Process control handout new1

ADAMA UNIVERSITY
Chapter I: Review of fundamentals of process control
What is a process? It is the method of changing or refining of raw materials that pass through
or remaining in a liquid, solid or gaseous state to create end products. And Process Control
refers to the methods that are used to control process variables when manufacturing a product.
To succeed in process control the designer must first establish a good understanding of the
process to be controlled. Since we do not wish to become too deeply involved in chemical or
process engineering, we need to find a way of simplifying the representation of the process we
wish to control. This is done by adopting a technique of block diagram modeling of the
process.
All processes have some basic characteristics in common, and if we can identify these, the job of
designing a suitable controller can be made to follow a well-proven and consistent path. The
trick is to learn how to make a reasonably accurate mathematical model of the process and use
this model to find out what typical control actions we can use to make the process operate at the
desired conditions.
Basic definitions and terms used in process control
Most basic process control systems consist of a control loop as shown in Figure 1.1, having four
main components:
1. A measurement of the state or condition of a process
2. A controller calculating an action based on this measured value against a preset or desired
value (setpoint)
3. An output signal resulting from the controller calculation, which is used to manipulate the
process action through some form of actuator
4. The process itself reacting to this signal, and changing its state or condition.
1

Figure 1.1 Block diagram showing the elements of a process control loop
The two most important signals used in process control are
1. Process variable or PV (The output is the process variable to be controlled.)
2. Manipulated variable or MV. (The variable (e.g. position of the valve) that can be controlled
by the controller output signals or by the actuator output signal). In industrial process control, the
PV is measured by an instrument in the field, and acts as an input to an automatic controller
which takes action based on the value of it. Alternatively, the PV can be an input to a data
display so that the operator can use the reading to adjust the process through manual control and
supervision.
The variable to be manipulated, in order to have control over the PV, is called the MV. For
instance, if we control a particular flow, we manipulate a valve to control the flow. Here, the
valve position is called the MV and the measured flow becomes the PV. In the case of a simple
automatic controller, the Controller Output Signal (OP) drives the MV. In more complex
automatic control systems, a controller output signal may drive the target values or reference
values for other controllers. The ideal value of the PV is often called the target value, and in the
case of an automatic control, the term setpoint (SP) value is preferred.
Process modeling
To perform an effective job of controlling a process, we need to know how the control input we
are proposing to use will affect the output of the process. If we change the input conditions we
shall need to know the following:
 Will the output rise or fall?
 How much response will we get?
 How long will it take for the output to change?
 What will be the response curve or trajectory of the response?
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The answers to these questions are best obtained by creating a mathematical model of the
relationship between the chosen input and the output of the process in question. Process control
designers use a very useful technique of block diagram modeling to assist in the representation
of the process and its control system. The principles that we should be able to apply to most
practical control loop situations are given below.
The process plant is represented by an input/output block as shown in Figure 1.2.
Figure 1.2 Basic block diagram for the process being controlled
In Figure 1.2 we see a controller signal that will operate on an input to the process, known as the
MV. We try to drive the output of the process to a particular value or SP by changing the input.
The output may also be affected by other conditions in the process or by external actions such as
changes in supply pressures or in the quality of materials being used in the process. These are all
regarded as disturbance inputs and our control action will need to overcome their influences as
best as possible.
The challenge for the process control designer is to maintain the controlled process variable at
the target value or change it to meet production needs, whilst compensating for the disturbances
that may arise from other inputs. For example, if you want to keep the level of water in a tank at a
constant height whilst others are drawing off from it, you will manipulate the input flow to keep the level
steady.
The value of a process model is that it provides a means of showing the way the output will
respond to the actions of the input. This is done by having a mathematical model based on the
physical and chemical laws affecting the process.
For example, the following figure shows a simple process control system to control the water
level in an open tank. The reference value is the initial setting of the lever- arm arrangement so
that it is just cuts off the water supply at a required level. When water is drawn from the tank the
float moves down wards with the water level. This causes the lever arrangement to rotate and so
3

allow water to enter the tank. This flow continues until the ball has risen to such a height that it
has moved the liver arrangement to cut off the water supply.
It is a closed loop control system with the following basic elements or process variables:
 Controlled variable…..water level in the tank (H)
 Reference value……….Initial setting of the lever arm according to the user’s interest
 Error signal……………the difference b/n the actual and the initial setting of the liver position
 Controller……………..the pivoted lever
 Correction element……the valve( an actuator that drives the valve)
 Process…………………the water in the tank
 Measuring device………the floating ball( it can be a sensor in other process types)
1.1 Process Controllers
Process controllers are control system components which basically have an input of the signal,
and an output of a signal to modify the system output. The ways in which process controllers
react to the error changes are known as Control Laws.
1.1.1 On-off control:
The oldest strategy for control is to use a switch giving simple on–off control. This is a
discontinuous form of control action, and is also referred to as two-position control. The
technique is crude, but can be a cheap and effective method of control if a fairly large fluctuation
of the process variable (PV) is acceptable.
A perfect on–off controller is ‘on’ when the measurement is below the setpoint (SP) and the
manipulated variable (MV) is at its maximum value. Above the SP, the controller is ‘off’ and the
MV is a minimum. On–off control is widely used in both industrial and domestic applications.
Example; Consider the control action on a domestic gas-fired boiler. When the temperature is
below the setpoint, the fuel is ‘on’; when the temperature rises above the setpoint, the fuel is
‘off’, as it is shown below:
4

Figure 1.5 Graphical example of on–off control
In general On-off control can be explained as follows:
u(t)=U1 ( for e(t) > 0 )
=U2 ( for e(t) < 0 )
Where: u(t) : output from the controller
e(t) : error signal
OR
The controller output of ideal on-off controller is:
Where: umax and umin denote the on and off values, respectively.
 On-off controller can be considered to be a special case of P controller with a very high
controller gain
Advantage: Simple and inexpensive controllers.
Disadvantage: - Not versatile and ineffective.
- Continuous cycling of the controlled variable and excess wear on the final
control element.
Usage:
 Thermostats in heating system
 Domestic refrigerator
 Noncritical industrial applications.
5

1.1.2 Proportional control
With the on-off method of control, the controller output is either an on or an off signal
and so the output is not related to the size of the error.
However, with the proportional control, the size of the controller output is proportional to
the size of the error, i.e. the controller input. Thus we have: controller output is directly
proportional to controller input.
Therefore,
Where KP is a constant called the gain. This means the correction element of the control
system will have an input of a signal which is proportional to the size of the correction
required.
 It is called proportional as its output changes proportionally with the error signal.
And the transfer function of the system will be the gain KP. That is :
 Since the control output is proportional to the input, it plays a role in pushing the
process output to the set point as much as the error.
Proportional band
Note that it is customary to express the output of a controller as a percentage of the full range of
output that it is capable of passing on to the correction element. And proportional band will be
the difference between the ranges of percentage errors (i.e. the difference b/n the extreme values
of the percentage errors).In general we will have the following relationships for a typical
proportional control system:
 Controller output as % = output value- minimum value x 100
maximum value- minimum value
 % controller output = Kp x % error
 Error as % = measured value – setpoint value of variable x 100
maximum value – minimum value of variable
 PB = % errormax - %errormin ; where PB = proportional band
6
Controller output = kp x controller input

PB as % = 1 x controller output span x 100
kp measurement span
Where: span means the difference b/n the two extreme values.
And Kp = proportional gain= total transfer function of the system
And also Kp = 100
PB
Limitations of proportional control
All proportional control systems have a steady state error. The proportional mode of control
tends to be used in processes where the gain Kp can be made large enough to reduce the steady
state error to an acceptable level. However, the larger the gain the greater the chance of the
system oscillating. The oscillation occurs because of time lags in the system, the higher the gain
the bigger will be the controlling action for a particular error and so the greater the chance that
the system will overshoot the set value and oscillations occur.
How to reduce offset (steady state error)?
 By decreasing the proportional band (adding gain to the system) can reduce offset
 By increasing the gain
However, if too much gain is introduced, the system may become unstable and oscillate.
Summary for proportional band
Advantage: easier to apply and immediate corrective action.
Disadvantage: existence of steady-state error (offset). It is the result of long-term deviations in
the controlled variable
Usage: when the steady-state error is tolerable (ex. level control which wants to prevent the
system from overflowing or drying), proportional-only controller is attractive because of its
simplicity. Seldom used only.
 To remove the steady-state error (offset), the integral control action should be included
in the feedback controller
1.1.3 integral control (I control)
Integral control is the control mode where the controller output is proportional to the integral of
the error with respect to time. That is controller output is directly proportional to the
integral of the error with time.
 Integral (or reset) mode of control is designed to eliminate offset in a system
 Integral control is always used in conjunction with proportional control
7
Integral controller output = Ki x integral of error with time

 As an error occurs within a system, the proportional component makes an initial
correction; if an error remains, the integral component adds to the corrective action
Output from controller
1.1.4 proportional + integral control (PI control)
The integral mode I of control is not usually used alone but generally in conjunction with the
proportional mode P.
 The amount of control added to the proportional signal is dependent upon the length of
time the error has been present, in other words, the integral of the time constant
 Proportional-integral control is used where load changes occur frequently and setpoint
changes are infrequent
 Proportional-integral control is also used when load changes are slow
When integral action is added to a proportional control system the controller output is given
by
Ki = Kp
Ti
1.1.5 Derivative Control
8
gainintegral:
)(
)(
)()(
0
i
i
t
i
K
s
K
sE
sU
dtteKtu =⇒= ∫

With derivative control the change in control output from the set point value is proportional
to the rate of change with time of the error signal, i.e. controller output is directly
proportional to rate of change of error. Thus we can write:
Where KD is the constant of proportionality and commonly referred to as derivative time
since it has the unit of time
1.1.6 PD control
Derivative controllers give responses to changing error signals but do not, however, respond
to constant error signals, since with a constant error the rate of change of error with time is
zero. Because of this derivative control D is combined with proportional control P.
Then,
OR, it can be sometimes written as
Where KD / Kp is called the derivative action time TD
That is
1.1.7 proportional+integral+derivative control (PID control)
Combining all three modes of control (proportional, integral and derivative) enables a
controller to be produced which has no steady state error and reduces the tendency for
oscillations. Such a controller is known as a three mode controller or PID controller.
A PID controller can be considered to be a proportional controller which has integral
control to eliminate the offset error and derivative control to reduce time lags
 The derivative mode is used in a control system to re-duce overshoot and oscillations
within a control system
 Derivative refers to a rate of change. A derivative controller produces a signal that is
proportional to the rate of change of the error signal
 Derivative control is never used alone
 Derivative control is sometimes referred to as anticipatory or predictive control
Output from controller
9
)
1
1(
)(
)(
)(
)()()(
0
sT
sT
K
sE
sU
dt
tde
TKdtte
T
K
teKtu
d
i
p
dp
t
i
p
p
++=
++= ∫
Derivative controller output = KD x rate of change of error
PD controller output = Kp x error + KD x rate of change of error with time
PD controller output = Kp( error + KD rate of change of error)
Kp
PD controller output = Kp(error + TD x rate of change of error)

Chapter summary
 Proportional control speeds up the process response and reduces the offset.
 Integral control eliminates offset but tends to make the response oscillatory.
 Derivative control reduces both the degree of oscillation and response time.
Effects off controller gain (kp)
 Increasing the controller gain results less sluggish process response.
 Too large controller gain results undesirable degree of oscillation or even unstable
response.
 An intermediate value of the controller gain gives best control result.
Effect of integral time (Ti)
 Increasing the integral time results more conservative (sluggish) process response.
 Too large integral time results too long time to reach to the set point after load upset or
set-point change occurs.
 Theoretically, offset will be eliminated for all values of Ti
Effect of derivative time TD
 Increasing the derivative time results improved response by reducing the maximum
deviation, response time and the degree of oscillation.
 Too large derivative time results measurement noise tends to be amplified and the
response may be oscillatory.
Intermediate value of Td is desirable
10

Chapter 2
Practical control strategies
2.1 Cascade control
Cascade control is a common control technique that uses two controllers with one feedback loop
nested inside the other. The output of the primary controller acts as the set point for the
secondary controller. The controller of the primary loop determines the setpoint of the summing
controller in the secondary loop
In cascade control the output of one controller may be used to manipulate the set point of
another. The two controllers are then said to be cascaded, one upon the other. Each
controller will have its own measurement input, but only the primary controller can have an
independent set point and only the secondary controller has an output to the process. The
manipulated variable, the secondary controller, and its measurement constitute a closed loop
within the primary loop.
Example:
Water Level Control using cascade control principle
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Figure 2.1 Cascade Control of Liquid Level in a Tank
A better control system, which reduces time lags, the effects of load changes and other
disturbances, is cascade control. Cascade control involves the use of two controllers and two
feedback loops as shown above (Fig. 2.1). The outer loop or main loop is concerned with the
control of the variable, in this case the level of liquid in the tank. The inner loop or minor loop is
concerned with some intermediate variable, such as the flow rate of liquid entering the tank .The
set point of the outer loop is the required level and is set by the person in charge of the process.
The set point of the inner loop is however determined by the outer loop controller. This means,
since the output of the outer loop control is determined by the error signal it receives, that the set
point is determined by the measurement made of the level of liquid in the tank.
With such an arrangement, if there is a change in the supply of fluid in the pipe to the tank then
the flow measurement indicates this and sends a signal to the inner control. The result is an error
signal and so an output from the control which changes the control valve opening to the correct
the changes before the liquid leaves the pipe and enters the tank. If the liquid level changes,
perhaps as a result of more being drawn from the tank, then the level measurement leads to an
error signal to the outer controller which then changes the set point of the inner controller and so
its output to the valve. Hence the effect of a supply change is corrected near to its source and
time lags are reduced.
N: B; Flow transmitters and temperature transmitters are sensor types (measuring element)
Another structure for cascade control
12

Figure 2.2. Cascade control of the temperature of a furnace, which is taken to be the same as that of the
outlet process stream. The temperature controller does not actuate the regulating valve directly; it sends
its signal to a secondary flow rate control loop which in turn ensures that the desired fuel gas
To make clear the above structure (temperature control of a gas furnace, which is used to heat up
a cold process stream.) The fuel gas flow rate is the manipulated variable, and its flow is subject
to fluctuations due to upstream pressure variations.
In a simple single-loop system, we measure the outlet temperature, and the temperature
controller (TC) sends its signal to the regulating valve. If there is fluctuation in the fuel gas flow
rate, this simple system will not counter the disturbance until the controller senses that the
temperature of the furnace has deviated from the set point (Ts
).
A cascade control system can be designed to handle fuel gas disturbance more effectively
(Fig.2.2). In this case, a secondary loop (also called the slave loop) is used to adjust the
regulating valve and thus manipulate the fuel gas flow rate. The temperature controller (the
master or primary controller) sends its signal, in terms of the desired flow rate, to the secondary
flow control loop—in essence, the signal is the set point of the secondary flow controller (FC).
In the secondary loop, the flow controller compares the desired fuel gas flow rate with the
measured flow rate from the flow transducer (FT), and adjusts the regulating valve accordingly.
This inner flow control loop can respond immediately to fluctuations in the fuel gas flow to
ensure that the proper amount of fuel is delivered.
To be effective, the secondary loop must have a faster response time (smaller time constant) than
the outer loop. Generally, we use as high a proportional gain as feasible. In control jargon, we
say that the inner loop is tuned very tightly.
Block diagram of a simple cascade control system with reference to the furnace problem in figure x.x
This implementation of cascade control requires two controllers and two measured variables
(fuel gas flow and furnace temperature). The furnace temperature is the controlled variable, and
the fuel gas flow rate remains the only manipulated variable.
Advantages & disadvantages of Cascade control
Advantages:
Primary Loop:
 regulates part of the process having slower dynamics
 calculates setpoint for the secondary loop
Secondary Loop:
13

 regulates part of process having faster dynamics
 maintain secondary variable at the desired target given by primary controller
The principal advantages of cascade control are the following:
 Disturbances occurring in the secondary loop are corrected by the secondary controller
before they can affect the primary, or main, variable.
 The secondary controller can significantly reduce phase lag in the secondary loop,
thereby improving the speed or response of the primary loop.
 Gain variations due to nonlinearity in the process or actuator in the secondary loop are
corrected within that loop.
 The secondary loop enables exact manipulation of the flow of mass or energy by the
primary controller.
Disadvantages:
• Multiple control loops make physical and computational architecture more complex
• Additional controllers and sensors can be costly
2.2Fedforward control
Feedforward control: The basic idea is to take action before a disturbance reaches the
process. That means in feedforward control configuration, the disturbance is detected as it enters
the process and an appropriate change is made in the manipulated variable such that the
controlled variable is held constant. In this case, the corrective action begins as soon as a
disturbance enters the system.
Figure 2.3 Feedforward control.
As shown in Fig.2.3 above, the disturbance is detected as it enters the process and an appropriate
change is made in the manipulated variable such that the controlled variable is held constant.
Thus, we begin to take corrective action as soon as a disturbance entering the system is detected
instead of waiting (as we do with feedback control) for the disturbance to propagate all the way
through the process before a correction is made.
Advantages: One major advantage of feedward control is that it prevents large disturbances in
the given process output.
14

Disadvantages:
 It may not account for all potential disturbances in the input, leading to large
disturbances in the output.
 It is heavily dependent on model accuracy
Combined Feedback and feedforward control
Feedforward control is never used by itself; it is implemented in conjunction with a feedback
loop to provide the so-called feedback trim. Therefore, mostly it is advisable to include feedback
trim (feedback control action) along with the feedforward control strategies to take care of
modeling inaccuracies. As it is shown in the following block diagram, Feedback and
feedforward control loops are combined to keep the performance of the overall process.
Example:
2.3Ratio control
As the name implies, ratio control involves keeping constant the ratio of two or more flow rates.
The flow rate of the “wild” or uncontrolled stream is measured, and the flow rate of the
manipulated stream is changed to keep the two streams at a constant ratio with each other.
Common examples include holding a constant reflux ratio on a distillation column, keeping
stoichiometric amounts of two reactants being fed into a reactor, and purging off a fixed
percentage of the feed stream to a unit. Ratio control is often part of afeedforward control
structure,
Additional definitions:
Ratio control systems are installed to maintain the relationship between two variables to control a
third variable. Ratio control systems actually are the most elementary form of feed forward
control. In addition to this ratio control is used to ensure that two or more flows are kept at the
same ratio even if the flows are changing.
Applications of ratio control:
• Blending (combining) two or more flows to produce a mixture with specified
composition.
• Blending two or more flows to produce a mixture with specified physical properties.
• Maintaining correct air and fuel mixture to combustion.
15

Example of ratio control
In the following process shown below, a concentrated solution of product is diluted continuously
to be sold as a final 10% solution. Flow rates coming from the unit feeding the pure product to
this mixing tank are not constant (therefore they are wild stream), and therefore a ratio controller
is used to properly dilute the solution.
Figure 2.3 Ratio control structure
In this example, the ratio controller would be set to a value of FC1/FC2 = RC1 = Q. The ratio
controller in this case would then work by the following logic:
• IF RC1 < Q, THEN ADJUST FC2 DOWN
• IF RC1 > Q, THEN ADJUST FC2 UP
Another structure for ratio control system
16

In the ratio control scheme shown above the two flow rates are measured and their ratio is
computed (by the divider). This computed ratio signal is fed into a conventional PI controller as
the process variable (PV) signal. The setpoint of the ratio controller is the desired ratio. The
output of the controller goes to the valve on the manipulated variable stream, which changes its
flow rate in the correct direction to hold the ratio of the two flows constant. This computed ratio
signal can also be used to trigger an alarm or an interlock.
Advantages
• Links two streams to produce a defined ratio
• Simple--does not require a complex model
Disadvantage
Assumes pressure from the pure product side is constant
2.4 Deadtime control
Deadtime control means minimizing the delay time of the process. But what is deadtime?
Delay time, transportation lag, or deadtime is frequently encountered in chemical engineering
systems. The deadtime (L) is the delay between the manipulated variable changing and a
noticeable change in the process variable. Deadtime exists in most processes because few, if any,
real world events are instantaneous. Suppose a process stream is flowing through a pipe in
essentially plug flow and that it takes D minutes for an individual element of fluid to flow from
the entrance to the exit of the pipe. Then the pipe represents a deadtime element.
Another example is the hot water system. When the hot tap is switched on there will be a certain
time delay as hot water from the heater moves along the pipes to the tap. This is the deadtime.
In processes involving the movement of mass, deadtime is a significant factor in the process
dynamics. It is a delay in the response of a process after some variable is changed, during which
no information is known about the new state of the process. Deadtime is the worst enemy of
good control and every effort should be made to minimize it.
Reduction of deadtime
The aim of good control is to minimize deadtime and to minimize the ratio of deadtime to the
time constant. The higher this ratio, the less likely the control system will work properly.
Deadtime can be reduced by reducing transportation lags, which can be done by increasing the
17

rates of pumping or agitation, reducing the distance between the measuring instrument and the
process, etc. (That is between the sensor and the process)
18

Chapter 3
Advanced Control Techniques
3.1 Nonlinear and Adaptive Control
 Linear vs Nonlinear
• Linear
 basis for most industrial control
 simpler model form, easy to identify
 easy to design controller
 poor prediction, adequate control
• Nonlinear
 reality
 more complex and difficult to identify
 need state-of-the-art controller design techniques to do the job
 better prediction and control
 Q: If the model of the process is nonlinear, how do we express it in terms of a
transfer function?
A: We have to approximate it by a linear one (i.e.Linearize) in order to take the Laplace
 Procedure to obtain transfer function from nonlinear process models
 Find steady-state of process
 Linearize about the steady-state
 Express in terms of deviations variables about the steady-state
 Take Laplace transform
 Isolate outputs in Laplace domain
 Express effect of inputs in terms of transfer functions
Adaptive Control deals with uncertain systems or time-varying systems.
 They are mainly applied for systems with known dynamics but unknown constant or
slowly-varying parameters.
 They parameterize the uncertainty in terms of certain unknown parameters and use
feedback to learn these parameters on-line, during the operation of the system.
 In a more elaborate adaptive scheme, the controller might be learning certain unknown
nonlinear functions, rather than just learning some unknown parameters.
19

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