes, with
no guarantees for the stability of the global loops. Section 4.3, summarizes a sub-
optimal solution for the case of control/scheduling co-design using a slotted timescale
based on the model predictive control approach. A convex optimization approach in
the framework of linear systems and linear quadratic control is provided in section
4.4. Finally, section 4.5 describes a LPV-based joint control and scheduling approach
applied to the control of a robot arm.
During system and network overload, excessive delays, or even data loss, may
occur. To maintain the QoC of an NCS, the implementation system overload must
be dealt with. As shown in Chapters 1 and 4, a common approach to deal with this
overload problem is to dynamically change the sampling period of the control loops.
In Chapter 5, an alternative to the explicit sampling period adjustment is proposed as
an indirect sampling period adjustment. It is based on selective sampling data drops
according to the (m, k)-firm model [HAM 95]. The interest of this alternative is its
ease of implementation, despite reduced adjustment quality since only the multiples
of the basic sampling period are used.
Chapter 6 deals with the processing of faults that may occur during the NCS op-
eration. These faults may affect the system’s physical components, or its sensors and
actuators, or even the network itself. From a safety point of view, it is important to
detect the occurrence of such faults, to determine the faulty physical components by
fault detection and isolation (FDI). FDI allows some automatic reaction to the super-
vision system (for instance automatic shut down in case of danger) or reaction to the
human operators in charge of the installation (for instance, manual control in open
loop). Sometimes, when these faults exceed the capabilities of robust control loops,
they can be accommodated by advanced control algorithms, compensating for the sys-
tem’s deficiencies by means of FTC. Section 6.2 recalls the basic results in FDI/FTC
for the centralized case. Then the drawbacks of networking for fault detection and
isolation are highlighted and some pragmatic solutions are given in section 6.4. More
advanced techniques for FDI/FTC over networks subject to delays and data loss, some
of which are still in the research field, are finally given in section 6.5.
Finally, Chapter 7 is devoted to the experimental validation of the approaches ex-
posed along the previous chapters, to assess their feasibility and effectiveness. A
quad-rotor miniature drone has been used throughout the SafeNecs project1 as a com-
mon setup to integrate contributions from the team’s partners, including variable sam-
pling control, control under (m, k)-firm scheduling constraints, diagnosis and FDI
1. SafeNecs is a research project funded by the French “Agence Nationale de la Recherche”
under grant ANR-05-SSIA-0015-03](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-31-320.jpg)
![Introduction and Problem Statement 15
over a network, dynamic priorities on a CAN bus and fault-tolerant control of the set
of actuators. The development process starts with simulation under Matlab/Simulink;
real-time constraints are then added and evaluated using the TrueTime toolbox. The
next step consists of setting up a “hardware_in_the_loop” real-time simulation before
performing tests on the real process.
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![16 Networked Control Systems Co-design
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![18 Networked Control Systems Co-design
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![20 Networked Control Systems Co-design
Besides the knowledge provided by basic education in control and computer sci-
ence, it appears that some topics that are useful in the joint design of control systems
over networks are too specific, or too new and not disseminated enough, to be cur-
rently a part of basic education in control or industrial computing. So the next sections
provide additional knowledge about such topics and will be useful in what follows.
Section 1.2 gives preliminary notions about real-time scheduling as well as some
popular real-time scheduling policies. A particular focus is given on the so-called
(m, k)-firm scheduling policy, which is, in particular, the groundwork for the con-
trol/networking co-design methodology that is developed in Chapter 5. Then, section
1.3 provides basic considerations and describes the current solutions for control-aware
computing, i.e. providing computing architecture designs able to improve the quality
of control of the system. One very appealing solution for the control of computing
and networking resources subject to variable and/or badly known operating condi-
tions uses a feedback-scheduling loop, whose basic design and implementation are
described in section 1.4. Finally, section 1.5 provides a brief state of the art about
fault diagnosis in control systems subject to network-induced effects.
1.2. Preliminary notions on real-time scheduling
When taking into account the implementation aspect of the control applications,
one of the fundamental problems is to ensure timely execution of the tasks and trans-
mission of messages related to control loops, e.g. transmission of a sampling data
from a sensor to a controller, execution of the control task on a multitasking operating
system (OS), sending the command from the controller to the actuator.
Control applications are typical real-time applications. The execution of a task or
transmission of data is under time constraint (often under deadline constraint) in order
to ensure the reactivity of the system and thus guarantee the stability and desired con-
trol performance. Real-time scheduling theory has been developed for studying how
to effectively schedule the access to a shared resource of the concurrent tasks (through
scheduling algorithm development) and to guarantee that the designed system can
meet time constraints (through schedulability analysis).
This section is not intended to give a comprehensive review of the real-time schedul-
ing theory, but rather provides the necessary basic background to facilitate the under-
standing of the remaining chapters of this book. Readers interested in more detail may
refer to [LIU 00], and also to [LEU 04] for a broader view on scheduling.
The notion of priority is commonly used to order access to the shared resources
such as a processor in multitask systems and a communication channel in networks.
In the following, except in case of necessity, we will always use the term task which](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-37-320.jpg)
![Preliminary Notions 21
may represent either a task execution on a processor or a packet/message transmitted
on a network channel.
A classic periodic task model is proposed by Liu and Layland [LIU 73]. Each
periodic task of priority i, denoted by τi, is characterized by its worst-case execution
time (WCET) Ci, its period Ti with which its execution is requested, and its relative
deadline Di. The problem is how to schedule a set of n independent periodic tasks
Γ = {τ1, τ2, ..., τn } on one processor to ensure that the deadline of each instance is
met (i.e. executed before the deadline). This is called hard real-time guarantee. In
priority-based scheduling, it is usual to use the value i = 1 for the highest priority
and larger integer of i for lower priority. During the execution of a task instance of
priority i, if a higher priority one arrives, two scheduling policies exist: pre-emptive
and non-pre-emptive. In the pre-emptive case, on-going lower priority task execution
is interrupted by the higher priority one and its execution is resumed after the end of
the execution of the higher priority one if there is no other released higher priority
ones. Pre-emption is often not allowed when dealing with packet transmission in a
communication channel, or when the pre-emption overhead is too high.
This classic task model can be used for representing the control task execution
on a processor where the deadline is deduced from the sampling period of the control
loop. When several control tasks (or one control task and several other tasks) share the
same processor, scheduling policies must be studied for ensuring the deadlines are met
and consequently the Quality of Control (QoC). However, as mentioned earlier in the
Introduction and Problem Statement, guaranteeing deadlines are met for all the task
instances (i.e. hard real-time guarantee) generally requires huge resource reservation
leading to the over-provisioning problem. While we know that feedback control loops
have certain robustness with respect to timing uncertainty. Occasional deadline miss
or instance non-execution can often be tolerated if they do not occur in a long-term
consecutive way. In this case, the (m, k)-firm model introduced by [HAM 95] seems
more suitable. In fact, a task meets the (m, k)-firm constraint if there are at least m
among any k consecutive task instances meet their deadline. This can thus be used to
specify how the deadline miss or instance discarding is tolerated.
In what follows, we will give some basic results on priority-based classic task
model scheduling and (m, k)-firm one.
1.2.1. Some basic results on classic task model scheduling
In this part two scheduling algorithms are presented: rate monotonic (RM) and
earliest deadline first (EDF). RM is a fixed-priority scheduling algorithm where the
priorities are assigned to the tasks according to their periods (or appearing rates). The
task with the smallest period has the highest priority. Note that the same principle can
be used to get some variants such as deadline monotonic (DM) or generally speaking](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-38-320.jpg)
![22 Networked Control Systems Co-design
fixed priority according to whatever importance criteria. EDF is a typical example of
dynamic priority scheduling algorithms. Priorities assigned to the tasks are inversely
proportional to the absolute deadlines of the active tasks. That is, the earlier the dead-
line, the higher the priority. The priority assigned to a task is of course dynamic and
recalculated every time there is a new active task or an execution completion.
Let us consider a set of n independent periodic tasks Γ = {τ1, τ2, ..., τn } on one
processor. For this system, the total normalized workload or processor utilization is
U =
n
i=1
Ci
Ti
, and the system is feasible when U ≤ 1.
1.2.1.1. Fixed priority scheduling
Let the priority of the tasks τi be classified in decreasing orders: i j ⇒ the
priority of τi is higher than that of τj ; in the case of RM or DM, the priority of τi is
1
min(Di ,Ti ) .
In [LIU 73], under pre-emptive RM, the following sufficient condition is estab-
lished on the feasibility of the task set for ∀i, Di = Ti:
n
i=1
Ci
min (Di, Ti)
≤ n ·
2
1
n − 1
. (1.1)
With n tending to infinity, n(21/n
− 1) approaches ln2 ≈ 69.31%.
In [LIU 73], it has also been shown that the worst-case response time is obtained
when the first instances of all the tasks are synchronized.
A sufficient and necessary condition for the non-concrete task set has been given
in [JOS 86] based on the technique called worst response time analysis (RTA).
Formally, for ∀i, Ri ≤ Di, Ri is iteratively calculated by taking into account
the interference caused by the higher priorities. For U ≤ 1 and ∀i, Di ≤ Ti, Ri is
obtained with the following fixed point calculation:
R0
i = Ci
∀k ≥ 1, Rk
i = Ci +
ji
Cj ·
Rk−1
i
Tj
.
The computing stops when the iteration can no longer progress (Rk
i = Rk−1
i = Ri)
or when Ri Di.
In a general case with unrelated Di and Ti, and especially for the case of Di Ti,
this RTA technique has been extended [TIN 94].
Note that this technique is also applicable to the non pre-emptive case by including
the blocking factor due to the on-execution low-priority task [TIN 94].](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-39-320.jpg)
![Preliminary Notions 23
1.2.1.2. EDF scheduling
For a set of independent periodic tasks Γ = {τ1, τ2, ..., τn } with ∀i, Di = Ti and
under pre-emptive EDF, the necessary and sufficient condition of the schedulability is
[LIU 73]:
U =
n
i=1
Ci
Ti
≤ 1. (1.2)
It is proved [BAR 90] that this condition is still true for the case ∀i, Di ≥ Ti. For a
task set with ∀i, Di ≤ Ti, the previous condition is no longer sufficient. In [BAR 90]
and [SPU 96], two necessary and sufficient conditions are given for task set with arbi-
trary Di and Ti.
Under non pre-emptive EDF, in the case of non-concrete tasks, a sufficient and
necessary schedulability test with pseudo-polynomial complexity is given in [JEF 91].
The test is based on the processor demand calculation. When the tasks are syn-
chronous, the same condition becomes only sufficient. It has been shown in [JEF 91]
and [GEO 95] that determining the schedulability is an NP-hard problem.
1.2.1.3. Discussion
Fixed priority scheduling is now supported by most of commercial off-the-shelf
(COTS) OS. It can also be found in some networks. For instance, CAN network uses
a priority-based MAC protocol so that CAN messages schedulability can be analyzed
using the RTA technique [TIN 94]. This scheduling algorithm is also present in some
Ethernet switches. Chapter 3 will study the control and network QoS co-design of the
NCS distributed around a CAN and switched Ethernet network, respectively.
EDF is known as an optimal scheduling algorithm. However its implementation
can induce unacceptable high overhead due to the frequent context changes related to
the dynamic priority assignment. Today, few COTS OS support EDF.
Ensuring hard real-time constraint by the schedulability analysis may lead to re-
source over-provisioning problem since in practice it is difficult to get a tight upper
bound on the WCET, especially when dealing with packet transmission in a network.
The worst-case workload scenario may never happen. To cope with these uncertain-
ties, a system designer may try to either prevent overloads by making safe assumptions
about workload or tolerate overloads (but still providing reduced-but-acceptable level
of service). The latter is particularly interesting for feedback control applications
thanks to the robustness of the control loops. For the overload management, fixed-
priority scheduling has an advantage over EDF. In fact, during an overload situation,
only low-priority tasks are affected in fixed-priority scheduling. EDF has very bad
behavior during overload since it tries to always give the highest priority to the task
that will miss its deadline, resulting in a general deadline miss of all tasks.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-40-320.jpg)
![24 Networked Control Systems Co-design
Many other approaches such as imprecise computation model, skippable model,
(m, k)-firm model have been developed to deal with overloads. We introduce in the
following some basic notions on (m, k)-firm. This model is then used in Chapters 2
and 5. Chapter 5 also gives further details before applying it to the overload manage-
ment when several control loops share the same processor.
1.2.2. (m,k)-firm model
A system meeting (m, k)-firm constraint requires a minimum QoS of m out of any
k consecutive deadlines to meet in the worst case, where m and k are two positive in-
tegers (the case where m = k is equivalent to the ideal case, which is noted by (k, k)-
firm and corresponds to the hard real-time constraint). In general cases, more than
m deadlines are met as the system does not always run at the worst-case condition.
This is to say that if the (m, k)-firm constraint is respected, during whatever window
of k consecutive instance occurrences, there exist at least m instances that meet their
deadline. Note that in general the k consecutive instance occurrences are not neces-
sarily periodic, so the window of k consecutive instances does not necessarily have a
constant time duration [LI 09]. However, in the networked control applications, most
of the cases are periodic ones due to the sampling principle. Therefore in this book, a
task τi is characterized by {Ci, Ti, Di, mi, ki}, with i = 1, 2, ..., n representing the
index of tasks (but not necessarily their priority). A task could be a stream of messages
to transmit or a periodic task to execute.
A task under (m, k)-firm constraint can be found in one of the two following states:
normal and dynamic failure [HAM 95]. Figure 1.1 shows an example of the state-
transition diagram for (2, 3)-firm: 1 denotes that a deadline is met and 0 denotes a
deadline missed, respectively. These states are evaluated according to the past situa-
tion of the system; every state that is either normal or dynamic failure depends on the
last three deadlines services. The next deadline’s meet or miss will cause the system
Figure 1.1. State-transition diagram with (2, 3)-firm](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-41-320.jpg)
![Preliminary Notions 25
to transit to another state. If there is more than 1 missed deadline, the system is in a
dynamic failure state. Otherwise, the system is in a normal state.
For the efficient overload management, we adopt dropping strategy: any instance
that cannot be executed before its deadline is dropped. So whenever talking about
(m, k)-firm in this book, a missed deadline is equivalent to an instance drop.
If a control system can accept control performance degradation until k − m dead-
lines misses (or equivalent packet losses) among any k consecutive ones, the system
can then be designed according to the (m, k)-firm approach to offer the variable levels
of control performance between (k, k)-firm (ideal case) and (m, k)-firm (worst case)
with as many intermediate levels as the possible values there are between k and m.
This results in a control system with graceful degradation of the control performance.
The problem of scheduling tasks under (m, k)-firm constraint has drawn particular
attention in real-time community. Some important results have been obtained.
The first category concerns the development of the specific scheduling algorithms.
The well-known one is distance-based priority (DBP) proposed in [HAM 95]. Con-
sidering n tasks sharing a common server (may be a processor or a communication
channel) and each has its own (mi, ki)-firm constraint, the principle is to dynamically
assign priorities to the different tasks according to the distance to the dynamic failure
state. The closer the task to a failure state, the higher its priority. A failure state occurs
when the task’s (mi, ki)-firm requirement is violated, i.e. there are more than ki − mi
deadlines missed within the last k-length window. So to know the current state of a
task we should examine the execution history of the last k instances. If we associate
1 with an instance with deadline met and 0 with an instance with deadline missed,
this history is then entirely described by a word of k bits called the k-sequence. The
k-sequence is a word of k ordered bits in which each bit keeps memory of whether
the deadline is missed (bit= 0) or met (bit=1). In the k-sequence, the bit is ordered the
most recent to the oldest task instance where the leftmost bit represents the oldest one.
Each newly arrived instance causes a shift of all the bits toward the left, the leftmost
exits the word and is no longer considered, while the rightmost will be a 1 if the in-
stance has met its deadline (i.e. it has been served within) or a 0 otherwise. Figure 1.2
gives an example with (3,5)-firm constraint.
Thus for each task τi under (mi, ki)-firm constraint, the priority is assigned based
on the number of consecutive deadline misses that leads the task to violate its (mi, ki)-
firm requirement. This number of missed deadlines is referred to as the distance to
failure state from the current state. DBP assigns priority to a given instance by the
distance from the current k-sequence to a failure state. Considering the above exam-
ple with (3, 5)-firm constraint, the current instance is assigned the priority of 2 if the
current 5-sequence is (11011), and is set the priority of 3 if the current 5-sequence
is (10111). Note that in case of equal priority, EDF is used to break the tie. For](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-42-320.jpg)
![26 Networked Control Systems Co-design
11011
1
1
Deadline
met
Deadline
missed 10110
10111
Figure 1.2. Evolution of the k-sequence
non-pre-emptive DBP, a first necessary schedulability condition has been given in
[POG 03]. A sufficient schedulability condition is presented in [LI 04a]. Dynamic
window constrained-scheduling (DWCS) is another similar algorithm proposed in
[WES 99] with its schedulability analysis in [WES 04]. Other scheduling algorithms
have also been developed specifically for control applications such as Markov chain-
driven algorithm (MDA), dropout-rate-driven algorithm (DDA), and feedback-driven
algorithm (FDA) [LIU 06].
The second category concerns the adaptation of the existing scheduling algorithms
to the (m, k)-firm constraint. In [RAM 99], the RM algorithm is adapted to the (m, k)-
firm model by defining the notion of (m, k)-pattern which is in fact a fixed k-sequence.
This allows the instances to be classified in two priorities: mandatory and optional.
The guarantee of the execution of the mandatory instances ensures meeting of the
(m, k)-firm constraint. The sufficient schedulability condition is also presented.
Enhanced fixed-priority (EFP) algorithm [QUA 00] proposes an improvement by in-
troducing a heuristic rotation algorithm to reduce the effect of the worst-case interfer-
ence point due to the superposition of the mandatory instances of tasks. This part will
be further detailed in Chapter 5.
1.3. Control aware computing
Control and real-time computing have been associated for a long time, with the
control of industrial plants and in embedded or mobile systems, e.g. automotive and
robotics. However, both parts, control and computing, are often designed with poor in-
teraction and mutual understanding. From the control design point of view, a constant
and unique period is usually assumed. Delays are supposed negligible or constants,
and jitter is ignored. The implementation design then follows, trying to meet these
assumptions.
Real-time scheduling has mainly focused on how to dimension resources to meet
deadlines, or equivalently, on the schedulability analysis for a given resource. Indeed,
the real-time community has usually considered that control tasks have fixed peri-
ods, hard deadlines, and worst-case execution times. This assumption has served the](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-43-320.jpg)
![Preliminary Notions 27
separation of control and scheduling designs, but has led to under-utilization of CPU
resources and inflexible design.
The hard and costly way consists in building a highly deterministic system, from
the hardware, operating system and communication protocols sides, so that the actual
implementation parameters meet the ideal ones. This extreme solution is used if, for
instance, determinism is requested for formal verification and/or certification purpose,
e.g. as in the synchronous programming approach [BEN 91] or in the time-triggered
paradigm [KOP 03]. However, trying to nullify (even virtually) latencies and jitter
generally leads to worst-case-based resources provisioning and tends to needlessly
overconstraint the system’s design and implementation.
In fact, the hard real-time constraints can be often relaxed in a controlled way,
e.g. considering the intrinsic robustness provided by the closed-loop paradigm. In a
real control implementation, latencies and sampling jitter inevitably exist, in particular
when actuators, sensors, and controllers are distributed over a network. A smart or-
ganization and use of network and processor resources, with control features in mind,
may lead to serious improvements in the control performance, resources usage and
overall cost.
1.3.1. Off-line approaches
A first set of methods consists of computing off-line the set of scheduling
parameters which (ideally) maximize the control performance under schedulability
constraints. The first step consists in getting a model of the control performance func-
tion of the execution parameters. The problem of optimal sampling period selection,
subject to schedulability constraints, was first introduced in [SET 96]. Considering
a bubble control system benchmark, the relationship between the control cost (corre-
sponding to a step response) and the sampling periods was approximated using convex
exponential functions. Using the Karush–Kuhn–Tucker (KKT) first-order optimality
conditions, the analytic expressions of the optimal off-line sampling periods were es-
tablished. The problem of the joint optimization of control and off-line scheduling has
been studied in [REH 04; LIN 02a; BEN 06].
In a multitasking system, several control tasks share a common computing re-
source: the resulting pre-emption induces latencies due to the computations them-
selves, but also due to the interleaving between their executions. Models of the control
behavior based on linear systems theory are used in [RYU 97] and [SAK 98] to derive
cost functions which depict the control performance, e.g. the rise time, as a function
of two execution parameters, the control period and loop delay. Then an optimization
iterative algorithm (simplex) is used to tune the execution parameters in order to max-
imize the overall control performance with respect to the implementation feasibility.
However, due to the complexity of the optimization process this method can be used
only off-line.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-44-320.jpg)
![28 Networked Control Systems Co-design
Often the lazy way to implement a controller consists of programming a single
real-time task when all the components of the controller are executed in sequence in
a single loop. However, it appears that all the components of a control algorithm
do not require the same timing parameters, and do not have the same weight in the
final performance and stability. Some parts of the controller are more critical w.r.t.
latencies, or require more frequent updating than others. Therefore, the controller can
be split into modules according to these timing requirements, so that latencies can be
minimized along some critical data paths, or to enforce the execution of safety critical
functions even in the case of transient overload.
For example, it is possible to split the controller of a linear system in several parts
according to their relative urgency, as shown in the following piece of pseudocode
[ÅST 97]:
loop{
Wait_Clock(); //waiting periodic request
Get_Sensors(); //read y(k)
Calculate_Output(); //u(k) = f(y(k), x̂(k − 1), ...)
Send_Control(); //send u(k)
Update_State(); //x̂(k) = g(y(k), x̂(k − 1), ...) }
Here the input/output latency is minimized, as the control signals are computed
and sent to the actuators immediately after updating the measures, while updating the
model and internal state of the controller can be delayed until the end of the control
period.
This method is, for example, used in [EKE 99] where this control task split is
applied to the control of a set of concurrent inverted pendulums: compared with the
naive implementation where all computations are made before sending the control sig-
nals, it provides an impressive increase in the control performance with no additional
computing cost. A more complex and nonlinear system can also benefit from such sep-
aration of the control algorithm between fast and critical control paths (e.g. low-level
stabilization loop) and slower components, e.g. vision-based navigation. Obviously
the operating system and associated run-time framework must allow for such multi-
task/multi-rate implementation [SIM 05a]. This modular timing analysis seems to be
an essential starting point for flexible and efficient real-time control implementation,
as in the example depicted in section 1.4.2.3.
1.3.2. Quality of Service and flexible scheduling
Other approaches define a QoS criterion to depict, e.g. the relations between the
performance and the controller’s period. This performance model can be used to con-
figure an admission controller managing the overall system load [ABD 97], or to per-
form an on-line negotiation involving periods and priorities as in [SAN 00].](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-45-320.jpg)
![Preliminary Notions 29
Besides control considerations, flexible and control aware solutions have also been
provided by the computer science side. For example, let us cite the “Elastic Tasks”
paradigm [BUT 00], where the sensitivity of the QoS relative to the execution period
for every task is modeled by a “stiffness” and takes into account bounds in the allowed
execution period. To make the task set schedulable, the task stack is “compressed”
until the accumulated execution load fit with the allocated CPU capacity. Although
this implementation is in open loop w.r.t. the actual QoS, it allows for an improved
adaptation against transient overloads.
As sharing the computing resource between controllers is a central issue, some
variants of the Control Bandwidth Server (CBS) approach [ABE 98] have been used
to enforce protection between competing control activities. For example in [CAC 00]
the nominal control periods of the competing controllers are computed thanks to the
optimization process of [SET 96] aiming at maximizing the control performance un-
der scheduling constraints. The on-line execution time variations of the controllers are
locally processed inside the computing budget allocated by the CBS server.
Let us cite also the control server ([CER 03b]) where a fraction of the total CPU
power is statically reserved to each control thread. Then the system behaves as if each
controller was isolated using its own computation resource, in particular an overloaded
controller does not disturb its neighbors. Inside each computing segment the individ-
ual controllers are organized to minimize their I/O latency and jitter. In the case of
transient overload, the missing computing budget for one controller is postponed to its
next reserved slice, with no impact on the others.
This mainly concerns the integration of control performance knowledge in the
scheduling parameters assignment. Indeed, once a control algorithm has been de-
signed, a first job consists of assigning timing parameters, i.e. period of tasks and
deadlines, so that the controller’s implementation meets the control objective. This
may be done off-line or on-line.
In off-line control/scheduling co-design, the task of setting adequate values for
the timing parameters rapidly fall into case studies based on simulation and experi-
ments. For instance in [RYU 97] off-line iterative optimization is used to compute an
adequate setting of periods, latencies, and gains resulting in a requested control perfor-
mance according to the available computing resource and implementation constraints.
Also in [SAN 02] the temporal requirements of the control system are described using
complex temporal attributes (e.g. nominal period and allowed variations, precedence
constraints, etc.): this model is then used by an off-line iterative heuristic procedure to
assign the scheduling parameters (e.g. priorities and offsets) to meet the constraints.
Concerning co-design for on-line implementation, recent results deal with vary-
ing sampling rates in control loops in the framework of linear systems: for example](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-46-320.jpg)
![30 Networked Control Systems Co-design
[SCH 02] show that, while switching between two stable controllers, too frequent con-
trol period switches may lead to instability. Unfortunately, most real-life systems are
nonlinear and the extrapolation of timing assignment through linearization often gives
rough estimations of allowable periods and latencies or they can even be meaningless.
In fact, as shown later in the examples, knowledge of the plant’s behavior is necessary
to get an efficient control/scheduling co-design.
1.4. Feedback-scheduling basics
Besides traditional assignment of fixed scheduling parameters, more flexible sche-
duling policies have been investigated. The main idea is that fast sampling and com-
puting are costly, so running the controllers only when useful or necessary is expected
to save computing power, network bandwidth and energy. Networked control systems
can be made of autonomous and/or mobile devices connected by wireless communi-
cations. As these devices may have a limited on-board energy storage, optimizing the
cost of computations and communications induced by the control activities is again
gaining interest.
As already mentioned in section 0.2, the on-line adaptation of the sampling interval
as a function of the system’s behavior and state has been studied from the beginning of
computer-controlled systems [DOR 62; HSI 74]. Besides the time-triggered approach
and variations around the sampling period adaptation, an even more radical approach
is the so-called “Event-based control” concept. Indeed, this approach is natural in
some application domains, as in engine control where the basic events scale is linked
to the crank-shaft position turning at a variable speed rather than to clocks. However,
it has been proposed as an alternative to time-triggered sampling when the execution
resources used by the controller are constrained.
Within the event-triggered control approach the decision to compute and apply a
new control action is based on the level crossing of some signal of interest, e.g. the
error signal between the desired set-point and actual measurement as in [ÅRZ 99]
and [DUR 09]. Note that even if the controller is sleeping most of the time waiting for
awaking events, the controlled plant must be continuously observed for event detection
at a rate fast enough to allow for fast reactions and effective disturbance rejection.
Anyway, effective real-time management of the computing and networking re-
sources needs to close the loop between the execution resource utilization and the
actual scheduling parameters. The feedback-scheduling approach has been initiated
both from the real-time computing side [LU 00; LU 02] and from the control side
[CER 00; EKE 00; CER 02]. The idea consists of adding to the process controller
an outer sampled feedback loop (“scheduling regulator”) to control the scheduling
parameters as a function of a QoC (Quality of Control) measure. It is expected that
an on-line adaptation of the scheduling parameters of the controller may increase its](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-47-320.jpg)
![Preliminary Notions 31
−
Uk
+
+
−
manager
Scheduling
controller
Scheduling
scheduler
Global objective
feedforward
admission controller
exceptions handling
QoS
Scheduling
Parameters
Process state estimates
Process objectives
CPU/network state load/latency estimates
Y
Instrumentation
RTOS
(QoC)
Plant modeling and actual QoCs
SAMP
controller
Process Process
ZOH
Figure 1.3. Hierarchical control structure
overall efficiency w.r.t. timing uncertainties coming from the unknown controlled en-
vironment. Also we know from control theory that closing the loop may increase
performance and robustness against disturbances when properly designed and tuned
(otherwise it may lead to instability).
Figure 1.3 gives an overview of a feedback scheduler architecture where an outer
loop (the scheduling controller) adapts in real time the scheduling parameters from
measurements taken on the computer’s activity, e.g. the computing load. Ideally it
would be also fed by measures related to the quality of control, thus really provid-
ing integrated control and scheduling, which is the topic of Chapter 4. Besides this
controller working periodically (at a rate larger than the sampling periods of the plant
control tasks), the system’s structure may evolve along a discrete time scale upon
occurrence of events, e.g. for new task admission or exception handling. These deci-
sional processes may be handled by another real-time task, the scheduling manager,
which is not further detailed in this paper. Notice that such a manager may give a
reference to the controller resource utilization.
The design problem can be stated as control performance optimization under con-
straint of available computing resources. Early results come from [EKE 00] where a
problem of optimal control under computation load constraints is theoretically solved
by a feedback scheduler, but leads to a solution too complex to be implemented in real
time. Then [CER 03a] shows that this optimal control problem can often be simply
implemented by computing the new task periods by the re-scaling:
hk+1
i = hk
i
U
Usp
,](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-48-320.jpg)
![32 Networked Control Systems Co-design
where Usp is the utilization set-point and U the estimated CPU load. The feedback
scheduler then controls the processor utilization by assigning task periods that op-
timize the overall control performance. This approach is well suited for a “quasi-
continuous” variation of the sampling periods of real-time tasks under control of a
pre-emptive real-time operating system (RTOS).
Another approach has been used in the framework of the so-called (m, k)-firm
schedulability policy, where the scheduling strategy ensures the successful execution
of at least m instances of a given task (or message sending) for each time window
of length k slots. Hence a selective data drop policy (as in [JIA 07]) or a computing
power allocation to selected tasks (as in [BEN 06]) can be used to perform optimal
control of a plant under constraint of computing or communication limitations. This
latter approach is well suited for non pre-emptive scheduling of control tasks and
for networked control systems subject to message loss: the tasks or messages are
scheduled to jointly perform congestion avoidance and optimal control.
Indeed, in all cases the adaptive behavior of a feedback scheduler, associated with
the relative tolerance of the control system w.r.t. the implementation induced timing
uncertainties, allows for the design and implementation of real-time control systems
based on their average execution behavior rather than on pessimistic worst-case esti-
mates.
1.4.1. Control of the computing resource
Feedback scheduling is a dynamic approach allowing a better use of the computing
resources, in particular when the workload changes e.g. due to the activation of an ad-
mitted new task. Indeed, the CPU activity will be controlled according to the resource
availability by adjusting scheduling parameters (i.e. period) of the plant control tasks.
In the approach proposed here, a way to take into account the resource sharing
over a multitasking process is developed. In what follows, the control design issue
is described including the control structure, the specification of control inputs and
measured outputs, as well as the modeling step.
1.4.1.1. Control structure
In Figure 1.4 scheduling is viewed as a dynamic system between control task fre-
quencies and processor utilization. As far as the adaptation of the control tasks is
concerned, the load of the other tasks is seen as an output disturbance.
1.4.1.2. Sensors and actuators
As stated in section 1.3, priorities must be assigned to control tasks according to
their relative urgency; this ordering remains the same in the case of a dynamic sched-
uler. Dynamic priorities, e.g. as used in EDF, only alter the interleaving of running
tasks and will fail in adjusting the computing load w.r.t. the control requirements.](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-49-320.jpg)
![Preliminary Notions 33
Ur
+
−
+
Uothers
+
Plant
control tasks
fi
Scheduling
controller
Figure 1.4. Feedback-scheduling block diagram
Consequently, we have elected the task periods to be the primary actuators of the
system running on top of a fixed-priority scheduler. Note that if the control timing set-
ting, based only on the scheduling adaptation, becomes out of reach (e.g. because the
requested intervals would be out of bounds), possible secondary actuators are variants
of the control algorithms, with different computing costs and QoS contributions to the
whole system. Such variants must be handled by the scheduling manager working on
a discrete events time scale.
As the aim is to adjust on-line the sampling periods of the controllers in order to
meet the computing resource requirements, the control inputs are thus the periods of
the control tasks. The measured output is the CPU utilization. Let us first recall that
the scheduling is here limited to periodic tasks. In this case the processor load induced
by a task is defined by U = c
h where c and h are the execution time and period of the
task. Hence, processor load induced by a task is estimated, in a similar way [CER 02],
for each period hs of the scheduling controller, as:
Ûkhs
= λ Û(k−1)hs
+ (1 − λ)
ckhs
h(k−1)hs
(1.3)
where h is the sampling frequency currently assigned to the plant control task (i.e. at
each sampling instant khs) and c is the mean of its measured job execution-time. λ is
a forgetting factor used to smooth the measure.
1.4.1.3. Control design and implementation
The proposed control design method for feedback scheduling is here developed.
First one should note that, as shown in [SIM 03], if the execution times are constant,
then the relation, U =
n
i=1 Cifi (where fi = 1/hi is the frequency of the task) is
a linear function (while it would not be the case if expressed as a function of the task
periods). Therefore, using (1.3), the estimated CPU load is given as:
Û(khS ) =
(1 − λ)
z − λ
n
i=1
ci(khS )fi(khS ) (1.4)
An illustration, for the case of a single control task system, is given in Figure 1.5 where
the estimated execution-times are used on-line to adapt the gain of the controller for](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-50-320.jpg)
![34 Networked Control Systems Co-design
K(z)
−
+
Task
H(z)
Uothers
Ur
+
+
f
1
c
Figure 1.5. Control scheme for CPU resources
the original CPU system (1.4) (this allows us to compensate the variations of the job
execution time).
As c depends on the run-time environment (e.g. processor speed) a “normalized”
linear model of the task i (i.e. independent of the execution time), Gi, is used for the
scheduling controller synthesis where c is omitted and will be compensated by on-line
gain scheduling (1/c) as shown below:
Gi(z) =
Û(z)
fi(z)
=
1 − λ
z − λ
, i = 1, . . . , n. (1.5)
According to this control scheme, the design of the controller K can be made using
any control methodology at hand. In fact all the control toolbox resources may be
adapted for feedback-scheduling purpose, e.g. as reviewed in [XIA 08].
One of the most frequently used is the well known P.I.D. control: it has been
for example used for the on-line regulation of purely computing systems as web and
mail servers, as shown in section 1.4.2.1. Another popular approach is the linear
quadratic (LQ) control method, whose application to scheduling control has also been
investigated as shown in section 1.4.2.2.
Model predictive control is known to cope well with control of complex systems
under control and/or state constraints. As scheduling control deals with control un-
der computing and/or communication limitations, this control design has also been
investigated, as shown by the example in section 4.3.
Finally, as a digital control system combines uncertainties and modeling errors
from both the plant and the control implementation, robustness seems to be a crucial
issue: the well known H∞ control theory, which can lead to a robust controller w.r.t
modeling errors (see [ZHO 96] for details on H∞ control), is also a good candidate
to perform. Moreover, it provides good properties in presence of external disturbance,
as emphasized in the robot control example below (1.4.2.3).](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-51-320.jpg)
![Preliminary Notions 35
1.4.2. Examples
1.4.2.1. Feedback scheduling a web server
One of the most popular and widely used controller for SISO systems is the so-
called proportional integral derivative (PID). The basic formulation for a continuous
time PID controller is [ÅST 97]
U = Kp .e + Kv .
de
dt
+ Ki.
t
0
e(τ).dτ,
where U is the control signal to be applied to the process input and e is the error
signal between the desired set-point yd and the measured output y. It is largely used
in industry as it can be applied to many SISO systems with an easy tuning and a
minimal modeling effort.
This simple design has been used to control and tune the behavior of computation
devices submitted to QoS constraints, for example web (Figure 1.6) or mail servers
([LU 01], [PAR 02]). Design basics, control oriented models for computing devices,
and case studies for feedback control of computing systems can be found in [LU 00;
LU 02], and [HEL 04] among other references.
RM/DM/EDF
Scheduler
QoS
controller
Admission
controller
CPU
Md
Scheduling
QoS levels
Admission.Rejection
Accepted tasks
Submitted tasks
dU(k)
PID
Control
Ud U(k)
Control
PID
M(k)
Md mode
switch
Figure 1.6. Web server closed-loop regulation](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-52-320.jpg)
![36 Networked Control Systems Co-design
For each period of the scheduling controller, the measures are the total CPU load
U(k) and the miss ratio M(k). The corresponding gains GA and GM are images of
the modeling uncertainties.
The execution of requests Ti is modeled by at least two levels of quality, i.e. cou-
ples (QoS contribution, execution cost). The actuation provided is the choice of the
execution mode corresponding to a given cost, at every sampling period. The accu-
mulated regulated cost is finally the global CPU load.
If the sampling period h is large enough, the transfer function of the CPU load
submitted to computing requests Δu can be modeled by an integrator, where GA and
GM are the weakly known gains of the open loop process:
U(k) = U(k − 1) + GA .Δu(k − 1)if CPU under-loaded,
M(k) = M(k − 1) + GM .Δu(k − 1) if CPU over-loaded.
Thus, a simple proportional regulator is able to control the server load
Δu(k) = Kpu .EU (k) où EU (k) = Us − U(k) if U ≤ 1,
Δu(k) = Kpm .EM (k) où EM (k) = Ms − M(k) if M 0.
Figure 1.7 (borrowed from [LU 02] with permission of the author) shows the
steady state behavior (CPU load U(k) and deadlines missed M(k)) as a function of the
desired load Ud. The role of the underlying scheduling policy can be observed: using
EDF (on the right picture) allows for nullifying the deadlines missed up to Ud = 1, but
exhibits degradation in the case of permanent overload faster than a static DM priority
policy. However, in all cases, the server shows some ability for automatic adaptation
to the arrival of sporadic requests and for recovery against sporadic overloads, thus
leading to a kind of self-administration at a very low-computing cost.
1.4.2.2. Optimal control-based feedback scheduling
The aforementioned PID regulation approach is very simple to design and tune.
The downside of the very limited number of tuning parameters is the limited capabil-
ities of, e.g. shaping robustness templates or decoupling several transfer modes.
Let us come back to the initial problem, which may consist formally in the opti-
mization of a control performance under constraints of limited computing resources.
This problem has been analytically solved by [EKE 00] and [CER 03a] for the fol-
lowing case study. A given computing resource is shared by n real-time control tasks,
each one is used to control a linear stochastic process; each controller has an hi period
and a Ci execution time. A sampling frequency dependent quality criterion Ji(hi) is](https://image.slidesharecdn.com/2150871-250601131701-bb31c556/85/Codesign-Approaches-For-Dependable-Networked-Control-Systems-Daniel-Simon-53-320.jpg)
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- 5. Co-design Approaches for Dependable Networked Control Systems
- 7. Dependable Networked Control Systems Edited by Christophe Aubrun Daniel Simon Ye-Qiong Song Co-design Approaches for
- 8. First published 2010 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd 2010 The rights of Christophe Aubrun, Daniel Simon and Ye-Qiong Song to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Simon, Ye-Qiong Song. p. cm. Includes bibliographical references and index. ISBN 978-1-84821-176-6 1. Feedback control systems--Reliability. 2. Feedback control systems--Design and construction. 3. Sensor networks--Reliability. 4. Sensor networks--Design and construction. I. Aubrun, Christophe. II. Simon, Daniel, 1954- III. Song, Ye-Qiong. TJ216.C62 2010 629.8'3--dc22 2009041851 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-84821-176-6 Edited and formatted by Aptara Corporation, New Delhi, India Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne Co-design approaches for dependable networked control systems / edited by Christophe Aubrun, Daniel
- 9. Contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Dominique SAUTER Introduction and Problem Statement . . . . . . . . . . . . . . . . . . . . . . 1 Christophe AUBRUN, Daniel SIMON and Ye-Qiong SONG 2 4 6 8 . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 15 Chapter 1. Preliminary Notions and State of the Art . . . . . . . . . . . . . 19 Christophe AUBRUN, Daniel SIMON and Ye-Qiong SONG 1.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2. Preliminary notions on real-time scheduling . . . . . . . . . . . . . . . . 20 1.2.1. Some basic results on classic task model scheduling . . . . . . . . 21 1.2.1.1. Fixed priority scheduling . . . . . . . . . . . . . . . . . . . . 22 1.2.1.2. EDF scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2.1.3. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2.2. (m,k)-firm model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3. Control aware computing . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.3.1. Off-line approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.3.2. Quality of Service and flexible scheduling . . . . . . . . . . . . . . 28 1.4. Feedback-scheduling basics . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.4.1. Control of the computing resource . . . . . . . . . . . . . . . . . . 32 v I.5. Diagnosis and fault tolerance in NCS I.7. Outline of the book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.4. Control and task/message scheduling . . . . . . . . . . . . . . . . . . . . I.2. Control design: from continuous time to networked implementation . . I.6. Co-design approaches I.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.3. Timing parameter assignment . . . . . . . . . . . . . . . . . . . . . . . . I.1. Networked control systems and control design challenges . . . . . . . .
- 10. vi Networked Control Systems Co-design 1.4.1.1. Control structure . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.4.1.2. Sensors and actuators . . . . . . . . . . . . . . . . . . . . . . 32 1.4.1.3. Control design and implementation . . . . . . . . . . . . . . 33 1.4.2. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.4.2.1. Feedback scheduling a web server . . . . . . . . . . . . . . . 35 1.4.2.2. Optimal control-based feedback scheduling . . . . . . . . . . 36 1.4.2.3. Feasibility: feedback-scheduler implementation for robot control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.5. Fault diagnosis of NCS with network-induced effects . . . . . . . . . . 43 1.5.1. Fault diagnosis of NCS with network-induced time delays . . . . 44 1.5.1.1. Low-pass post-filtering . . . . . . . . . . . . . . . . . . . . . 44 1.5.1.2. Structure matrix of network-induced time delay . . . . . . . 46 1.5.1.3. Robust deadbeat fault filter . . . . . . . . . . . . . . . . . . . 47 1.5.1.4. Other work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.5.2. Fault diagnosis of NCS with packet losses . . . . . . . . . . . . . . 50 1.5.2.1. Deterministic packet losses . . . . . . . . . . . . . . . . . . . 50 1.5.2.2. Stochastic packet losses . . . . . . . . . . . . . . . . . . . . . 50 1.5.3. Fault diagnosis of NCS with limited communication . . . . . . . . 51 1.5.4. Fault-tolerant control of NCS . . . . . . . . . . . . . . . . . . . . . 52 1.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 2. Computing-aware Control . . . . . . . . . . . . . . . . . . . . . . 63 Mongi BEN GAID, David ROBERT, Olivier SENAME, Alexandre SEURET and Daniel SIMON 2.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.2. Robust control w.r.t. computing and networking-induced latencies . . . 65 2.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.2.2. What happens when delays appear? . . . . . . . . . . . . . . . . . 67 2.2.2.1. Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.2.2.2. Infinite dimensional systems . . . . . . . . . . . . . . . . . . 68 2.2.3. Delay models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.2.4. Stability analysis of TDS using Lyapunov theory . . . . . . . . . . 71 2.2.4.1. The second method . . . . . . . . . . . . . . . . . . . . . . . 71 2.2.4.2. The Lyapunov–Razumikhin approach . . . . . . . . . . . . . 72 2.2.4.3. The Lyapunov–Krasovskii approach . . . . . . . . . . . . . . 73 2.2.5. Summary: time-delay systems and networking . . . . . . . . . . . 75 2.3. Weakly hard constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.3.1. Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.3.2. Notion of accelerable control . . . . . . . . . . . . . . . . . . . . . 79 2.3.3. Design of accelerable controllers . . . . . . . . . . . . . . . . . . . 79 2.3.4. Accelerable LQR design for LTI systems . . . . . . . . . . . . . . 80 2.3.5. Kalman filtering and accelerability . . . . . . . . . . . . . . . . . . 82
- 11. Contents vii 2.3.6. Robustifying feedback scheduling using weakly hard scheduling concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.3.7. Application to the attitude control of a quadrotor . . . . . . . . . . 85 2.4. LPV adaptive variable sampling . . . . . . . . . . . . . . . . . . . . . . 89 2.4.1. A polytopic discrete-plant model . . . . . . . . . . . . . . . . . . . 90 2.4.2. Performance specification . . . . . . . . . . . . . . . . . . . . . . . 92 2.4.3. LPV/H∞ control design . . . . . . . . . . . . . . . . . . . . . . . . 93 2.4.4. Experimental assessment . . . . . . . . . . . . . . . . . . . . . . . 94 2.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chapter 3. QoC-aware Dynamic Network QoS Adaptation . . . . . . . . . 105 Christophe AUBRUN, Belynda BRAHIMI, Jean-Philippe GEORGES, Guy JUANOLE, Gérard MOUNEY, Xuan Hung NGUYEN and Eric RONDEAU 3.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.2. Dynamic CAN message priority allocation according to the control application needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.2.1. Context of the study . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.2.1.1. The considered process control application . . . . . . . . . . 107 3.2.1.2. Control performance evaluation . . . . . . . . . . . . . . . . 108 3.2.1.3. The implementation through a network . . . . . . . . . . . . 108 3.2.1.4. Evaluation of the influence of the network on the behavior of the process control application . . . . . . . . . . . . . . . . 110 3.2.1.5. Idea of hybrid priority schemes: general considerations . . . 111 3.2.2. Three hybrid priority schemes . . . . . . . . . . . . . . . . . . . . 114 3.2.2.1. hp scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.2.2.2. (hp+sts) scheme . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.2.2.3. (hp+dts) scheme . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.2.3. Study of the three schemes based on hybrid priorities . . . . . . . 119 3.2.3.1. Study conditions . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.2.3.2. hp scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3.2.3.3. (hp+sts) scheme . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.2.3.4. (hp+dts) scheme . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.2.4. QoC visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.2.5. Comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.3. Bandwidth allocation control for switched Ethernet networks . . . . . . 132 3.3.1. NCS performance analysis . . . . . . . . . . . . . . . . . . . . . . 134 3.3.2. NCS modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.3.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.3.2.2. Network modeling . . . . . . . . . . . . . . . . . . . . . . . . 135 3.3.2.3. System modeling . . . . . . . . . . . . . . . . . . . . . . . . . 138 3.3.2.4. Controller modeling . . . . . . . . . . . . . . . . . . . . . . . 139 3.3.3. Network adaptation mechanism . . . . . . . . . . . . . . . . . . . . 141
- 12. viii Networked Control Systems Co-design 3.3.4. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 3.3.4.1. Maximum delay computation . . . . . . . . . . . . . . . . . . 141 3.3.4.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 3.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 3.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Chapter 4. Plant-state-based Feedback Scheduling . . . . . . . . . . . . . . 149 Mongi BEN GAID, David ROBERT, Olivier SENAME and Daniel SIMON 4.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 4.2. Adaptive scheduling and varying sampling robust control . . . . . . . . 151 4.2.1. Extended elastic tasks controller . . . . . . . . . . . . . . . . . . . 152 4.2.2. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.3. MPC-based integrated control and scheduling . . . . . . . . . . . . . . . 156 4.3.1. Resource constrained systems . . . . . . . . . . . . . . . . . . . . . 157 4.3.2. Optimal integrated control and scheduling of resource constrained systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.4. A convex optimization approach to feedback scheduling . . . . . . . . . 162 4.4.1. Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 162 4.4.2. Cost function definition and approximation . . . . . . . . . . . . . 164 4.4.2.1. Cost function definition . . . . . . . . . . . . . . . . . . . . . 164 4.4.2.2. Introductory example: quadrotor attitude control . . . . . . . 165 4.4.3. Optimal sampling period selection . . . . . . . . . . . . . . . . . . 166 4.4.3.1. Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 166 4.4.3.2. Problem solving . . . . . . . . . . . . . . . . . . . . . . . . . 167 4.4.3.3. Feedback-scheduling algorithm deployment . . . . . . . . . 167 4.4.4. Application to the attitude control of a quadrotor . . . . . . . . . . 168 4.5. Control and real-time scheduling co-design via a LPV approach . . . . 170 4.5.1. A LPV feedback scheduler sensible to the plant’s closed-loop performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 4.5.2. Application to a robot-arm control . . . . . . . . . . . . . . . . . . 174 4.5.2.1. Performance evaluation of the control tasks in view of optimal resource distribution . . . . . . . . . . . . . . . . . . 174 4.5.2.2. Simulation with TrueTime . . . . . . . . . . . . . . . . . . . 175 4.5.2.3. Feasibility and possible extensions . . . . . . . . . . . . . . . 177 4.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Chapter 5. Overload Management Through Selective Data Dropping . . . 185 Flavia FELICIONI, Ning JIA, Françoise SIMONOT-LION and Ye-Qiong SONG 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5.1.1. System architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.1.2. Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 5.2. Scheduling under (m, k)-firm constraint . . . . . . . . . . . . . . . . . . 188
- 13. Contents ix 5.2.1. Dynamic scheduling policy under (m,k)-firm constraints . . . . . 189 5.2.2. Static scheduling policy under (m,k)-firm constraints and schedulability issue . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5.2.3. Static scheduling under (m, k)-constraints and mechanical words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 5.2.4. Sufficient condition for schedulability assessment under (m,k)-pattern defined by a mechanical word . . . . . . . . . . . . . 191 5.2.5. Systematic dropping policy in control applications . . . . . . . . . 192 5.3. Stability analysis of a multidimensional system . . . . . . . . . . . . . 193 5.3.1. Generic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 5.3.2. Example of multidimensional system . . . . . . . . . . . . . . . . 194 5.3.2.1. Sampling period definition . . . . . . . . . . . . . . . . . . . 195 5.3.2.2. Controller parameters . . . . . . . . . . . . . . . . . . . . . . 195 5.3.3. Stability condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 5.4. Optimized control and scheduling co-design . . . . . . . . . . . . . . . 197 5.4.1. Optimal control and individual cost function . . . . . . . . . . . . 198 5.4.2. Global optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 200 5.4.3. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5.4.3.1. Plants and controllers . . . . . . . . . . . . . . . . . . . . . . 203 5.4.3.2. Scheduling parameters . . . . . . . . . . . . . . . . . . . . . . 203 5.4.3.3. Optimal controller . . . . . . . . . . . . . . . . . . . . . . . . 203 5.4.3.4. Simulation scenario . . . . . . . . . . . . . . . . . . . . . . . 204 5.4.3.5. Simulation results for hard real-time constraints . . . . . . . 204 5.4.3.6. Simulation results for (m, k)-firm constraints . . . . . . . . . 205 5.5. Plant-state-triggered control and scheduling adaptation and optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.5.1. Closed-loop stability of switching systems . . . . . . . . . . . . . 210 5.5.2. On-line plant state detection . . . . . . . . . . . . . . . . . . . . . . 210 5.5.3. Global optimization of control tasks taking into account the plant state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 5.5.4. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5.5.4.1. Simulation scenario . . . . . . . . . . . . . . . . . . . . . . . 214 5.5.4.2. Observed performance . . . . . . . . . . . . . . . . . . . . . . 217 5.5.4.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 5.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 5.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Chapter 6. Fault Detection and Isolation, Fault Tolerant Control . . . . . . 223 Christophe AUBRUN, Cédric BERBRA, Sylviane GENTIL, Suzanne LESECQ and Dominique SAUTER 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 6.2. FDI and FTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.2.1. Introduction to diagnosis . . . . . . . . . . . . . . . . . . . . . . . 224
- 14. x Networked Control Systems Co-design 6.2.2. Quantitative model-based residuals . . . . . . . . . . . . . . . . . . 226 6.2.2.1. Parity relations . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.2.2.2. Observers bank . . . . . . . . . . . . . . . . . . . . . . . . . . 229 6.2.3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 6.2.3.1. The system-residual generation . . . . . . . . . . . . . . . . . 231 6.2.3.2. Observer-based residuals . . . . . . . . . . . . . . . . . . . . 233 6.2.4. Diagnostic summary . . . . . . . . . . . . . . . . . . . . . . . . . . 235 6.2.5. Introduction to FTC . . . . . . . . . . . . . . . . . . . . . . . . . . 236 6.3. Networked-induced effects . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.3.1. Example of network-induced drawbacks . . . . . . . . . . . . . . . 239 6.3.2. Modeling data dropouts . . . . . . . . . . . . . . . . . . . . . . . . 240 6.3.3. Modeling network delays . . . . . . . . . . . . . . . . . . . . . . . 242 6.4. Pragmatic solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 6.4.1. Data synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . 244 6.4.1.1. Clock synchronization . . . . . . . . . . . . . . . . . . . . . . 244 6.4.1.2. Data reconstruction . . . . . . . . . . . . . . . . . . . . . . . 245 6.4.1.3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 6.4.2. Data loss and diagnostic blocking . . . . . . . . . . . . . . . . . . 247 6.5. Advanced techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 6.5.1. Residual generation with transmission delay . . . . . . . . . . . . 248 6.5.2. Adaptive thresholding . . . . . . . . . . . . . . . . . . . . . . . . . 249 6.5.2.1. Optimization-based approach for threshold selection . . . . 250 6.5.2.2. Network calculus-based thresholding . . . . . . . . . . . . . 251 6.5.3. Fault isolation filter design in the presence of packet dropouts . . 256 6.5.4. Estimation and diagnosis with data loss . . . . . . . . . . . . . . . 259 6.5.4.1. Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 259 6.5.4.2. Kalman filter with partial data loss . . . . . . . . . . . . . . . 260 6.6. Conclusion and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . 262 6.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Chapter 7. Implementation: Control and Diagnosis for an Unmanned Aerial Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Cédric BERBRA, Sylviane GENTIL, Suzanne LESECQ and Daniel SIMON 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 7.2. The quadrotor model, control and diagnosis . . . . . . . . . . . . . . . . 269 7.2.1. The system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 7.2.2. The physical system model . . . . . . . . . . . . . . . . . . . . . . 270 7.2.2.1. Introduction to quaternions . . . . . . . . . . . . . . . . . . . 270 7.2.2.2. The quadrotor model . . . . . . . . . . . . . . . . . . . . . . . 271 7.2.2.3. The inertial measurement unit (IMU) model . . . . . . . . . 273 7.2.3. The attitude control . . . . . . . . . . . . . . . . . . . . . . . . . . 274 7.2.3.1. Nonlinear control . . . . . . . . . . . . . . . . . . . . . . . . 274 7.2.3.2. Linear quadratic control . . . . . . . . . . . . . . . . . . . . . 274
- 15. Contents xi 7.2.4. The attitude observer . . . . . . . . . . . . . . . . . . . . . . . . . . 276 7.2.4.1. Nonlinear observer . . . . . . . . . . . . . . . . . . . . . . . . 276 7.2.4.2. Extended Kalman filter . . . . . . . . . . . . . . . . . . . . . 277 7.2.4.3. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 279 7.2.5. The quadrotor diagnosis . . . . . . . . . . . . . . . . . . . . . . . . 279 7.2.5.1. Sensor diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . 279 7.2.5.2. Actuator diagnosis . . . . . . . . . . . . . . . . . . . . . . . . 282 7.3. Simulation of the network . . . . . . . . . . . . . . . . . . . . . . . . . . 282 7.3.1. Architecture of the networked control system . . . . . . . . . . . . 282 7.3.2. Network design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 7.3.3. Tool implemented in the network simulation . . . . . . . . . . . . 285 7.4. Hardware in the loop architecture . . . . . . . . . . . . . . . . . . . . . . 285 7.4.1. The ORCCAD approach . . . . . . . . . . . . . . . . . . . . . . . . . 286 7.4.2. Quadrotor simulation setup . . . . . . . . . . . . . . . . . . . . . . 288 7.5. Experiments and results . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 7.5.1. Basic attitude control . . . . . . . . . . . . . . . . . . . . . . . . . 290 7.5.2. Packet loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7.5.2.1. Pragmatic solution . . . . . . . . . . . . . . . . . . . . . . . . 291 7.5.2.2. (m, k)-firm solutions . . . . . . . . . . . . . . . . . . . . . . 292 7.5.2.3. Dynamic priorities . . . . . . . . . . . . . . . . . . . . . . . . 295 7.5.2.4. Extended Kalman filter . . . . . . . . . . . . . . . . . . . . . 297 7.5.3. Hardware-in-the loop experiment . . . . . . . . . . . . . . . . . . . 298 7.5.3.1. Basic scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 298 7.5.3.2. Packet loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 7.5.3.3. Sensor failure . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 7.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 7.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Glossary and Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
- 16. Foreword Modeling, analysis and control of networked control systems (NCS) have recently emerged as topics of significant interest to the control community. The defining fea- ture of any NCS is that information (reference input, plant output, control input) is exchanged using a digital band-limited serial communication channel among control system components (sensors, controller, actuators) and usually shared by other feed- back control loops. The insertion of a communication network in the feedback control loop makes the analysis and design of an NCS more challenging. Conventional control theory with many ideal assumptions, such as synchronized control and non-delayed sensing and actuation, must be revisited so that the limitations on communication ca- pabilities within the control design framework can be integrated. Furthermore, the new trend is to implement the realization of fault diagnosis (FD) and fault tolerant control (FTC) systems that employ supervision functionalities (per- formance evaluation, fault diagnosis) and reconfiguration mechanisms by using co- operative functions that are also distributed on a networked architecture. A critical issue, therefore, which must always be considered in the design of any networked process control system, is its robustness with respect to failure situations, including system component failures as well as network failures. By network failure, we mean a total breakdown in the communication between the control system components as a result of, for example, some physical malfunction in the networking devices or severe overloading of the network resources that cause a network shut down. In this framework, dependability of NCS represents the emergence of an important research field. Dependability groups together with three properties that the NCS must satisfy in order to be designed: safety, reliability, and availability. Therefore, the design of a dependable NCSs implies a multidisciplinary approach; more precisely, dealing with a deep knowledge of both fault tolerant control and computer science (mainly real time scheduling and communication protocols). xiii
- 17. xiv Networked Control Systems Co-design The content of this book gives an overview of the main results obtained after three years of research work within the safe-NECS project funded by the French “Agence Nationale de la Recherche—ANR”. During these three years, five research groups have cooperated intensively to propose a framework for the design of dependable net- worked control systems. In this context, the research of safe-NECS took into consid- eration process control functions, FDI/FTC and their implementation over a network as an integrated system. In particular, the project aim was to develop, in a coordinated way, a “co-design” approach that integrates several kinds of parameters: the charac- teristics modeling the Quality of Control (QoC), the dependability properties required for a system and the parameters of real-time scheduling (tasks and messages). Issues such as network-induced delays, data losses and signal quantization as well as sensor and actuator faults represent some of the more common problems that have motivated the extensive research work developed within the safe-NECS project. The research work in the safe-NECS project aimed at enhancing the integration of control, real-time scheduling and networking. The safe-NECS project was clearly a multi-disciplinary project in that it brought together partners from the control and computer science communities. A major difficulty for this project came from the fact that both communities manipulate objects and formalisms of very different natures. We consider that one of the major contributions of this project was to promote a syn- ergistic approach, which is a necessary condition for achieving the objectives of the co-design which is demonstrated in this project. Safe-NECS project focuses on the following points, which are reported in this book: – specification of a dependable system and performance evaluation; – modeling the effect of a real-time distributed implementation (i.e. scheduling parameters and networking protocols) on Quality of Control (QoC) and dependability; – an integrated control and scheduling co-design method realized by developing feedback scheduling algorithms, taking into account both QoC parameters and de- pendability constraints; – fault tolerance and the on-line re-configuration of NECS with distributed diag- nostic and decision-making mechanisms; – testing and validation using a UAV-type quadrotor. Dominique SAUTER
- 18. Introduction and Problem Statement Networked control systems (NCS) are feedback control systems wherein the con- trol loops are closed over a shared network. Control and feedback signals are trans- mitted among the system’s components as information flows through a network, as to close the control loops: sensors to collect information on the controlled plant’s state, controllers to provide decisions and commands, actuators to apply the control signals and communication networks to enable communications between the NCS compo- nents. Introduction written by Christophe AUBRUN, Daniel SIMON and Ye-Qiong SONG. 1 depicted in figure I.1. A fully featured NCS is made up of four kinds of components Figure I.1. Typical NCS architecture
- 19. 2 Networked Control Systems Co-design Compared with conventional point-to-point control systems, the advantages of NCS are lighter wiring, lower installation costs, and greater abilities in diagnosis, reconfigurability and maintenance. Furthermore, the technologies used in computer and industrial networks, both wired and wireless, have progressed rapidly providing high bandwidth, quality of service (QoS) guarantees and low communication costs. Because of these distinctive benefits, typical application of these systems nowadays ranges over various fields of industry and services. X-by-wire automotive systems, coordinated control of swarms of mobile robotics and advanced aircraft on-board con- trol and housekeeping are examples of NCS usage in the field of embedded systems. Large-scale utility systems are deployed in order to control and monitor water, gas, energy networks, and transportation services on roads and railways. The capabilities of wireless sensor networks, which are widespread and cost very little to cooperatively monitor physical or environmental conditions, can be enhanced by adding some actu- ation capacities to make them control systems, such as in smart automated buildings. Networked control systems and control design challenges The design of NCS combines the domains of control systems, computer networks, and real-time computing. Historically, tools for the design and analysis of systems related to these disciplines have been designed and used with limited interaction. The increasing complexity of modern computer systems and the rapidly evolving technol- ogy of computer networks require more integrated methodologies, specifically suited to NCS. From a control-theoretic point of view, the main problem to be solved is the achievement of a control objective (i.e. a mixture of stability, performance and relia- bility requirements), despite the disturbances induced by the distribution of the control system over a network. For instance, the sharing of common computing resources and communication bandwidths by competing control loops along with other general pur- pose applications introduces random delays and even data losses. Moreover, as the computations are supported by heterogenous computers and the communication be- tween distributed components may spread over different levels of area networks, NCS become more and more complex and difficult to model. A key built-in feature of a multi-layer NCS is the availability of redundant information pathways, as well as the distributed nature of the overall task that the NCS has to perform. Hence the distri- bution of devices on nodes provides the ability for computing load distribution and re-routing information pathways in the event of a component or a subsystem of the network malfunctioning. This leads to the ability to reconfigure a new system from a nominally configured NCS. Control is playing an increasing role in the design and run-time management of large interconnected systems to enhance high performance in nominal modes and safe reconfiguration processes in the occurrence of faults and failures. In fact, it appears I.1.
- 20. Introduction and Problem Statement 3 that the achievement of system-level requirements by far exceed the achievable relia- bility of individual components [MUR 03]. The deep intrication of components and sub-systems, which come from different technologies, and which are subject to vari- ous constraints, calls for a joint design to solve potentially conflicting constraints early on. The fact that control has the ability to cope with uncertainty and disturbances, due to closed loops based on sensing the current system’s state, makes it a basic method- ology to be used in such complex systems design. Besides reaching the specified performance in normal situations, reliability and safety-related problems are of a constant concern for system designers. A general and integrated concept is dependability, which is the system property that includes various attributes such as availability, reliability, safety, confidentiality, integrity, and maintainability [LAP 92]. Being confronted with faults, errors and failures, a system’s dependability can be achieved in different ways, i.e. fault prevention, fault tolerance, fault removal and fault forecasting [AVI 00]. While these concepts have been formal- ized for systems in a broad sense, it appears that the existing control toolbox already provides concepts, e.g. robust and fault tolerant control, which are likely to achieve control system dependability. A better integration of advanced control, computing power and redundancy based on resource distribution is expected to further enhance this capability. Except in the case of failures due to hardware or software components, most pro- cesses usually run with nominal behavior: however, even in the nominal modes, nei- ther the process nor the execution resource parameters are ever perfectly known or modeled. A very conservative viewpoint consists of allocating system resources to sat- isfy the worst case, but this results in the execution resources being over-provisioned and thus wasted. From the control viewpoint, specific deficiencies to be considered include poorly predictable timing deviations, delays, and data loss. Control usually deals with modeling uncertainty, dynamic adaptation, and distur- bance attenuation. More precisely, as shown with recent results obtained on NCS [BAI 07], control loops are often robust and can tolerate computing and networking performance induced disturbances, up to a certain extent. Therefore, timing devia- tions such as jitter or data loss, as long as they remain inside the bounds which are compliant with the control specification, may be considered as features of the nom- inal system, not exceptions. Relying on control robustness allows for provisioning the execution resources according to average needs rather than for worst cases, and to consider system reconfiguration only when the failures exceed the capabilities of the running controller tolerance. An NCS is made up of a heterogenous collection of physical devices, falling within the realm of continuous time, and information sub-systems basically working with discrete timescales. During an NCS design process, many conflicting constraints
- 21. 4 Networked Control Systems Co-design must be simultaneously solved before reaching a satisfactory and implementable so- lution. For example, trade-offs must be negotiated between processing and network- ing speed, control tracking performance, robustness, redundancy and reconfigurabil- ity, energy consumption, and overall cost effectiveness. These conventional design process problems from the different domains in succession prevent any coherent and effective integration of methodologies, technologies or associated constraints. Traditionally control usually deals with a single process and a single computer, and it is often assumed that the limitations of communication links and computing resources do not significantly affect performance, or they are taken into account in a limited way. Existing tools dealing with modeling and identification, robust control, fault diagnosis and isolation, fault tolerant control and flexible real-time scheduling need to be enhanced, adapted and extended to cope with the networked characteristics of the control system. Finally, the concept of a co-design system approach has emerged to allow progress in the integration of control, control, and communications in the NCS design [MUR 03] and to develop implementation-aware control system co-design approaches [BAI 07]. According to the systems scientist and philosopher, C.W. Churchman, “the system approach begins when first you view the world through the eyes of another” [CHU 79]. The basic aspect of co-design applied to NCS is that the design of controllers and the design of the execution resources, i.e. the real-time computing and communication sub-systems, are integrated right from the early design steps to jointly solve the con- straints arising from all sides. Control design: from continuous time to networked implementation In the early age of control, analog computers were used to work out the control signals, firstly from mechanical devices, and then from electronic amplifiers and in- tegrators: both the plant and the controller remained in the realm of continuous time, while frequency analysis and Laplace transform were the main tools at hand. The main drawbacks of analog computing come from limited accuracy and bandwidth, drift and noise, and from limited capabilities to handle nonlinearities. Pure and known delays could, however, be handled at control synthesis time by using the well-known Smith predictor. Then, due to the increasing power and availability of cheap numerical processors, digital controllers gradually took over the analogue technology. However, controlling a continuous plant with a discrete digital system inevitably introduces timing distor- tions. In particular, it becomes necessary to sample and convert the sensors measure- ments to binary data, and conversely to convert them back to physically related values I.2.
- 22. Introduction and Problem Statement 5 and hold the control signals to actuators. The sampling theory and the z transform became the standard tools for digital control systems analysis and design. A smart property of the z transform is that it keeps the linearity of the system through the sampling process. As the underlying assumption behind the z transform is equidistant sampling, periodic sampling became the standard for the design and implementation of digital controllers. Note that, at the infancy of digital control, where computing power was weak and memory was expensive, it was important to minimize the controllers’ complexity and needed operating power. It is not obvious that the periodic sampling assumption is always the best choice: for example, [DOR 62] show that adaptive sampling, where the sampling frequency is changed according to the value of the derivative of the error signal, can be more effective than equidistant sampling in terms of the number of com- puted samples (but possibly not in terms of disturbance rejection [SMI 71]). [HSI 72] and [HSI 74] provide a summary of these efforts. However, due to the constantly increasing power and decreasing costs of computing, interest in sampling adaptabil- ity and the related computing power savings has progressively vanished, while the linearity preservation property of equidistant sampling has helped it to remain the in- disputable standard for years. From the computing side, real-time scheduling modeling and analysis were intro- duced in the illustrious seminal paper [LIU 73]. This first schedulability analysis was based on restrictive assumptions, one of them being the periodicity of all the real-time tasks in the system. Even if more general assumptions have been progressively in- troduced to cope with more realistic problems and tasks sets [AUD 95; SHA 04], the periodicity assumption remains very popular, e.g. see today’s success of rate mono- tonic analysis (RMA) based tools in industry, e.g. [SHA 90; DOY 94; HEC 94]. The combination of these popular modeling and analysis methods and tools has likely rein- forced the understanding that control systems are basically periodic and hard real-time systems. More recently, again due to the progress in electronic devices technology, it has become possible to distribute control loops over networks. Networking allows for the dissemination of sensors, actuators, and controllers on different physical nodes. Moreover, the topology of the network can be time varying, thus allowing the control devices to be mobile: hence, the whole control system can be highly adaptive in a dynamic environment. In particular, wireless communications allow for a cheap de- ployment of sensor networks and remotely controlled devices. However, networking also induces disturbances in control loops, such as variable and potentially long de- lays, data corruption, message desequencing and occasional data loss. These timing uncertainties and disturbances are in addition to those coming from the digital imple- mentation of the controllers in the network nodes.
- 23. 6 Networked Control Systems Co-design Timing parameter assignment Digital control systems can be implemented as a set of tasks running on top of a commercial off-the-shelf real-time operating system (RTOS) using fixed-priority and pre-emption. The performance of a control loop, e.g. measured by the tracking error, and even more importantly its stability, strongly relies on the values of the sampling rates and sensor-to-actuator latencies (the latency considered for control purposes is the delay between the instant when a measure qn is taken at a sensor and the instant when the control signal U(qn ) is received by the actuators [ÅST 97]. Therefore, it is essential that the implementation of the controller respects an adequate timing be- havior to meet the expected performance. However, implementation constraints such as multi-rate sampling, pre-emption, synchronization, and various sources of delays make the run-time behavior of the controller very difficult to accurately predict. Deal- ing with closed-loop controllers may take advantage of the robustness and adaptivity of such systems to design and implement flexible and adaptive real-time control archi- tectures. Closed-loop digital control systems use a computer to sample sensors, calculate a control law and send control signals to the actuators of a physical process. The control algorithm can be either designed in continuous time and then discretized or directly synthesized in discrete time, taking into account a model of the plant sampled by a zero-order holder. A control theory for linear systems sampled at fixed rates was established a long time ago [ÅST 97]. Assigning an adequate value for the sampling rate is a decisive duty, as this value has a direct impact on the control performance and stability. While an absolute lower limit for the sampling rate is given by Shannon’s theorem, in practice, rules of thumb are used to give a useful range of control frequencies according to the process dy- namics and the desired closed loop bandwidth. Among others, such a rule of thumb is given in [ÅST 97] as ωc h ≈ 0.15 . . . 0.5, where ωc is the desired closed-loop pulsation and h is the sampling period. Note that such rules only give preliminary information about the sampling rate to be actually implemented, and sampling rate selection needs to be further refined by simulations and experiments. In particular, it appears that the actual sampling rate to be used with some nonlinear systems, as those described in sections 1.4.2.3, 2.4.4, and in Chapter 7, must be far faster to achieve closed-loop stability. However, most often, it can be stated that the lower the control period and latencies are, the better the control performance is, e.g. measured by the tracking error or disturbance rejection. This assumption can be reinforced by providing a suitable control structure and parameter tuning, as shown in section 2.3 with the discussion on weakly hard real-time constraints and accelerable control tasks. While timing uncertainties have an impact on the control performance, the actual scheduling parameters are difficult to model accurately or constrain within precisely known bounds. Thus, it is worth examining the sensitivity of control systems w.r.t. I.3.
- 24. Introduction and Problem Statement 7 Sampling rate Performance degradation Best performance Continuous control Acceptable performance zone Unacceptable performance zone Instability Digital control Networked control A B C PA PB PC control vs. sampling rate timing fluctuations. The accepted wisdom is that the lower the control period is, the better the control performance is. However, the underlying implementation system is a limited resource and cannot accommodate arbitrarily high sampling rates; thus, there must be a trade-off between the control performance and the execution resource uti- lization. This is particularly true for distributed embedded system design with limited resources due to weight, cost and energy consumption constraints. In [MOY 07] and ing a good sampling period which gives a trade-off between control performance and the related network load. sampling rate range from PB to PC . Increasing the sampling rate beyond PC will increase the network load and lead to longer network-induced delays. This results in a control performance degradation. Note that for a given control application, the affordable network bandwidth can also vary accordingly. This can provide a network QoS designer with a larger solution space for designing the QoS mechanisms with more flexibility. The hard real-time assumption must be softened to better cope with the reality of closed-loop control, for instance, changing the hard timing constraints for “weakly- hard” constraints [BER 01]. For example, hard deadlines may be replaced by statisti- cal models, e.g. to specify the jitter characteristics compliant with the requested con- trol performance. They may also be changed for deadline miss or data-loss patterns, e.g. to specify the number of deadline misses allowed over a specified time window Figure I.2. Performance comparison of continuous control, digital control, and networked [LIA 02], the illustrative chart in Figure I.2 is given to show the importance of choos- From Figure I.2, it can be seen that the control performance is acceptable for a
- 25. 8 Networked Control Systems Co-design according to the so-called (m, k)-firm model [HAM 95]. More precisely, a task meets the (m, k)-firm constraint if at least m among any k consecutive task instances meet their deadline. Note that to be fully exploited, weakly hard constraints should be as- sociated with a decisional process: tasks missing their deadline can, for example, be delayed, aborted or skipped according to their impact on the control law behavior, e.g. as analyzed in [CER 05]. Finding the values of such weakly hard constraints for a given control law is cur- rently out of the scope of current control theory, in general. However, the intrinsic robustness of closed-loop controllers allows for relying on softened timing constraint specification and flexible scheduling design, leading to an adaptive system with grace- ful performance degradation during system overloads. Chapter 5 gives an example of finding the values of m and k when the (m, k)-firm constraint is applied to the control- loop task execution requirement. Control and task/message scheduling From the implementation point of view, real-time systems are often modeled as a set of periodic tasks assigned to one or several processors. In distributed real-time systems, messages are exchanged among related tasks through a network. To ensure the execution of tasks on a processor, the worst-case response time analysis technique is often used to analyze fixed-priority real-time systems. Well-known scheduling poli- cies, such as rate monotonic for fixed priorities and EDF for dynamic priorities, assign priorities according to timing parameters, respectively, sampling periods and dead- lines. They are said to be “optimal” as they maximize the number of task sets which can be scheduled with respect to deadlines, under some restrictive assumptions. Un- fortunately, they are not optimized for control purposes. They hardly take into account precedence and synchronization constraints, which naturally appear in a control algo- rithm. The relative urgency or criticality of the control tasks can be unrelated with the timing parameters. Thus, the timing requirements of control systems w.r.t. the performance specification do not fit well into scheduling policies based purely on schedulability achievement. It has been shown through experiments, e.g. [CER 03], that a blind use of such traditional scheduling policy can lead to an inefficient controller implementation; on the other hand, a scheduling policy based on an application’s requirements, associ- ated with a smart partition of the control algorithm into real-time modules may give better results. It may be that improving some computing related feature is in con- tradiction with another one targeted to improve the control behavior. For example, the case studies examined in [BUT 07] show that an effective method to minimize the output control jitter consists of systematically delaying the output delivery at the I.4.
- 26. Introduction and Problem Statement 9 end of the control period: however, this method also introduces a systematic one pe- riod input/output latency, and therefore most often provides the worst possible control performance among the set of considered strategies. Another example of unsuitability between computing and control requirements arises when using priority inheritance or priority ceiling protocols to bypass priority inversion due to mutual exclusion, e.g. to ensure the integrity of shared data. While they are designed to avoid deadlocks and minimize priority inversion lengths, such protocols jeopardize the initial schedule at run time, although it was carefully designed with latencies and control requirements in mind. As a consequence, latencies along some control paths can be largely increased, leading to a poor control performance or even instability. In a distributed system design, not only should the task set schedulability be en- sured, but also message transmission through the network, since sensor to actuator latencies heavily depend on transmission delay. Also, the schedulability tests must consider tasks and messages as a whole, since a message is produced by a task exe- cution and it may be needed to trigger another task execution. In [TIN 94], a holistic approach is proposed. It consists of applying the worst-case response time analysis technique to evaluating the end-to-end response time of a set of tasks distributed over a controller area network (CAN). Periodic messages over CAN are scheduled under a non pre-emptive, fixed priority policy. Their release jitters are caused by local task scheduling. The worst case is considered where all messages are assumed to be re- leased at the same time. This approach can effectively be used to validate distributed control applications, but suffers from the resource over-provisioning problem because of the obligation to consider the worst-case. The inherent robustness of the closed- loop control application is not exploited. Finally, off-line schedulability analysis relies on correctly estimating the tasks’ worst-case execution time (WCET). Even in embedded systems the processors use caches and pipelines to improve the average computing speed, but this decreases the timing predictability. When a network is included, additional timing uncertainty is emphasized. Depending on the network protocols, the network-induced delay and data loss can be very different. For instance, let us just take as an example the two widely used industrial networks CAN and switched Ethernet. A CAN uses a global priority-based medium access control protocol. High priority messages have lower transmission latencies while low priority ones can suffer from longer transmission delays [LIA 01]. An Ethernet switch can also deal with messages using quite different scheduling policies (e.g. FIFO, WRR, fixed priority), resulting in very different transmission delays. For real-time computing and networking design- ers, the new challenge is how to design the quality of service (QoS) mechanisms in scheduling both tasks in multitasking computing and messages managed by network protocols, e.g. message scheduling at the MAC level, routing, etc. to meet specified
- 27. 10 Networked Control Systems Co-design control-loop requirements. In fact, traditional QoS approaches assume that there is a deadline for each application, and a static resource allocation principle based on the worst-case situation is often used to provide delay/deadline guarantees. This ap- proach also leads to a resource over-provisioning problem since a worst-case scenario is considered. Another source of uncertainty may come from some parts of the estimation and control algorithms themselves. For example, the duration of a vision process highly depends on incoming data from a dynamic scene. Also, some algorithms are iterative, with a poorly predictable convergence rate, so the time before reaching a predefined threshold is unknown (and must be bounded by a timeout associated with a recovery process). In a dynamic environment, some of the less important control activities can be suspended or resumed in the case of transient overload, or alternative control algorithms with different costs can be scheduled according to various control modes, leading to large variations in the computing load. Thus, real-time control design based on worst-case execution time, maximum ex- pected delay, and strict deadlines inevitably lead to a low average usage of the com- puting resources and to a poor adaptability w.r.t. a complex execution environment. All these drawbacks call for a better integration of control objectives with comput- ing and communication capabilities through a co-design approach taking into account both actual application requirements and the implementation system characteristics. Diagnosis and fault tolerance in NCS Due to an increasing complexity of dynamic systems, as well as the need for reliability, safety and efficient operation, model-based fault diagnosis has became an important subject in modern control theory and practice, e.g. [WIL 76; FRA 90; GER 98]. Different techniques of model-based methods include observer based-, parity relation- and parameter estimation approaches [CHE 99; MAN 00; ZHA 03]. When sampling and control data are transmitted over the network, many network- induced effects such as time delays and packet losses will naturally arise. Owing to the network-induced effects, the theories for traditional point-to-point systems should be revisited when dealing with NCSs. Different studies have shown the importance of taking into account characteristics of networks in the design of a fault diagnosis system [DIN 06; LLA 06]. The main idea of these approaches is to minimize the false alarms caused by transmission delays. In this case, a network-induced delay is consid- ered when designing the FDI filter. On the other hand, FDI algorithms require specific information on the process, thus the implementation of such algorithms increases the network load and consequently, affects its QoS. The number of signals to be transmit- ted may be reduced by allowing only a part of sensors and actuators to have access to the network. In this case, less information is available for FDI at each sampling time. I.5.
- 28. Introduction and Problem Statement 11 In [ZHA 05], observability conditions are established for the reduced communication pattern. Based on the fault diagnosis algorithm for NCSs, fault-tolerant control of NCSs can be obtained. The existing methods of fault-tolerant control techniques against actuator faults can be categorized into two groups: passive [SEO 96; CHE 04] and active approaches [ZHA 02; ZHA 06]. [ZHE 03] proposed a passive controller for NCSs considering random time delays. Although the passive controllers are easy to implement, their performances are relatively conservative. The reason is that this class of controllers, based on the alleged set of component failures and with a fixed struc- ture and parameters, is used to deal with all the different failure scenarios possible. If a failure occurs out of those considered in the design, the stability and performance of the closed-loop system is unanticipated. Such potential limitations of passive ap- proaches are behind the motivation for the research on active FTC (AFTC). AFTC procedures require an on-line and real-time fault diagnosis process and a controller reconfiguration mechanism. Because AFTC approaches propose a kind of flexibility to select different controllers according to different component failures, better perfor- mance of the closed loop system is expected. However, the above case holds only if the fault diagnosis process provides a correct, or synchronous, decision. Some preliminary results have been obtained on AFTC which tend to make the reconfiguration mechanism immune from imperfect fault diagnosis decisions, as in [MAH 03] and [WU 97]. [MAK 04] further discussed the above issue by using the guaranteed cost control approach and on-line controller switching in such a way that the closed-loop system was stable at all times. However, [MAK 04] did not consider the plant controlled over the network. Co-design approaches NCS encompasses the control-loop application and the implementation system (CPU and the networks managed by operating systems and protocols). Research work on NCS mainly focuses on the robust control-loop design which takes into account the implementation-induced delays and data loss. Network delays are assumed to be either constant (can be realized by input data buffering) or randomly distributed, following a well-known probability distribution. Data losses are assumed to follow a Bernoulli process [ANT 07a; ZAM 08]. From these works, it appears that the as- sumptions on network delay or data loss patterns seldom consider the actual network characteristics nor the possible QoS mechanisms which are specific for each type of network. In fact, using a prioritized bus like CAN, a switched Ethernet or a wireless sensor network will result in fundamentally different QoS characteristics. This point is of primary importance especially when the network is shared by several control loops and other applications whose exact characteristics are often unknown at the control loop design step. In this case, the traffic scheduling has a great impact on both delay I.6.
- 29. 12 Networked Control Systems Co-design variations and packet loss, which in turn impacts the control quality (stability and per- formance) of the control loops. One solution to this problem relies on a tight coupling between the control specification and the implementation system at design time. Generally speaking, two ways to achieve an efficient NCS design can be distin- guished. One way that is currently being explored by the control theorists can be called “implementation-aware control law design.” The idea is to make on-line adap- tations to the control loops parameters by adjusting, for example, the control loop sampling period using a LQ approach in [EKE 00; CER 03], sample-time and/or de- lay dependent gain scheduling in [MAR 04] and [SAL 05], a robust H∞ design in [SIM 05], a hybrid rate adaptation in [ANT 07b], or both the actuation intervals and control gains using model predictive control and hybrid modeling as in [Ben 06], or LQ control associated with a (m, k)-firm policy as in [JIA 07] and [FEL 08]. Another is the so-called “control-aware QoS adaptation,” which is being explored by the network QoS designers. The idea is to re-allocate the implementation system resources on-line to maintain or increase the QoS level required by the control appli- cation. In [JUA 07], a hybrid CAN message priority allocation scheme is proposed. When there is an urgent transmission need, a dynamic priority field can be used to give it even higher priority. This work exhibits a link between the hybrid priority scheme and the control loop performance. In [DIO 07], the dynamic allocation of bandwidth sharing in Ethernet switches with weighted round-robin (WRR) scheduler based on both observed delay and the variation in the control quality (i.e. the difference be- tween the reference and the process state) is presented. For this purpose, bandwidth sharing (i.e. the weight assigned to each data flow or Ethernet switch port) is defined as a function of the sensor to actuator delay and the current quality of control (QoC) level. Of course, a combination of both approaches will contribute to a more efficient NCS design. Another very important aspect is the diagnosis and fault tolerance in NCS. This aspect is to be integrated in the co-design approach for achieving efficient and dependable NCS design. Outline of the book This book intends to provide an introduction to the problems that arise in NCS design and to present the different co-design approaches. The first chapter provides preliminary concepts, together with state of the art tech- niques and existing solutions to implement distributed process control and diagno- sis. In particular, control-aware static computing and network resource allocation schemes are first reviewed. Then, the real-time adaptive resource allocation approach I.7.
- 30. Introduction and Problem Statement 13 through feedback scheduling is described, and its feasibility is assessed through a robot control application. Techniques for diagnosis and fault tolerance for networked control systems are also reviewed. A first step toward dependable control systems consists of using robust controllers, e.g. controllers which are weakly sensitive to both process model and execution re- source incertitude. Chapter 2 deals with implementation-aware or more precisely computing-aware robust control. Computation durations, pre-emption between tasks and communication over networks provide various sources of delays in the control loops. Although the control systems with constant delays have been studied earlier, taking into account more realistic variables or badly known delays recently brought new and powerful results which are surveyed in section 2.2. Traditionally, real-time control systems have been considered as “hard real-time”, i.e. systems where tim- ing deviations such as deadline misses are forbidden. In fact, closed-loop systems have some intrinsic robustness against timing uncertainties, which can be enhanced, as shown in section 2.3, by being devoted to weakly hard control tasks. Robustness can be considered as a passive approach w.r.t. timing uncertainties which are not mea- sured and which are only assumed to have known bounds. In the case where the con- trol intervals can be controlled, an adaptation of the controller gains w.r.t. the varying control interval can be used in combination with robust control design, as developed in section 2.4. In addition to the controllers design, different approaches to enhance the QoC consist of techniques enabling to adjust the QoS offered by a network. Chapter 3 deals with control-aware dynamic network QoS adaptation. The key point here relies on the determination of the relation between QoC and QoS. QoC might be formulated in terms of overshoot or damping for instance, whereas QoS is often expressed in terms of delays. As the QoS adaptation mechanisms differ with the kinds of networks being considered, two approaches are illustrated in this chapter. One approach is based on CAN bus, the second is based on switched Ethernet architectures. These two protocols are widely used in industrial networks. In the case of the CAN protocol, a dynamic hybrid message-priority allocation, taking into account the control application needs, is proposed. In the case of switched Ethernet networks, bandwidth allocation control strategies are defined. For both approaches, the network feedback control is based on both the current QoS and the dynamic application-related parameters such as process state output deviation or certain control loop cost functions. Finally, since networks might have to support several applications, the QoS offered to each one is adjusted according to its specific needs. Feedback scheduling, as presented in the previous chapters, provides an effec- tive but limited adaptability of execution resource allocation w.r.t. varying opera- tion conditions because the control performance is not directly taken into account in the scheduling parameter tuning. Chapter 4 describes other elaborate control and
- 31. 14 Networked Control Systems Co-design scheduling co-design schemes, coupling control performance, and scheduling param- eters more tightly, through the means of a few case studies. In section 4.2 the varying sampling control laws are used as building blocks for such co-design schemes, with no guarantees for the stability of the global loops. Section 4.3, summarizes a sub- optimal solution for the case of control/scheduling co-design using a slotted timescale based on the model predictive control approach. A convex optimization approach in the framework of linear systems and linear quadratic control is provided in section 4.4. Finally, section 4.5 describes a LPV-based joint control and scheduling approach applied to the control of a robot arm. During system and network overload, excessive delays, or even data loss, may occur. To maintain the QoC of an NCS, the implementation system overload must be dealt with. As shown in Chapters 1 and 4, a common approach to deal with this overload problem is to dynamically change the sampling period of the control loops. In Chapter 5, an alternative to the explicit sampling period adjustment is proposed as an indirect sampling period adjustment. It is based on selective sampling data drops according to the (m, k)-firm model [HAM 95]. The interest of this alternative is its ease of implementation, despite reduced adjustment quality since only the multiples of the basic sampling period are used. Chapter 6 deals with the processing of faults that may occur during the NCS op- eration. These faults may affect the system’s physical components, or its sensors and actuators, or even the network itself. From a safety point of view, it is important to detect the occurrence of such faults, to determine the faulty physical components by fault detection and isolation (FDI). FDI allows some automatic reaction to the super- vision system (for instance automatic shut down in case of danger) or reaction to the human operators in charge of the installation (for instance, manual control in open loop). Sometimes, when these faults exceed the capabilities of robust control loops, they can be accommodated by advanced control algorithms, compensating for the sys- tem’s deficiencies by means of FTC. Section 6.2 recalls the basic results in FDI/FTC for the centralized case. Then the drawbacks of networking for fault detection and isolation are highlighted and some pragmatic solutions are given in section 6.4. More advanced techniques for FDI/FTC over networks subject to delays and data loss, some of which are still in the research field, are finally given in section 6.5. Finally, Chapter 7 is devoted to the experimental validation of the approaches ex- posed along the previous chapters, to assess their feasibility and effectiveness. A quad-rotor miniature drone has been used throughout the SafeNecs project1 as a com- mon setup to integrate contributions from the team’s partners, including variable sam- pling control, control under (m, k)-firm scheduling constraints, diagnosis and FDI 1. SafeNecs is a research project funded by the French “Agence Nationale de la Recherche” under grant ANR-05-SSIA-0015-03
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- 36. Chapter 1 Preliminary Notions and State of the Art 1.1. Overview Basically, co-design needs to share, compare, and gather the knowledge and per- spectives brought by the stakeholders involved in the design process. Indeed, the de- sign of safe networked control systems involves many basic methodologies and tech- nologies. The essential methodologies involved here are feedback control, real-time scheduling, fault detection and isolation (FDI), filtering and identification, network- ing protocols, and QoS metrics: each of them relies on theoretic concepts and specific domains of applied mathematics such as optimization and information theory. On the other hand, these concepts are implemented via various technologies and devices, for example, involving mechanical or chemical engineering, continuous and digital electronics and software engineering. These basic domains are explained in existing literature; hence, this chapter is not meant to give an exhaustive overview of all the methodologies and technologies used further in the book. This book is also not meant to provide an exhaustive state of the art nor to be a definitive treatise on the open topic of safe NCS; it is aimed at recording and disseminating the experience gathered by the authors during the joint SAFENECS academic research project. The team brought together people from different horizons, with basic backgrounds in control or computer science, and expertise in various do- mains and technologies such as digital control design, modeling of dynamic systems, real-time scheduling, identification, and diagnosis. Fault-tolerant control (FTC), net- working protocols, quality of service (QoS) analysis in networks, and model-based software development, among others. Chapter written by Christophe AUBRUN, Daniel SIMON and Ye-Qiong SONG. 19
- 37. 20 Networked Control Systems Co-design Besides the knowledge provided by basic education in control and computer sci- ence, it appears that some topics that are useful in the joint design of control systems over networks are too specific, or too new and not disseminated enough, to be cur- rently a part of basic education in control or industrial computing. So the next sections provide additional knowledge about such topics and will be useful in what follows. Section 1.2 gives preliminary notions about real-time scheduling as well as some popular real-time scheduling policies. A particular focus is given on the so-called (m, k)-firm scheduling policy, which is, in particular, the groundwork for the con- trol/networking co-design methodology that is developed in Chapter 5. Then, section 1.3 provides basic considerations and describes the current solutions for control-aware computing, i.e. providing computing architecture designs able to improve the quality of control of the system. One very appealing solution for the control of computing and networking resources subject to variable and/or badly known operating condi- tions uses a feedback-scheduling loop, whose basic design and implementation are described in section 1.4. Finally, section 1.5 provides a brief state of the art about fault diagnosis in control systems subject to network-induced effects. 1.2. Preliminary notions on real-time scheduling When taking into account the implementation aspect of the control applications, one of the fundamental problems is to ensure timely execution of the tasks and trans- mission of messages related to control loops, e.g. transmission of a sampling data from a sensor to a controller, execution of the control task on a multitasking operating system (OS), sending the command from the controller to the actuator. Control applications are typical real-time applications. The execution of a task or transmission of data is under time constraint (often under deadline constraint) in order to ensure the reactivity of the system and thus guarantee the stability and desired con- trol performance. Real-time scheduling theory has been developed for studying how to effectively schedule the access to a shared resource of the concurrent tasks (through scheduling algorithm development) and to guarantee that the designed system can meet time constraints (through schedulability analysis). This section is not intended to give a comprehensive review of the real-time schedul- ing theory, but rather provides the necessary basic background to facilitate the under- standing of the remaining chapters of this book. Readers interested in more detail may refer to [LIU 00], and also to [LEU 04] for a broader view on scheduling. The notion of priority is commonly used to order access to the shared resources such as a processor in multitask systems and a communication channel in networks. In the following, except in case of necessity, we will always use the term task which
- 38. Preliminary Notions 21 may represent either a task execution on a processor or a packet/message transmitted on a network channel. A classic periodic task model is proposed by Liu and Layland [LIU 73]. Each periodic task of priority i, denoted by τi, is characterized by its worst-case execution time (WCET) Ci, its period Ti with which its execution is requested, and its relative deadline Di. The problem is how to schedule a set of n independent periodic tasks Γ = {τ1, τ2, ..., τn } on one processor to ensure that the deadline of each instance is met (i.e. executed before the deadline). This is called hard real-time guarantee. In priority-based scheduling, it is usual to use the value i = 1 for the highest priority and larger integer of i for lower priority. During the execution of a task instance of priority i, if a higher priority one arrives, two scheduling policies exist: pre-emptive and non-pre-emptive. In the pre-emptive case, on-going lower priority task execution is interrupted by the higher priority one and its execution is resumed after the end of the execution of the higher priority one if there is no other released higher priority ones. Pre-emption is often not allowed when dealing with packet transmission in a communication channel, or when the pre-emption overhead is too high. This classic task model can be used for representing the control task execution on a processor where the deadline is deduced from the sampling period of the control loop. When several control tasks (or one control task and several other tasks) share the same processor, scheduling policies must be studied for ensuring the deadlines are met and consequently the Quality of Control (QoC). However, as mentioned earlier in the Introduction and Problem Statement, guaranteeing deadlines are met for all the task instances (i.e. hard real-time guarantee) generally requires huge resource reservation leading to the over-provisioning problem. While we know that feedback control loops have certain robustness with respect to timing uncertainty. Occasional deadline miss or instance non-execution can often be tolerated if they do not occur in a long-term consecutive way. In this case, the (m, k)-firm model introduced by [HAM 95] seems more suitable. In fact, a task meets the (m, k)-firm constraint if there are at least m among any k consecutive task instances meet their deadline. This can thus be used to specify how the deadline miss or instance discarding is tolerated. In what follows, we will give some basic results on priority-based classic task model scheduling and (m, k)-firm one. 1.2.1. Some basic results on classic task model scheduling In this part two scheduling algorithms are presented: rate monotonic (RM) and earliest deadline first (EDF). RM is a fixed-priority scheduling algorithm where the priorities are assigned to the tasks according to their periods (or appearing rates). The task with the smallest period has the highest priority. Note that the same principle can be used to get some variants such as deadline monotonic (DM) or generally speaking
- 39. 22 Networked Control Systems Co-design fixed priority according to whatever importance criteria. EDF is a typical example of dynamic priority scheduling algorithms. Priorities assigned to the tasks are inversely proportional to the absolute deadlines of the active tasks. That is, the earlier the dead- line, the higher the priority. The priority assigned to a task is of course dynamic and recalculated every time there is a new active task or an execution completion. Let us consider a set of n independent periodic tasks Γ = {τ1, τ2, ..., τn } on one processor. For this system, the total normalized workload or processor utilization is U = n i=1 Ci Ti , and the system is feasible when U ≤ 1. 1.2.1.1. Fixed priority scheduling Let the priority of the tasks τi be classified in decreasing orders: i j ⇒ the priority of τi is higher than that of τj ; in the case of RM or DM, the priority of τi is 1 min(Di ,Ti ) . In [LIU 73], under pre-emptive RM, the following sufficient condition is estab- lished on the feasibility of the task set for ∀i, Di = Ti: n i=1 Ci min (Di, Ti) ≤ n · 2 1 n − 1 . (1.1) With n tending to infinity, n(21/n − 1) approaches ln2 ≈ 69.31%. In [LIU 73], it has also been shown that the worst-case response time is obtained when the first instances of all the tasks are synchronized. A sufficient and necessary condition for the non-concrete task set has been given in [JOS 86] based on the technique called worst response time analysis (RTA). Formally, for ∀i, Ri ≤ Di, Ri is iteratively calculated by taking into account the interference caused by the higher priorities. For U ≤ 1 and ∀i, Di ≤ Ti, Ri is obtained with the following fixed point calculation: R0 i = Ci ∀k ≥ 1, Rk i = Ci + ji Cj · Rk−1 i Tj . The computing stops when the iteration can no longer progress (Rk i = Rk−1 i = Ri) or when Ri Di. In a general case with unrelated Di and Ti, and especially for the case of Di Ti, this RTA technique has been extended [TIN 94]. Note that this technique is also applicable to the non pre-emptive case by including the blocking factor due to the on-execution low-priority task [TIN 94].
- 40. Preliminary Notions 23 1.2.1.2. EDF scheduling For a set of independent periodic tasks Γ = {τ1, τ2, ..., τn } with ∀i, Di = Ti and under pre-emptive EDF, the necessary and sufficient condition of the schedulability is [LIU 73]: U = n i=1 Ci Ti ≤ 1. (1.2) It is proved [BAR 90] that this condition is still true for the case ∀i, Di ≥ Ti. For a task set with ∀i, Di ≤ Ti, the previous condition is no longer sufficient. In [BAR 90] and [SPU 96], two necessary and sufficient conditions are given for task set with arbi- trary Di and Ti. Under non pre-emptive EDF, in the case of non-concrete tasks, a sufficient and necessary schedulability test with pseudo-polynomial complexity is given in [JEF 91]. The test is based on the processor demand calculation. When the tasks are syn- chronous, the same condition becomes only sufficient. It has been shown in [JEF 91] and [GEO 95] that determining the schedulability is an NP-hard problem. 1.2.1.3. Discussion Fixed priority scheduling is now supported by most of commercial off-the-shelf (COTS) OS. It can also be found in some networks. For instance, CAN network uses a priority-based MAC protocol so that CAN messages schedulability can be analyzed using the RTA technique [TIN 94]. This scheduling algorithm is also present in some Ethernet switches. Chapter 3 will study the control and network QoS co-design of the NCS distributed around a CAN and switched Ethernet network, respectively. EDF is known as an optimal scheduling algorithm. However its implementation can induce unacceptable high overhead due to the frequent context changes related to the dynamic priority assignment. Today, few COTS OS support EDF. Ensuring hard real-time constraint by the schedulability analysis may lead to re- source over-provisioning problem since in practice it is difficult to get a tight upper bound on the WCET, especially when dealing with packet transmission in a network. The worst-case workload scenario may never happen. To cope with these uncertain- ties, a system designer may try to either prevent overloads by making safe assumptions about workload or tolerate overloads (but still providing reduced-but-acceptable level of service). The latter is particularly interesting for feedback control applications thanks to the robustness of the control loops. For the overload management, fixed- priority scheduling has an advantage over EDF. In fact, during an overload situation, only low-priority tasks are affected in fixed-priority scheduling. EDF has very bad behavior during overload since it tries to always give the highest priority to the task that will miss its deadline, resulting in a general deadline miss of all tasks.
- 41. 24 Networked Control Systems Co-design Many other approaches such as imprecise computation model, skippable model, (m, k)-firm model have been developed to deal with overloads. We introduce in the following some basic notions on (m, k)-firm. This model is then used in Chapters 2 and 5. Chapter 5 also gives further details before applying it to the overload manage- ment when several control loops share the same processor. 1.2.2. (m,k)-firm model A system meeting (m, k)-firm constraint requires a minimum QoS of m out of any k consecutive deadlines to meet in the worst case, where m and k are two positive in- tegers (the case where m = k is equivalent to the ideal case, which is noted by (k, k)- firm and corresponds to the hard real-time constraint). In general cases, more than m deadlines are met as the system does not always run at the worst-case condition. This is to say that if the (m, k)-firm constraint is respected, during whatever window of k consecutive instance occurrences, there exist at least m instances that meet their deadline. Note that in general the k consecutive instance occurrences are not neces- sarily periodic, so the window of k consecutive instances does not necessarily have a constant time duration [LI 09]. However, in the networked control applications, most of the cases are periodic ones due to the sampling principle. Therefore in this book, a task τi is characterized by {Ci, Ti, Di, mi, ki}, with i = 1, 2, ..., n representing the index of tasks (but not necessarily their priority). A task could be a stream of messages to transmit or a periodic task to execute. A task under (m, k)-firm constraint can be found in one of the two following states: normal and dynamic failure [HAM 95]. Figure 1.1 shows an example of the state- transition diagram for (2, 3)-firm: 1 denotes that a deadline is met and 0 denotes a deadline missed, respectively. These states are evaluated according to the past situa- tion of the system; every state that is either normal or dynamic failure depends on the last three deadlines services. The next deadline’s meet or miss will cause the system Figure 1.1. State-transition diagram with (2, 3)-firm
- 42. Preliminary Notions 25 to transit to another state. If there is more than 1 missed deadline, the system is in a dynamic failure state. Otherwise, the system is in a normal state. For the efficient overload management, we adopt dropping strategy: any instance that cannot be executed before its deadline is dropped. So whenever talking about (m, k)-firm in this book, a missed deadline is equivalent to an instance drop. If a control system can accept control performance degradation until k − m dead- lines misses (or equivalent packet losses) among any k consecutive ones, the system can then be designed according to the (m, k)-firm approach to offer the variable levels of control performance between (k, k)-firm (ideal case) and (m, k)-firm (worst case) with as many intermediate levels as the possible values there are between k and m. This results in a control system with graceful degradation of the control performance. The problem of scheduling tasks under (m, k)-firm constraint has drawn particular attention in real-time community. Some important results have been obtained. The first category concerns the development of the specific scheduling algorithms. The well-known one is distance-based priority (DBP) proposed in [HAM 95]. Con- sidering n tasks sharing a common server (may be a processor or a communication channel) and each has its own (mi, ki)-firm constraint, the principle is to dynamically assign priorities to the different tasks according to the distance to the dynamic failure state. The closer the task to a failure state, the higher its priority. A failure state occurs when the task’s (mi, ki)-firm requirement is violated, i.e. there are more than ki − mi deadlines missed within the last k-length window. So to know the current state of a task we should examine the execution history of the last k instances. If we associate 1 with an instance with deadline met and 0 with an instance with deadline missed, this history is then entirely described by a word of k bits called the k-sequence. The k-sequence is a word of k ordered bits in which each bit keeps memory of whether the deadline is missed (bit= 0) or met (bit=1). In the k-sequence, the bit is ordered the most recent to the oldest task instance where the leftmost bit represents the oldest one. Each newly arrived instance causes a shift of all the bits toward the left, the leftmost exits the word and is no longer considered, while the rightmost will be a 1 if the in- stance has met its deadline (i.e. it has been served within) or a 0 otherwise. Figure 1.2 gives an example with (3,5)-firm constraint. Thus for each task τi under (mi, ki)-firm constraint, the priority is assigned based on the number of consecutive deadline misses that leads the task to violate its (mi, ki)- firm requirement. This number of missed deadlines is referred to as the distance to failure state from the current state. DBP assigns priority to a given instance by the distance from the current k-sequence to a failure state. Considering the above exam- ple with (3, 5)-firm constraint, the current instance is assigned the priority of 2 if the current 5-sequence is (11011), and is set the priority of 3 if the current 5-sequence is (10111). Note that in case of equal priority, EDF is used to break the tie. For
- 43. 26 Networked Control Systems Co-design 11011 1 1 Deadline met Deadline missed 10110 10111 Figure 1.2. Evolution of the k-sequence non-pre-emptive DBP, a first necessary schedulability condition has been given in [POG 03]. A sufficient schedulability condition is presented in [LI 04a]. Dynamic window constrained-scheduling (DWCS) is another similar algorithm proposed in [WES 99] with its schedulability analysis in [WES 04]. Other scheduling algorithms have also been developed specifically for control applications such as Markov chain- driven algorithm (MDA), dropout-rate-driven algorithm (DDA), and feedback-driven algorithm (FDA) [LIU 06]. The second category concerns the adaptation of the existing scheduling algorithms to the (m, k)-firm constraint. In [RAM 99], the RM algorithm is adapted to the (m, k)- firm model by defining the notion of (m, k)-pattern which is in fact a fixed k-sequence. This allows the instances to be classified in two priorities: mandatory and optional. The guarantee of the execution of the mandatory instances ensures meeting of the (m, k)-firm constraint. The sufficient schedulability condition is also presented. Enhanced fixed-priority (EFP) algorithm [QUA 00] proposes an improvement by in- troducing a heuristic rotation algorithm to reduce the effect of the worst-case interfer- ence point due to the superposition of the mandatory instances of tasks. This part will be further detailed in Chapter 5. 1.3. Control aware computing Control and real-time computing have been associated for a long time, with the control of industrial plants and in embedded or mobile systems, e.g. automotive and robotics. However, both parts, control and computing, are often designed with poor in- teraction and mutual understanding. From the control design point of view, a constant and unique period is usually assumed. Delays are supposed negligible or constants, and jitter is ignored. The implementation design then follows, trying to meet these assumptions. Real-time scheduling has mainly focused on how to dimension resources to meet deadlines, or equivalently, on the schedulability analysis for a given resource. Indeed, the real-time community has usually considered that control tasks have fixed peri- ods, hard deadlines, and worst-case execution times. This assumption has served the
- 44. Preliminary Notions 27 separation of control and scheduling designs, but has led to under-utilization of CPU resources and inflexible design. The hard and costly way consists in building a highly deterministic system, from the hardware, operating system and communication protocols sides, so that the actual implementation parameters meet the ideal ones. This extreme solution is used if, for instance, determinism is requested for formal verification and/or certification purpose, e.g. as in the synchronous programming approach [BEN 91] or in the time-triggered paradigm [KOP 03]. However, trying to nullify (even virtually) latencies and jitter generally leads to worst-case-based resources provisioning and tends to needlessly overconstraint the system’s design and implementation. In fact, the hard real-time constraints can be often relaxed in a controlled way, e.g. considering the intrinsic robustness provided by the closed-loop paradigm. In a real control implementation, latencies and sampling jitter inevitably exist, in particular when actuators, sensors, and controllers are distributed over a network. A smart or- ganization and use of network and processor resources, with control features in mind, may lead to serious improvements in the control performance, resources usage and overall cost. 1.3.1. Off-line approaches A first set of methods consists of computing off-line the set of scheduling parameters which (ideally) maximize the control performance under schedulability constraints. The first step consists in getting a model of the control performance func- tion of the execution parameters. The problem of optimal sampling period selection, subject to schedulability constraints, was first introduced in [SET 96]. Considering a bubble control system benchmark, the relationship between the control cost (corre- sponding to a step response) and the sampling periods was approximated using convex exponential functions. Using the Karush–Kuhn–Tucker (KKT) first-order optimality conditions, the analytic expressions of the optimal off-line sampling periods were es- tablished. The problem of the joint optimization of control and off-line scheduling has been studied in [REH 04; LIN 02a; BEN 06]. In a multitasking system, several control tasks share a common computing re- source: the resulting pre-emption induces latencies due to the computations them- selves, but also due to the interleaving between their executions. Models of the control behavior based on linear systems theory are used in [RYU 97] and [SAK 98] to derive cost functions which depict the control performance, e.g. the rise time, as a function of two execution parameters, the control period and loop delay. Then an optimization iterative algorithm (simplex) is used to tune the execution parameters in order to max- imize the overall control performance with respect to the implementation feasibility. However, due to the complexity of the optimization process this method can be used only off-line.
- 45. 28 Networked Control Systems Co-design Often the lazy way to implement a controller consists of programming a single real-time task when all the components of the controller are executed in sequence in a single loop. However, it appears that all the components of a control algorithm do not require the same timing parameters, and do not have the same weight in the final performance and stability. Some parts of the controller are more critical w.r.t. latencies, or require more frequent updating than others. Therefore, the controller can be split into modules according to these timing requirements, so that latencies can be minimized along some critical data paths, or to enforce the execution of safety critical functions even in the case of transient overload. For example, it is possible to split the controller of a linear system in several parts according to their relative urgency, as shown in the following piece of pseudocode [ÅST 97]: loop{ Wait_Clock(); //waiting periodic request Get_Sensors(); //read y(k) Calculate_Output(); //u(k) = f(y(k), x̂(k − 1), ...) Send_Control(); //send u(k) Update_State(); //x̂(k) = g(y(k), x̂(k − 1), ...) } Here the input/output latency is minimized, as the control signals are computed and sent to the actuators immediately after updating the measures, while updating the model and internal state of the controller can be delayed until the end of the control period. This method is, for example, used in [EKE 99] where this control task split is applied to the control of a set of concurrent inverted pendulums: compared with the naive implementation where all computations are made before sending the control sig- nals, it provides an impressive increase in the control performance with no additional computing cost. A more complex and nonlinear system can also benefit from such sep- aration of the control algorithm between fast and critical control paths (e.g. low-level stabilization loop) and slower components, e.g. vision-based navigation. Obviously the operating system and associated run-time framework must allow for such multi- task/multi-rate implementation [SIM 05a]. This modular timing analysis seems to be an essential starting point for flexible and efficient real-time control implementation, as in the example depicted in section 1.4.2.3. 1.3.2. Quality of Service and flexible scheduling Other approaches define a QoS criterion to depict, e.g. the relations between the performance and the controller’s period. This performance model can be used to con- figure an admission controller managing the overall system load [ABD 97], or to per- form an on-line negotiation involving periods and priorities as in [SAN 00].
- 46. Preliminary Notions 29 Besides control considerations, flexible and control aware solutions have also been provided by the computer science side. For example, let us cite the “Elastic Tasks” paradigm [BUT 00], where the sensitivity of the QoS relative to the execution period for every task is modeled by a “stiffness” and takes into account bounds in the allowed execution period. To make the task set schedulable, the task stack is “compressed” until the accumulated execution load fit with the allocated CPU capacity. Although this implementation is in open loop w.r.t. the actual QoS, it allows for an improved adaptation against transient overloads. As sharing the computing resource between controllers is a central issue, some variants of the Control Bandwidth Server (CBS) approach [ABE 98] have been used to enforce protection between competing control activities. For example in [CAC 00] the nominal control periods of the competing controllers are computed thanks to the optimization process of [SET 96] aiming at maximizing the control performance un- der scheduling constraints. The on-line execution time variations of the controllers are locally processed inside the computing budget allocated by the CBS server. Let us cite also the control server ([CER 03b]) where a fraction of the total CPU power is statically reserved to each control thread. Then the system behaves as if each controller was isolated using its own computation resource, in particular an overloaded controller does not disturb its neighbors. Inside each computing segment the individ- ual controllers are organized to minimize their I/O latency and jitter. In the case of transient overload, the missing computing budget for one controller is postponed to its next reserved slice, with no impact on the others. This mainly concerns the integration of control performance knowledge in the scheduling parameters assignment. Indeed, once a control algorithm has been de- signed, a first job consists of assigning timing parameters, i.e. period of tasks and deadlines, so that the controller’s implementation meets the control objective. This may be done off-line or on-line. In off-line control/scheduling co-design, the task of setting adequate values for the timing parameters rapidly fall into case studies based on simulation and experi- ments. For instance in [RYU 97] off-line iterative optimization is used to compute an adequate setting of periods, latencies, and gains resulting in a requested control perfor- mance according to the available computing resource and implementation constraints. Also in [SAN 02] the temporal requirements of the control system are described using complex temporal attributes (e.g. nominal period and allowed variations, precedence constraints, etc.): this model is then used by an off-line iterative heuristic procedure to assign the scheduling parameters (e.g. priorities and offsets) to meet the constraints. Concerning co-design for on-line implementation, recent results deal with vary- ing sampling rates in control loops in the framework of linear systems: for example
- 47. 30 Networked Control Systems Co-design [SCH 02] show that, while switching between two stable controllers, too frequent con- trol period switches may lead to instability. Unfortunately, most real-life systems are nonlinear and the extrapolation of timing assignment through linearization often gives rough estimations of allowable periods and latencies or they can even be meaningless. In fact, as shown later in the examples, knowledge of the plant’s behavior is necessary to get an efficient control/scheduling co-design. 1.4. Feedback-scheduling basics Besides traditional assignment of fixed scheduling parameters, more flexible sche- duling policies have been investigated. The main idea is that fast sampling and com- puting are costly, so running the controllers only when useful or necessary is expected to save computing power, network bandwidth and energy. Networked control systems can be made of autonomous and/or mobile devices connected by wireless communi- cations. As these devices may have a limited on-board energy storage, optimizing the cost of computations and communications induced by the control activities is again gaining interest. As already mentioned in section 0.2, the on-line adaptation of the sampling interval as a function of the system’s behavior and state has been studied from the beginning of computer-controlled systems [DOR 62; HSI 74]. Besides the time-triggered approach and variations around the sampling period adaptation, an even more radical approach is the so-called “Event-based control” concept. Indeed, this approach is natural in some application domains, as in engine control where the basic events scale is linked to the crank-shaft position turning at a variable speed rather than to clocks. However, it has been proposed as an alternative to time-triggered sampling when the execution resources used by the controller are constrained. Within the event-triggered control approach the decision to compute and apply a new control action is based on the level crossing of some signal of interest, e.g. the error signal between the desired set-point and actual measurement as in [ÅRZ 99] and [DUR 09]. Note that even if the controller is sleeping most of the time waiting for awaking events, the controlled plant must be continuously observed for event detection at a rate fast enough to allow for fast reactions and effective disturbance rejection. Anyway, effective real-time management of the computing and networking re- sources needs to close the loop between the execution resource utilization and the actual scheduling parameters. The feedback-scheduling approach has been initiated both from the real-time computing side [LU 00; LU 02] and from the control side [CER 00; EKE 00; CER 02]. The idea consists of adding to the process controller an outer sampled feedback loop (“scheduling regulator”) to control the scheduling parameters as a function of a QoC (Quality of Control) measure. It is expected that an on-line adaptation of the scheduling parameters of the controller may increase its
- 48. Preliminary Notions 31 − Uk + + − manager Scheduling controller Scheduling scheduler Global objective feedforward admission controller exceptions handling QoS Scheduling Parameters Process state estimates Process objectives CPU/network state load/latency estimates Y Instrumentation RTOS (QoC) Plant modeling and actual QoCs SAMP controller Process Process ZOH Figure 1.3. Hierarchical control structure overall efficiency w.r.t. timing uncertainties coming from the unknown controlled en- vironment. Also we know from control theory that closing the loop may increase performance and robustness against disturbances when properly designed and tuned (otherwise it may lead to instability). Figure 1.3 gives an overview of a feedback scheduler architecture where an outer loop (the scheduling controller) adapts in real time the scheduling parameters from measurements taken on the computer’s activity, e.g. the computing load. Ideally it would be also fed by measures related to the quality of control, thus really provid- ing integrated control and scheduling, which is the topic of Chapter 4. Besides this controller working periodically (at a rate larger than the sampling periods of the plant control tasks), the system’s structure may evolve along a discrete time scale upon occurrence of events, e.g. for new task admission or exception handling. These deci- sional processes may be handled by another real-time task, the scheduling manager, which is not further detailed in this paper. Notice that such a manager may give a reference to the controller resource utilization. The design problem can be stated as control performance optimization under con- straint of available computing resources. Early results come from [EKE 00] where a problem of optimal control under computation load constraints is theoretically solved by a feedback scheduler, but leads to a solution too complex to be implemented in real time. Then [CER 03a] shows that this optimal control problem can often be simply implemented by computing the new task periods by the re-scaling: hk+1 i = hk i U Usp ,
- 49. 32 Networked Control Systems Co-design where Usp is the utilization set-point and U the estimated CPU load. The feedback scheduler then controls the processor utilization by assigning task periods that op- timize the overall control performance. This approach is well suited for a “quasi- continuous” variation of the sampling periods of real-time tasks under control of a pre-emptive real-time operating system (RTOS). Another approach has been used in the framework of the so-called (m, k)-firm schedulability policy, where the scheduling strategy ensures the successful execution of at least m instances of a given task (or message sending) for each time window of length k slots. Hence a selective data drop policy (as in [JIA 07]) or a computing power allocation to selected tasks (as in [BEN 06]) can be used to perform optimal control of a plant under constraint of computing or communication limitations. This latter approach is well suited for non pre-emptive scheduling of control tasks and for networked control systems subject to message loss: the tasks or messages are scheduled to jointly perform congestion avoidance and optimal control. Indeed, in all cases the adaptive behavior of a feedback scheduler, associated with the relative tolerance of the control system w.r.t. the implementation induced timing uncertainties, allows for the design and implementation of real-time control systems based on their average execution behavior rather than on pessimistic worst-case esti- mates. 1.4.1. Control of the computing resource Feedback scheduling is a dynamic approach allowing a better use of the computing resources, in particular when the workload changes e.g. due to the activation of an ad- mitted new task. Indeed, the CPU activity will be controlled according to the resource availability by adjusting scheduling parameters (i.e. period) of the plant control tasks. In the approach proposed here, a way to take into account the resource sharing over a multitasking process is developed. In what follows, the control design issue is described including the control structure, the specification of control inputs and measured outputs, as well as the modeling step. 1.4.1.1. Control structure In Figure 1.4 scheduling is viewed as a dynamic system between control task fre- quencies and processor utilization. As far as the adaptation of the control tasks is concerned, the load of the other tasks is seen as an output disturbance. 1.4.1.2. Sensors and actuators As stated in section 1.3, priorities must be assigned to control tasks according to their relative urgency; this ordering remains the same in the case of a dynamic sched- uler. Dynamic priorities, e.g. as used in EDF, only alter the interleaving of running tasks and will fail in adjusting the computing load w.r.t. the control requirements.
- 50. Preliminary Notions 33 Ur + − + Uothers + Plant control tasks fi Scheduling controller Figure 1.4. Feedback-scheduling block diagram Consequently, we have elected the task periods to be the primary actuators of the system running on top of a fixed-priority scheduler. Note that if the control timing set- ting, based only on the scheduling adaptation, becomes out of reach (e.g. because the requested intervals would be out of bounds), possible secondary actuators are variants of the control algorithms, with different computing costs and QoS contributions to the whole system. Such variants must be handled by the scheduling manager working on a discrete events time scale. As the aim is to adjust on-line the sampling periods of the controllers in order to meet the computing resource requirements, the control inputs are thus the periods of the control tasks. The measured output is the CPU utilization. Let us first recall that the scheduling is here limited to periodic tasks. In this case the processor load induced by a task is defined by U = c h where c and h are the execution time and period of the task. Hence, processor load induced by a task is estimated, in a similar way [CER 02], for each period hs of the scheduling controller, as: Ûkhs = λ Û(k−1)hs + (1 − λ) ckhs h(k−1)hs (1.3) where h is the sampling frequency currently assigned to the plant control task (i.e. at each sampling instant khs) and c is the mean of its measured job execution-time. λ is a forgetting factor used to smooth the measure. 1.4.1.3. Control design and implementation The proposed control design method for feedback scheduling is here developed. First one should note that, as shown in [SIM 03], if the execution times are constant, then the relation, U = n i=1 Cifi (where fi = 1/hi is the frequency of the task) is a linear function (while it would not be the case if expressed as a function of the task periods). Therefore, using (1.3), the estimated CPU load is given as: Û(khS ) = (1 − λ) z − λ n i=1 ci(khS )fi(khS ) (1.4) An illustration, for the case of a single control task system, is given in Figure 1.5 where the estimated execution-times are used on-line to adapt the gain of the controller for
- 51. 34 Networked Control Systems Co-design K(z) − + Task H(z) Uothers Ur + + f 1 c Figure 1.5. Control scheme for CPU resources the original CPU system (1.4) (this allows us to compensate the variations of the job execution time). As c depends on the run-time environment (e.g. processor speed) a “normalized” linear model of the task i (i.e. independent of the execution time), Gi, is used for the scheduling controller synthesis where c is omitted and will be compensated by on-line gain scheduling (1/c) as shown below: Gi(z) = Û(z) fi(z) = 1 − λ z − λ , i = 1, . . . , n. (1.5) According to this control scheme, the design of the controller K can be made using any control methodology at hand. In fact all the control toolbox resources may be adapted for feedback-scheduling purpose, e.g. as reviewed in [XIA 08]. One of the most frequently used is the well known P.I.D. control: it has been for example used for the on-line regulation of purely computing systems as web and mail servers, as shown in section 1.4.2.1. Another popular approach is the linear quadratic (LQ) control method, whose application to scheduling control has also been investigated as shown in section 1.4.2.2. Model predictive control is known to cope well with control of complex systems under control and/or state constraints. As scheduling control deals with control un- der computing and/or communication limitations, this control design has also been investigated, as shown by the example in section 4.3. Finally, as a digital control system combines uncertainties and modeling errors from both the plant and the control implementation, robustness seems to be a crucial issue: the well known H∞ control theory, which can lead to a robust controller w.r.t modeling errors (see [ZHO 96] for details on H∞ control), is also a good candidate to perform. Moreover, it provides good properties in presence of external disturbance, as emphasized in the robot control example below (1.4.2.3).
- 52. Preliminary Notions 35 1.4.2. Examples 1.4.2.1. Feedback scheduling a web server One of the most popular and widely used controller for SISO systems is the so- called proportional integral derivative (PID). The basic formulation for a continuous time PID controller is [ÅST 97] U = Kp .e + Kv . de dt + Ki. t 0 e(τ).dτ, where U is the control signal to be applied to the process input and e is the error signal between the desired set-point yd and the measured output y. It is largely used in industry as it can be applied to many SISO systems with an easy tuning and a minimal modeling effort. This simple design has been used to control and tune the behavior of computation devices submitted to QoS constraints, for example web (Figure 1.6) or mail servers ([LU 01], [PAR 02]). Design basics, control oriented models for computing devices, and case studies for feedback control of computing systems can be found in [LU 00; LU 02], and [HEL 04] among other references. RM/DM/EDF Scheduler QoS controller Admission controller CPU Md Scheduling QoS levels Admission.Rejection Accepted tasks Submitted tasks dU(k) PID Control Ud U(k) Control PID M(k) Md mode switch Figure 1.6. Web server closed-loop regulation
- 53. 36 Networked Control Systems Co-design For each period of the scheduling controller, the measures are the total CPU load U(k) and the miss ratio M(k). The corresponding gains GA and GM are images of the modeling uncertainties. The execution of requests Ti is modeled by at least two levels of quality, i.e. cou- ples (QoS contribution, execution cost). The actuation provided is the choice of the execution mode corresponding to a given cost, at every sampling period. The accu- mulated regulated cost is finally the global CPU load. If the sampling period h is large enough, the transfer function of the CPU load submitted to computing requests Δu can be modeled by an integrator, where GA and GM are the weakly known gains of the open loop process: U(k) = U(k − 1) + GA .Δu(k − 1)if CPU under-loaded, M(k) = M(k − 1) + GM .Δu(k − 1) if CPU over-loaded. Thus, a simple proportional regulator is able to control the server load Δu(k) = Kpu .EU (k) où EU (k) = Us − U(k) if U ≤ 1, Δu(k) = Kpm .EM (k) où EM (k) = Ms − M(k) if M 0. Figure 1.7 (borrowed from [LU 02] with permission of the author) shows the steady state behavior (CPU load U(k) and deadlines missed M(k)) as a function of the desired load Ud. The role of the underlying scheduling policy can be observed: using EDF (on the right picture) allows for nullifying the deadlines missed up to Ud = 1, but exhibits degradation in the case of permanent overload faster than a static DM priority policy. However, in all cases, the server shows some ability for automatic adaptation to the arrival of sporadic requests and for recovery against sporadic overloads, thus leading to a kind of self-administration at a very low-computing cost. 1.4.2.2. Optimal control-based feedback scheduling The aforementioned PID regulation approach is very simple to design and tune. The downside of the very limited number of tuning parameters is the limited capabil- ities of, e.g. shaping robustness templates or decoupling several transfer modes. Let us come back to the initial problem, which may consist formally in the opti- mization of a control performance under constraints of limited computing resources. This problem has been analytically solved by [EKE 00] and [CER 03a] for the fol- lowing case study. A given computing resource is shared by n real-time control tasks, each one is used to control a linear stochastic process; each controller has an hi period and a Ci execution time. A sampling frequency dependent quality criterion Ji(hi) is
- 54. Preliminary Notions 37 Utilization CPU U 100 80 60 40 20 0 0 20 Average total requested utilization (%) (a) DM/PA (b) EDF/P Average miss ratio, Average utilization (%) 40 60 80100120140160180200 Miss ratio M 100 80 60 40 20 0 0 20 Average total requested utilization (%) Average miss ratio, Average utilization (%) 40 60 80100120140160180200 100 50 0 0 50 100 Time (S) (a) DM/PA U(k); B(k); M(k) (%) 150 200 250 300 350 400 50 100 Time (S) (b) EDF/P 150 200 250 300 350 400 Us U(k) B(k) M(k) 100 50 0 0 U(k); B(k); M(k) (%) Us U(k) B(k) M(k) Figure 1.7. Load response of the server (steady state and dynamic response) attached to each controller. The control goal is the maximization of a global cost function over the set of controller, with respect of a desired computing load Ud: min n J = n i=1 Ji(hi) under constraint n i=1 Ci/hi ≤ Ud. The control variables are the control periods hi. The problem is solved using the cost function J(h) = 1 h h 0 xT (t) uT (t) Q x(t) u(t) dt.
- 55. Another Random Document on Scribd Without Any Related Topics
- 56. also true of this: it is very rarely offered for sale, can only be found upon occasion, and commands a high price. In the year 1841 Dr. Thaddeus William Harris published A Report on the Insects of Massachusetts which are Injurious to Vegetation. This work, which was originally brought out in pursuance of an order of the legislature of Massachusetts, by the Commissioners of the Zoölogical and Botanical Survey of the State, was republished in 1842, and was followed by a third edition in 1852. The last edition, revised and improved by Charles L. Flint, Secretary of the Massachusetts State Board of Agriculture, appeared in 1862. This work contains a number of figures and descriptions of the butterflies of New England, and, while now somewhat obsolete, still contains a great deal of valuable information, and is well worth being rescued by the student from the shelves of the second-hand book-stalls in which it is now and then to be found. For the New England student of entomology it remains to a greater or less extent a classic. In 1860 the Smithsonian Institution published a Catalogue of the Described Lepidoptera of North America, a compilation prepared by the Rev. John G. Morris. This work, though very far from complete, contains in a compact form much valuable information, largely extracted from the writings of previous authors. It is not illustrated. With the book prepared by Dr. Morris the first period in the development of a literature relating to our subject may be said to close, and the reader will observe that until the end of the sixth decade of this century very little had been attempted in the way of systematically naming, describing, and illustrating the riches of the insect fauna of this continent. Almost all the work, with the exception of that done by Harris, Leconte, and Morris, had been done by European authors. Later Writers.—At the close of the Civil War this country witnessed a great intellectual awakening, and every department of science began to find its zealous students. In the annals of entomology the year 1868 is memorable because of the issue of the first part of the
- 57. great work by William H. Edwards, entitled The Butterflies of North America. This work has been within the last year (1897) brought to completion with the publication of the third volume, and stands as a superb monument to the scientific attainments and the inextinguishable industry of its learned author. The three volumes are most superbly illustrated, and contain a wealth of original drawings, representing all the stages in the life-history of numerous species, which has never been surpassed. Unfortunately, while including a large number of the species known to inhabit North America, the book is nevertheless not what its title would seem to imply, and is far from complete, several hundreds of species not being represented in any way, either in the text or in the illustrations. In spite of this fact it will remain to the American student a classic, holding a place in the domain of entomology analogous to that which is held in the science of ornithology by the Birds of America, by Audubon. A work even more elaborate in its design and execution, contained in three volumes, is The Butterflies of New England, by Dr. Samuel Hubbard Scudder, published in the year 1886. No more superbly illustrated and exhaustive monograph on any scientific subject has ever been published than this, and it must remain a lasting memorial of the colossal industry and vast learning of the author, one of the most eminent scientific men whom America has produced. While the two great works which have been mentioned have illustrated to the highest degree not only the learning of their authors, but the vast advances which have been made in the art of illustration within the last thirty years, they do not stand alone as representing the activity of students in this field. A number of smaller, but useful, works have appeared from time to time. Among these must be mentioned The Butterflies of the Eastern United States, by Professor G.H. French. This book, which contains four hundred and two pages and ninety-three figures in the text, was published in Philadelphia in 1886. It is an admirable little work, with the help of which the student may learn much in relation to the
- 58. subject; but it greatly lacks in illustration, without which all such publications are not attractive or thoroughly useful to the student. In the same year appeared The Butterflies of New England, by C.J. Maynard, a quarto containing seventy-two pages of text and eight colored plates, the latter very poor. In 1878 Herman Strecker of Reading, Pennsylvania, published a book entitled Butterflies and Moths of North America, which is further entitled A Complete Synonymical Catalogue. It gives only the synonymy of some four hundred and seventy species of butterflies, and has never been continued by the author, as was apparently his intention. It makes no mention of the moths, except upon the title-page. For the scientific student it has much value, but is of no value to a beginner. The same author published in parts a work illustrated by fifteen colored plates, entitled Lepidoptera-Rhopaloceres and Heteroceres —Indigenous and Exotic, which came out from 1872 to 1879, and contains recognizable figures of many North American species. In 1891 there appeared in Boston, from the pen of C.J. Maynard, a work entitled A Manual of North American Butterflies. This is illustrated by ten very poorly executed plates and a number of equally poorly executed cuts in the text. The work is unfortunately characterized by a number of serious defects which make its use difficult and unsatisfactory for the correct determination of species and their classification. In 1893 Dr. Scudder published two books, both of them useful, though brief, one of them entitled The Life of a Butterfly, the other, A Brief Guide to the Commoner Butterflies of the Northern United States and Canada. Both of these books were published in New York by Messrs. Henry Holt Co., and contain valuable information in relation to the subject, being to a certain extent an advance upon another work published in 1881 by the same author and firm, entitled Butterflies. Periodical Literature.—The reader must not suppose that the only literature relating to the subject that we are considering is to be found in the volumes that have been mentioned. The original
- 59. descriptions and the life-histories of a large number of the species of the butterflies of North America have originally appeared in the pages of scientific periodicals and in the journals and proceedings of different learned societies. Among the more important publications which are rich in information in regard to our theme may be mentioned the publications relating to entomology issued by the United States National Museum, the United States Department of Agriculture, and by the various American commonwealths, chief among the latter being Riley's Missouri Reports. Exceedingly valuable are many of the papers contained in the Transactions of the American Entomological Society, Psyche, the Bulletin of the Brooklyn Entomological Society (1872-85), Papilio (1881-84), Entomologica Americana (1885-90), the Journal of the New York Entomological Society, the Canadian Entomologist, and Entomological News. All of these journals are mines of original information, and the student who proposes to master the subject thoroughly will do well to obtain, if possible, complete sets of these periodicals, as well as of a number of others which might be mentioned, and to subscribe for such of them as are still being published. There are a number of works upon general entomology, containing chapters upon the diurnal lepidoptera, which may be consulted with profit. Among the best of these are the following: A Guide to the Study of Insects, by A.S. Packard, Jr., M.D. (Henry Holt Co., New York, 1883, pp. 715, 8vo); A Textbook of Entomology, by Alpheus S. Packard, M.D., etc. (The Macmillan Company, New York, 1898, pp. 729, 8vo); A Manual for the Study of Insects, by John Henry Comstock (Comstock Publishing Company, Ithaca, New York, 1895, pp. 701, 8vo). HUGO'S FLOWER TO BUTTERFLY Sweet, live with me, and let my love Be an enduring tether;
- 60. Oh, wanton not from spot to spot, But let us dwell together. You've come each morn to sip the sweets With which you found me dripping, Yet never knew it was not dew, But tears, that you were sipping. You gambol over honey meads Where siren bees are humming; But mine the fate to watch and wait For my beloved's coming. The sunshine that delights you now Shall fade to darkness gloomy; You should not fear if, biding here, You nestled closer to me. So rest you, love, and be my love, That my enraptured blooming May fill your sight with tender light, Your wings with sweet perfuming. Or, if you will not bide with me
- 61. Upon this quiet heather, Oh, give me wing, thou beauteous thing, That we may soar together. Eugene Field. THE BUTTERFLIES
- 62. OF NORTH AMERICA NORTH OF MEXICO Lo, the bright train their radiant wings unfold! With silver fringed, and freckled o'er with gold: On the gay bosom of some fragrant flower They, idly fluttering, live their little hour; Their life all pleasure, and their task all play, All spring their age, and sunshine all their day. Mrs. Barbauld
- 64. FAMILY I NYMPHALIDÆ (THE BRUSH-FOOTED BUTTERFLIES) The family of the Nymphalidæ is composed of butterflies which are of medium and large size, though a few of the genera are made up of species which are quite small. They may be distinguished from all other butterflies by the fact that the first pair of legs in both sexes is atrophied or greatly reduced in size, so that they cannot be used in walking, but are carried folded up upon the breast. The fore feet, except in the case of the female of the snout-butterflies (Libytheinæ), are without tarsal claws, and hence the name Brush- footed Butterflies has been applied to them. As the anterior pair of legs is apparently useless, they have been called The Four-footed Butterflies, which is scientifically a misnomer. Egg.—The eggs of the Nymphalidæ, for the most part, are dome- shaped or globular, and are marked with raised longitudinal lines extending from the summit toward the base over the entire surface or over the upper portion of the egg. Between these elevations are often found finer and less elevated cross-lines. In a few genera the surface of the eggs is covered with reticulation arranged in geometrical patterns (see Fig. 1). Caterpillar.—The caterpillars of the Nymphalidæ, as they emerge from the egg, have heads the diameter of which is larger than that of the body, and covered with a number of wart-like elevations from which hairs arise. The body of the immature larva generally tapers from before backward (see Plate III, Figs. 7 and 11). The mature larva is cylindrical in form, sometimes, as in the Satyrinæ, thicker in the middle. Often one or more of the segments are greatly swollen
- 65. in whole or in part. The larvæ are generally ornamented with fleshy projections or branching spines. Chrysalids.—The chrysalids are for the most part angular, and often have strongly marked projections. As a rule, they hang with the head downward, having the cremaster, or anal hook, attached to a button of silk woven to the under surface of a limb of a tree, a stone, or some other projecting surface. A few boreal species construct loose coverings of threads of silk at the roots of grasses, and here undergo their transformations. The chrysalids are frequently ornamented with golden or silvery spots. This is the largest of all the families of butterflies, and it is also the most widely distributed. It is represented by species which have their abode in the cold regions of the far North and upon the lofty summits of mountains, where summer reigns for but a few weeks during the year; and it is enormously developed in equatorial lands, including here some of the most gloriously colored species in the butterfly world. But although these insects appear to have attained their most superb development in the tropics, they are more numerous in the temperate regions than other butterflies, and a certain fearlessness, and fondness for the haunts of men, which seems to characterize some of them, has brought them more under the eyes of observers. The literature of poetry and prose which takes account of the life of the butterfly has mainly dealt with forms belonging to this great assemblage of species. In the classification of the brush-footed butterflies various subdivisions have been suggested by learned authors, but the species found in the United States and the countries lying northward upon the continent may be all included in the following six groups, or subfamilies: 1. The Euplœinœ, the Euplœids. 2. The Ithomiinœ, the Ithomiids. 3. The Heliconiinœ, the Heliconians. 4. The Nymphalinœ, the Nymphs.
- 66. 5. The Satyrinœ, the Satyrs. 6. The Libytheinœ, the Snout-butterflies. The insects belonging to these different subfamilies may be distinguished by the help of the following analytical table, which is based upon that of Professor Comstock, given in his Manual for the Study of Insects (p. 396), which in turn is based upon that of Dr. Scudder, in The Butterflies of New England (vol. i, p. 115). Key to the subfamilies of the Nymphalidæ of the United States and Canada I. With the veins of the fore wings not greatly swollen at the base. A. Antennæ naked. (a) Fore wings less than twice as long as broad— Euplœinœ. (b) Fore wings twice as long as broad and often translucent, the abdomen extending far beyond the inner margin of the hind wings —Ithomiinœ. B. Antennæ clothed with scales, at least above. (a) Fore wings at least twice as long as broad—Heliconiinœ. (b) Fore wings less than twice as long as broad. 1. Palpi not as long as the thorax—Nymphalinœ. 2. Palpi much longer than the thorax—Libytheinœ. II. With some of the veins of the fore wings greatly swollen at the base—Satyrinœ. We now proceed to present the various genera and species of this family which occur within the territorial limits of which this book treats. The reader will do well to accompany the study of the descriptions, which are at most mere sketches, by a careful examination of the figures in the plates. In this way a very clear idea of the different species can in most instances be obtained. But with the study of the book should always go, if possible, the study of the living things themselves. Knowledge of nature founded upon books
- 67. is at best second-hand. To the fields and the woods, then, net in hand! Splendid as may be the sight of a great collection of butterflies from all parts of the world, their wings Gleaming with purple and gold, no vision is so exquisite and so inspiring as that which greets the true aurelian as in shady dell or upon sun-lit upland, with the blue sky above him and the flowers all around him, he pursues his pleasant, self-imposed tasks, drinking in health at every step.
- 68. SUBFAMILY EUPLŒINÆ (THE MILKWEED BUTTERFLIES) Lazily flying Over the flower-decked prairies, West; Basking in sunshine till daylight is dying, And resting all night on Asclepias' breast; Joyously dancing, Merrily prancing, Chasing his lady-love high in the air, Fluttering gaily, Frolicking daily, Free from anxiety, sorrow, and care! C.V. Riley. Butterfly.—Large butterflies; head large; the antennæ inserted on the summit, stout, naked, that is to say, not covered with scales, the club long and not broad; palpi stout; the thorax somewhat compressed, with the top arched. The abdomen is moderately stout, bearing on the eighth segment, on either side, in the case of the male, clasps which are quite conspicuous. The fore wings are greatly
- 69. produced at the apex and more or less excavated about the middle of the outer border; the hind wings are rounded and generally much smaller than the fore wings; the outer margin is regular, without tails, and the inner margin is sometimes channeled so as to enfold the abdomen. The fore legs are greatly atrophied in the male, less so in the female; these atrophied legs are not provided with claws, but on the other legs the claws are well developed. Egg.—The eggs are ovate conical, broadly flattened at the base and slightly truncated at the top, with many longitudinal ribs and transverse cross-ridges (see Fig. 4). Plate VII. Caterpillar.—On emerging from the chrysalis the head is not larger than the body; the body has a few scattered hairs on each segment. On reaching maturity the head is small, the body large, cylindrical, without hair, and conspicuously banded with dark stripes upon a lighter ground, and on some of the segments there are generally erect fleshy processes of considerable length (see Fig. 16). The caterpillars feed upon different species of the milkweed (Asclepias). Chrysalis.—The chrysalis is relatively short and thick, rounded, with very few projections, tapers very rapidly over the posterior part of the abdomen, and is suspended by a long cremaster from a button of silk (see Fig. 24). The chrysalis is frequently ornamented with golden or silver spots. This subfamily reaches its largest development in the tropical regions of Asia. Only one genus is represented in our fauna, the genus Anosia. Genus ANOSIA, Hübner Butterfly.—Large-sized butterflies; fore wings long, greatly produced at the apex, having a triangular outline, the outer margin
- 70. Fig. 78.—Neuration of the genus Anosia. approximately as long as the inner margin; the costal border is regularly bowed; the outer border is slightly excavated, the outer angle rounded; the hind wings are well rounded, the costal border projecting just at the base, the inner margin likewise projecting at the base and depressed so as to form a channel clasping the abdomen. On the edge of the first median nervule of the male, about its middle, there is a scent-pouch covered with scales. Egg.—The egg is ovate conical, ribbed perpendicularly with many raised cross-lines between the ridges. The eggs are pale green in color. Caterpillar.—The caterpillar is cylindrical, fleshy, transversely wrinkled, and has on the second thoracic and eighth abdominal segment pairs of very long and slender fleshy filaments; the body is ornamented by dark bands upon a greenish-yellow ground- color; the filaments are black. Chrysalis.—The chrysalis is stout, cylindrical, rapidly tapering on the abdomen, and is suspended from a button of silk by a long cremaster. The color of the chrysalis is pale green, ornamented with golden spots. The larvæ of the genus Anosia feed for the most part upon the varieties of milkweed (Asclepias), and they are therefore called milkweed butterflies. There are two species of the genus found in our fauna, one, Anosia plexippus, Linnæus, which is distributed over the entire continent as far north as southern Canada, and the other, Anosia berenice, Cramer, which is confined to the extreme southwestern portions of the United States, being found in Texas and Arizona.
- 71. (1) Anosia plexippus, Linnæus, Plate VII, Fig. 1, ♂ (The Monarch). Butterfly.—The upper surface of the wings of this butterfly is bright reddish, with the borders and veins broadly black, with two rows of white spots on the outer borders and two rows of pale spots of moderately large size across the apex of the fore wings. The males have the wings less broadly bordered with black than the females, and on the first median nervule of the hind wings there is a black scent-pouch. Egg.—The egg is ovate conical, and is well represented in Fig. 4 in the introductory chapter of this book. Caterpillar.—The caterpillar is bright yellow or greenish-yellow, banded with shining black, and furnished with black fleshy thread- like appendages before and behind. It likewise is well delineated in Fig. 16, as well as in Plate III, Fig. 5. Chrysalis.—The chrysalis is about an inch in length, pale green, spotted with gold (see Fig. 24, and Plate IV, Figs. 1-3). The butterfly is believed to be polygoneutic, that is to say, many broods are produced annually; and it is believed by writers that with the advent of cold weather these butterflies migrate to the South, the chrysalids and caterpillars which may be undeveloped at the time of the frosts are destroyed, and that when these insects reappear, as they do every summer, they represent a wave of migration coming northward from the warmer regions of the Gulf States. It is not believed that any of them hibernate in any stage of their existence. This insect sometimes appears in great swarms on the eastern and southern coasts of New Jersey in late autumn. The swarms pressing southward are arrested by the ocean. The writer has seen stunted trees on the New Jersey coast in the middle of October, when the foliage has already fallen, so completely covered with clinging masses of these butterflies as to present the appearance of trees in full leaf (Fig. 79).
- 72. Fig. 79.—Swarms of milkweed butterflies resting on a tree. Photographed at night by Professor C.F. Nachtrieb. (From Insect Life, vol. v, p. 206, by special permission of the United States Department of Agriculture.) This butterfly is a great migrant, and within quite recent years, with Yankee instinct, has crossed the Pacific, probably on merchant vessels, the chrysalids being possibly concealed in bales of hay, and has found lodgment in Australia, where it has greatly multiplied in the warmer parts of the Island Continent, and has thence spread northward and westward, until in its migrations it has reached Java and Sumatra, and long ago took possession of the Philippines. Moving eastward on the lines of travel, it has established a more or
- 73. less precarious foothold for itself in southern England, as many as two or three dozen of these butterflies having been taken in a single year in the United Kingdom. It is well established at the Cape Verde Islands, and in a short time we may expect to hear of it as having taken possession of the continent of Africa, in which the family of plants upon which the caterpillars feed is well represented. (2) Anosia berenice, Cramer, Plate VII, Fig. 2, ♂ (The Queen). This butterfly is smaller than the Monarch, and the ground-color of the wings is a livid brown. The markings are somewhat similar to those in A. plexippus, but the black borders of the hind wings are relatively wider, and the light spots on the apex of the fore wings are whiter and differently located, as may be learned from the figures given in Plate VII. There is a variety of this species, which has been called Anosia strigosa by H.W. Bates (Plate VII, Fig. 3, ♂), which differs only in that on the upper surface of the hind wings the veins as far as the black outer margin are narrowly edged with grayish-white, giving them a streaked appearance. This insect is found in Texas, Arizona, and southern New Mexico. All of the Euplœinæ are protected insects, being by nature provided with secretions which are distasteful to birds and predaceous insects. These acrid secretions are probably due to the character of the plants upon which the caterpillars feed, for many of them eat plants which are more or less rank, and some of them even poisonous to the higher orders of animals. Enjoying on this account immunity from attack, they have all, in the process of time, been mimicked by species in other genera which have not the same immunity. This protective resemblance is well illustrated in Plate VII. The three upper figures in the plate represent, as we have seen, species of the genus Anosia; the two lower figures represent two species of the genus Basilarchia. Fig. 4 is the male of B. disippus, a very common species in the northern United States, which mimicks the Monarch. Fig. 5 represents the same sex of B. hulstii, a species
- 74. which is found in Arizona, and there flies in company with the Queen, and its variety, A. strigosa, which latter it more nearly resembles.
- 75. SUBFAMILY ITHOMIINÆ (THE LONG-WINGS) There be Insects with little hornes proaking out before their eyes, but weak and tender they be, and good for nothing; as the Butterflies.—Pliny, Philemon Holland's Translation. Butterfly.—This subfamily is composed for the most part of species of moderate size, though a few are quite large. The fore wings are invariably greatly lengthened and are generally at least twice as long as broad. The hind wings are relatively small, rounded, and without tails. The wings in many of the genera are transparent. The extremity of the abdomen in both sexes extends far beyond the margin of the hind wings, but in the female not so much as in the male. The antennæ are not clothed with scales, and are very long and slender, with the club also long and slender, gradually thickening to the tip, which is often drooping. The fore legs are greatly atrophied in the males, the tibia and tarsi in this sex being reduced to a minute knob-like appendage, but being more strongly developed in the females. The life-history of none of the species reputed to be found in our fauna has been carefully worked out. The larvæ are smooth, covered in most genera with longitudinal rows of conical prominences. The chrysalids are said to show a likeness to those of the Euplœinæ, being short, thick, and marked with golden spots. Some authors are inclined to view this subfamily as merely constituting a
- 76. section of the Euplœinæ. The insects are, however, so widely unlike the true Euplœinæ that it seems well to keep them separate in our system of classification. In appearance they approach the Heliconians more nearly than the Euplœids. Ithomiid butterflies swarm in the tropics of the New World, and several hundreds of species are known to inhabit the hot lands of Central and South America. But one genus is found in the Old World, Hamadryas, confined to the Australian region. They are protected like the Euplœids and the Heliconians. In flight they are said to somewhat resemble the dragon-flies of the genus Agrion, their narrow wings, greatly elongated bodies, and slow, flitting motion recalling these insects, which are known by schoolboys as darning-needles. Three genera are said to be represented in the extreme southwestern portion of the United States. I myself have never received specimens of any of them which indisputably came from localities within our limits, and no such specimens are found in the great collection of Mr. W.H. Edwards, which is now in my possession. A paratype of Reakirt's species, Mechanitis californica, is contained in the collection of Theodore L. Mead, which I also possess. Mr. Mead obtained it from Herman Strecker of Reading, Pennsylvania. Reakirt gives Los Angeles as the locality from which his type came; but whether he was right in this is open to question, inasmuch, so far as is known, the species has not been found in that neighborhood since described by Reakirt. Genus MECHANITIS, Fabricius Butterfly.—Butterflies of moderate size, with the fore wings greatly produced, the inner margin bowed out just beyond the base, and deeply excavated between this projection and the inner angle. The lower discocellular vein in the hind wings is apparently continuous with the median vein, and the lower radial vein being parallel with the median nervules, the median vein has in consequence the appearance of being four-branched. The submedian vein of the fore wings is forked at the base. The costal margin of the hind wings is clothed with tufted erect hairs in the male sex. The fore legs of the
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