Coordination control modelling in batch production systems by means of petri nets

Compurers them. Engng, Vol. 16, No. 1, pp. I-10, 1992
Printedin Great Britain.All rights reserved
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copyrightQ 1992 FergamonPressplc
COORDINATION CONTROL MODELLING IN BATCH
PRODUCTION SYSTEMS BY MEANS OF PETRI NETS
H.-M. HANISCH
Department of Chemical Engineering, Technical University Leuna-Me-burg,
Otto-Nuschke-StraBe, D-4200 Merseburg. Fed. Rep. Germany
(Received 7May 1991;finai revision received II September 199I; receivedforpublication 25 September 1991)
Absiract-The paper presents an introduction to a mathematical method for modelling discrete
coordination control in batch production systems.
The process to be controlled is modelled usingPetrinet theory,a tool that is suitablefor the design
of discrete supervisory controllers, as well as for performance evaluation of the controlled process. As an
illustration, simple condition/event systems and higher Petri nets are applied to model a dye-stuff
production pro&s.
1. INTRODUCTTON
Most of the modern design methods for automatic
control systems are based on process models. Batch
production systems are not an exception, only in that
the models are different from those used to describe
continuous processes mostly because of the appreci-
able amount of discrete control actions. These usually
simple binary switching operations give rise to the
discrete control problem the complexity of which
increases with the number of logical interactions,
such as interlocked flows of material, energy and
shared resources as is typical for multipurpose batch
production systems. In order to achieve the desired
performance of entire production systems precise
models describing the discrete system behaviour on
this level are needed.
Up to now, coordination control tasks of this kind
have been mainly described in a non-formal, textual
form, which in most cases is extensive and rarely
unambiguous. Such a textual representation is by no
means sufficient, neither for an exact analysis of
interactions in a complex process nor for a computer-
aided formulation of the control problems. In order
to solve these problems, a general mathematical
formulation is called for which allows to analyze the
interactions of the different process units and which
is suitable for the design of discrete supervisory
controller units.
2. NEED FOR COORDINATION CONTROL
Objectives, control tasks and models for auto-
mation of complex multipurpose batch production
systems can be arranged in a hierarchical control
system such as is shown in Fig. 1.
The present paper deals with control tasks on
the synchronization and coordination level of batch
processes. As a rule, batch process systems are com-
posed of several process units working in parallel
coupled by flows of mass and energy. The coupling
pattern is time-dependent and many of the control
actions are of a discrete nature such as opening and
closing of control valves or starting and stopping of
pumps etc.
Example
Figure 2 shows an example of a batch production
system of an organic dye. The solid main product,
produced in reactor 1, is dispersed in a liquid phase.
Two filter subsystems (2,3) and (4, 5) are provided
for the separation of solid and liquid phases. The
liquid phase is stored in the storage tanks (3,5) to be
recycled in a subsequent batch, the solid is discharged
from the filters after completion of the washing
process.
Most of the time, reactor and filter systems work
independently, i.e. in parallel. On two occasions,
however, these units interact which are:
1. At the completion of the reaction process the
product must be discharged into one of the filter
systems.
2. After the filtration is completed the liquid phase
is recycled and reused in a subsequent batch.
Further interactions between process units may
arise from limitations of jointly used resources such
as:
-available metering tanks
-capacity of utilities (steam, electric power etc.)
-capacity of reactors and storage tanks
-available trained operators.
Example
In our example, the goal of coordination control is
to guarantee that:
1.
1
At the end of the reaction the whole batch is
discharged from the reactor into only one of the
filter systems.

H.-M. HANISCH

I
Saqurncc Control Lava1
(81)
I
several procrrrer
In a multipurpoma plant
(for instance dye pro-
duction)
several procarr unit6
forming a batab procemm
syrtem
ring10 batch preemss,
procerr unit
(for Inetancea drying,
reaction)
logical group8 of one ar
more procees variable6
(for inrtmce~ prerrure.
temperature, conarntration)
I
Meamarimg and Actuating
Level (HAL)
I
I I I I
I BATCH PROCESS
I
Fig. 1. Hierarchicalsystem.
2. At the beginning of a batch the liquid phase 1982; Starke, 1980). This method and its derivatives
from only one filter system is recycled. gained a leading position mostly because they are
characterized by a well-balanced relation between
3. DISCRETE-EVENT SYSTEMS MODELLINC WITH
graphical representation and mathematical abstrac-
PETRI NETS tion (Helms et al., 1989). Petri nets have no consider-
3.1. Modelerling capabilities of Petri nets
able advantage over other related modelhng methods
(automata-graphs and -tables, BOOLEan equations,
In the last two decades, Petri nets proved to be a sequential flowcharts etc.) when modelling pure
powerful tool for describing and analyzing concur- sequential operations as they are typical for the
rent processes (Brauer, 1980; Peterson, 1981; Reisig, control of single-unit batch processes. As part of a
f ... Reactor
24 ._. Filters
qS... Storage tanks
for liquid @use
solid purge of liquid
product phW9
Fig. 2. Flowsheet.

Coordination control modelling in batch production systems 3
ordinary Petri nets
(token weight of all
arcs -fI
higher Petri nets
Fig. 3. Classes of Petri nets.
model hierarchy, Petri nets are more useful for mod-
elling coordination problems on the upper control
levels and less useful for describing the details of the
sequential processes. Hence, they are usually applied
to control tasks on the synchronization and coordi-
nation level as described in Section 2.
Commonly, Petri nets are thought to represent
condition/event systems (C/E systems), but in fact,
C/E systems are only the simplest class of Petri
nets.
Figure 3 illustrates “classical” Petri nets. Beyond
these, a number of modifications and extensions
are known. This paper utilizes only classical Petri
nets.
The modelling capabilities of the various classes of
Petri nets differ considerably:
-C/E systems may be applied to model simple
interactions in small systems
-Place/transition nets (P/T nets) are suitable
for the modelling of medium-s&d systems of
medium complexity
-Predicate/transition nets (Pr/T nets) are used for
modelling complex interactions in large-scale
systems such as multiproduct or multipurpose
batch plants.
The general strategy of designing discrete controllers
handling the coordination control problem of batch
processes using Petri nets can be illustrated by dis-
cussing simple C/E systems. Hence, this paper deals
mainly with C/E systems (Sections 3 and 4). Section
5 discusses the modelling capabilities of higher classes
of Petri nets.
3.2. Formal properties of C/E systems
Formally, Petri nets are directed graphs with two
kinds of nodes.
Conditions are represented by circles and may be
true or false. In the graphical representation, the
circle carries a token (usually a black dot) if the
condition is true and no token otherwise. A condition
carrying a token is called a marked condition.
Events are represented by bars. Activities are
a special kind of event and are represented by
rectangles.
The net structure consists of directed arcs. They
link conditions with events or events with conditions,
but never two conditions or two events. Arcs are
represented by arrows.
Figure 4 shows an event and several conditions.
Relative to event e, the set of conditions can be
divided into preconditions of e (arrow from the
condition to the event) and postconditions of e
(arrow from the event to the condition). Post-
conditions of an event may be preconditions of
another event and so on. The structure of a
net represents the causal relations of the modelled
system. These relations are time-independent (static}.
Dynamic changes of the states are represented by the
flow of tokens in the net. The net may contain several
tokens in several conditions, called the marking of the
net. The modelling of concurrent processes is possible
by the existence of more than one token.
The rules for changing the marking depend on the
net class. C/E systems are controlled by a very simple
rule, higher Petri nets by more complicated ones.
Generally, the rule for changing the marking consists
of two parts.
EnabIing rule. An event e is enabled if all pre-
conditions of e are marked and all postconditions
of e are not marked (Fig. 4). Only an enabled event
may fire.
Firing rule. By firing e all preconditions of e
lose their tokens and all postconditions of e receive
one token. Figure 4 illustrates the firing of e. Firing
ireconditions pohconditions
ofe of 8
e is enabled e fires marking after firing of e
Fig. 4. Firing of an event.

4 H.-M. HANIXH
t
Fig. 5. Couplingof two tanks.
an event may change the number of tokens in the The process information in C/E models is given as
net. follows:
The firing of an event does not take any time.
Ideally, the firing occurs exactly at a particular
instant in time. Activities are an exception to this rule.
They represent sequential processes that are not
described on this modelling level. Hence, the ex-
ecution of activities may require some finite time. The
details of an activity are modelled using separate
models and are controlled on the sequential control
level (cf. Fig. 1).
1. Conditions are labelled with ranges of values of
process variables denoting discrete states of the
process units.
Each process state requires certain values of
control variables that must be realized by the
controller. Such values of control variables are
also assigned to the conditions.
4. APPLICATION OF C/E SYSTEMS
4.1. Process information in C/E systems
Originally, the formal mechanism of Petri nets is
free of any semantics. Thus, if Petri nets are to be
applied to particular processes, the elements of the
Petri net must be completed with additional process
information describing the relations between the
formal Petri net model and the particular process.
Only the combination of both the Petri net and the
process information represents a complete descrip-
tion of the process.
Example-Figure 5 shows the coupling of
two tanks (B,, B2) through a mass flow. The
state description is given in Table 1. Condition
c, denotes a certain state of B, (B, is full) which
determines the values of two binary control
variables (V, closed, V, closed).
Condition c, represents a state of B2 (Bz is
being discharged). For this I’, must be open.
These models comprise two major pieces of infor-
mation:
The marking of the net denotes the current state
of the modelled system.
Example-The marking of the net in Fig. 5
shows that B, is full and B2 is being discharged.
1. The performance of the process (desired mode
of operation).
2. The control operations necessary to achieve the
performance defined in 1.
Evenrs denote state transitions of the modelled
system. State transitions are caused by switching
binary control variables. Usually, binary con-
trol variables must be switched by the controller
when process variables reach predetermined
limits.
It is assumed that the process (controlled by the
controllers of the PL and SL-see Fig. 1) guarantees
the execution of the control operations imposed by
the discrete supervisory controller.
Table 1. Process information of the net
It is important to recognize that the combination
of the two parts, namely the performance of the
process and the corresponding control operations,
do not describe the discrete controller being used to
supervise the plant but that they model the process as
a discrete event system.
model of Fig. 5
Process variables Control variables
=I L, = kn..x v, ( v, closed
f2 0 -c L2-z L2m.r V3 open
c3 0 -c L, < =hnlx V, closed, V, open
c4 O-=La-=Lz,, V, closed
fJ L, = 0 V,, I’, closed
% I? = Lnax v, closed
e, & = 0 is reached close v,, open v,
e, L, = 0 is reached close v,

Coordinationcontrol moclellingin batch productionsystems
Hence, events are labelled with limits of pro-
cess variables and the corresponding switching
operations of control variables.
I
4. The structure of the net represents the causal
relations between the states (conditions) and the
state transitions (events) of process units. The
preconditions and postconditions of an event
are the causes and the results of the state
transition described by the event.
Example-Event ez in Fig. 5 denotes the
termination of the mass transfer from B, to B2_
Termination requires that the mass transfer
is actually taking place (denoted by the pre-
conditions cj and c, of e2) at that particular
moment. The result of the termination, when
the level in B, reaches zero, is described by the
postconditions of e,: B, is empty (cj) and B, is
full (c.&
5. The change of the marking according to the
enabling and the firing rules represents the
change of the current state of the modelled
system.
Example-With the marking given in Fig. 5,
event e, is enabled. Event e, occurs at the
moment when the level in B2 reaches zero. Now
V, is opened, and the state of the system changes
(B, is being discharged, B2 is being filled). This
state transition is represented in the model by
the change of marking. According to the firing
rule, c, and c, lose their tokens, and cj and c,
receive tokens. The new marking represents the
new state.
4.2. Application to a dye production process
Example-Event e, in Fig. 5 indicates that
the discharge of B2 is completed when the level
of B2 reaches zero. Consequently V, must be
closed and V, opened thus starting the transfer
of the content of B, to B2.
Event e2 describes the switching operation
that stops the mass transfer. This operation
must be performed when the level in B, reaches
zero. Then V, must be closed.
In this section, a Petri net model of the system
shown in Fig. 2 is developed.
The process information, given in Tables 2-4, is of
textual nature only for the sake of a simple example,
the conditions and events describing the operation of
the sample process neither include the valves nor the
pump. Normally, this description should also include
this type of information as was previously mentioned
and is shown in Table 1.
Figure 6 shows a very simple Petri net which
describes the interactions between the reactor (left
subnet) and the filter system (2, 3) (right subnet).
The product transfer from the reactor into the filter
Reacror I Filrer system I 2,3 1
Fig. 6. Simple C/E system model.
system and the recycling of the liquid phase are
represented in a clear and simple way. The model
assumes the following sequence of operations for
discharging the reactor.
The product transfer is started by opening the
bottom valve of the reactor (es). Simultaneously, the
filter system (2,3) starts to separate the liquid phase
from the solid product (en). The liquid phase is
stored for recycling (No. 3 in Fig. 2). The product
transfer lasts until the reactor level reaches zero (es).
The separation process lasts until all product has
been separated (e,). In fact, no causal dependence
between e, and e, exists. Therefore, the pre- and
postconditions of e6 and e, are disjoint.
Figure 7 shows the same model with the sequential
processes being replaced by activities and events er
and e,, merged in en (see Table 2). Note that the
recycling of the liquid phase is a process that takes
time, which is the reason this process is represented
as an activity.
Lastly, the filter system (4,5) must be integrated
into the model. The subnet describing this part has
the same structure as the one describing the filter
system (2, 3). Figure 8 shows the net including both
filter systems. The current state of the system, as
indicated by the marking of the net of Fig. 8, shows
that the reactor and filter system (2,3) are empty
(c,, clz) in this state, whereas filter system (4, 5) is
waiting for the recycling of the liquid phase from a
preceding batch (c13).
The marking expresses a state that represents a
desired mode of operation. All other states can be
computed by successive firing of enabled events or
activities (see Section 6). With the given marking, a,

H.-M. HANIXH
Cl
II
1 a1 j
I
I
I =7
Reactor
I Filter system 12,3)
Fig. 7. Introductionof activities.
can fire, afterwards czror a, (concurrently), e,r or e,5
(exclusively) and so on.
5. APPLICATIONOF HIGHERPETRINETS
5.1. Place/transition nets (P/T nets)
Place/transition nets are C/E systems with a few
added features.
Conditions, called places in P/T nets, may carry
more than one token. Each place has an assigned
capacity which is the maximum number of tokens the
particular place may carry.
Graphically, a place is again represented by a
circle. As a general rule, it is assumed that if no
capacity is assigned to a place, the capacity of this
place is one, which corresponds to the definition used
in C/E systems.
Arcs of a P/T net may be weighted with a non-
negative integer value called a token weight or multi-
plicity. The token weight denotes how many tokens
flow across the arc when the corresponding event
(now culled trnnsition) fires. In the graphical rep-
resentation the token weight is assigned to the corre-
sponding arrow. If no token weight is assigned to an
arc, then it has the value one, which again corre-
sponds to the definition used in C/E systems.
A transition t is enabled if:
-the marking of all preplaces oft is larger than or
equal to the token weight of the corresponding
arc
-the capacities of all postplaces of t are large
enough to receive a number of tokens given by
the token weight of the corresponding arc.
The change of the marking by firing t is shown in
Fig. 9.
An exact definition of P/T nets is given in
Reisig (1982) and Starke (1980) and their use for
modelling technological processes by adding process
information is described in Han&h (1987a, b).
Application. For the purpose of illustrating the
modelling capabilities of P/T nets, the production
system of Fig. 2 is modified by assuming that the
product is discharged only when five batches have
been separated in the filter system.
Figure 10 shows the corresponding net. The pro-
cess information is given in Table 3. The number of
tokens on p10 and P,~ express how many batches have
already been separated by the filter system, whereas
the number of tokens on p,* and pks denote how many
batches are still to be separated before the discharge
of the product can be performed. The activities a, and
a, model the discharge of the product as above.
However, they fire only if five tokens have accumu-
lated on p,,, or P,~.
By firing a3 or a, all the tokens are removed from
plo or p14 and p12 or p15 receives five tokens. This
means that after discharging the product, five batches
must be separated before the product is discharged
again. Thus, the operational requirements are exactly
met.
Note that p,, and p18 are necessary in order to
guarantee the required behaviour of the system.
Table 2. Process informationof the net model of Figs 6-8
Reactor is empty
Reactor is being filled with liquid phase
Reactor contains liquid phase
Reaction
Reactor contains product
Reactor is being discharged
Product is being separated by filter system (2.3)
Filter system (2, 3) contains liquid phase to be recycled
Discharge of liquid phase from fitter system (2.3)
Filter system (2,3) does not contain liquid phase
Discharge of the product from filter system (2,3)
Filter system (2.3) is empty
Filter system (4, 5) contains liquid phase to bc recycled
Filter system (4,5) does not contain liquid phase
Filter system (4.5) is empty
Product is being separated by filter system (4.5)
Filling of the reactor with liquid phase starts
Fillina of the reactor with liauid uhase ends
Rexcon starts
_ .
Reaction ends
Discharge of the reactor starts
DiSChUge of the reactor ends
Separation by filter system (2.3) ends
Discharge of liquid phase from filter system (2,3) starts
Discharge of liquid phase from filter system (2.3) ends
Discharge of product from filter system (2, 3) starts
Discharge of product from filter system (2, 3) ends
Separation by filter system (2,3) starts
Discharge of the reactor and separation by filter system (2.3)
start
Discharge of the reactor and separation by filter system (4.5)
start
Separation by filter system (4,5) ends
Transfer of liquid phase from filter system (2,3) into the
reactor
Reaction
Discharge of product from filter system (2. 3)
Transfer of liquid phase from filter system (4, 5) into the
reactor
Discharge of product from filter system (4. 5)

Coordination control modelling in batch production systems 7
I ‘6 I c7
I I
Fittersystem (4,s) 1 Reactor I Fittersystem f 2,31
Fig. 8. Complete C/E system model.
Otherwise, a batch could be discharged into a filter
system that has just finished separating a preceding
batch and is waiting for the recycling of the liquid
phase (ps or pII are marked). This would cause an
overflow of the storage tanks.
5.2. Predicate/transition nets (Pr/T nets)
Pr/T nets are developed from P/T nets by adding
the concept of individual tokens. The tokens in Pr/T
nets are no longer indistinguishable black dots,
but have their own individuality and are therefore
distinguishable.
Places are now calledpredicates and may carry one
or more individual tokens (again limited by a defined
capacity).
Arcs transfer one or more individual tokens (given
by the token weight). An inscription at the arc denotes
which types of tokens are transferred by the arc.
Transitions may be labelled with logical expressions.
The enabling and firing rules are similar to those of
P/T nets with the extension that the individual tokens
must be in agreement with the inscriptions at the arcs
and the logical expression at the transition must be
true.
2
Pr/T nets are defined in detail in Genrich and
Lautenbach (1981) and their use for modelling tech-
nological processes by adding process information is
described in Hanisch (1987a, b).
Application. Figure 11 (see also Table 4) gives a
very brief introduction to the use of Pr/T nets for the
modelling of batch processes. In Section 4, it has been
shown that the two subnets of the filter systems (2,3)
and (4, 5) have the same structure. The only differ-
ence is that these two subnets describe two different
filter systems. On the conceptual level of Pr/T nets,
these two subnets can be “folded” into one subnet as
shown in Fig. 11. The two filter systems are distin-
guished by the individual tokens “1” [for filter system
(2, 3)] and “2” [for filter system (4, 5)]. The arcs of
this subnet are labelled with the variable x, that may
assume the values “1” or “2”. This means that one
of the individual tokens “1” or “2” must flow across
the arc, but it does not denote which one of the
individual tokens it must be. That depends on the
marking of the prepredicates of a transition.
Note that the filter systems work independently
from each other. Therefore, the capacities of the
predicates p,, ps, p10 and p,2 must be 2 because it is
2
r is enobled t fires marking after firing of t
Fig. 9. Firing of a transition.

8 H.-M. -H
Filter system (4.5) 1 Reactor 1 Filter system (2,3j
Fig. 10. P/T net model.
possible for both filter systems to perform the same
operation at the same time. Thus, the corresponding
predicate must be able to carry two tokens.
Note also that there is no need for introducing an
individual token for the reactor because there is only
one reactor. Hence, the left subnet is similar to those
in Fig. 7. The process information given in Table 4
also includes the variable x. It depends on the actual
value of x as to which filter system this description
refers to. The marking of the net in Fig. 11 describes
the following state [m( pi) denotes the marking of
predicate p,]:
-the reactor contains product [m(pS)]
-filter system (2, 3) is empty [m(p,,), x = l]
-filter system (4, 5) contains the liquid phase to be
recycled [m(p,), x = 21
On the conceptual level of Pr/T nets, very complex
and flexible systems can be modelled. For instance,
the inclusion of a third filter system into the system
would not cause a change of the net topology, only
a third individual token would have to be added. This
additional flexibility makes this net class an ideal tool
for modelling flexible batch production systems (mul-
tipurpose batch plants) with dynamic allocation of
resources. This tool has been used extensively by
developing several models of multipurpose batch
production systems. One of these models is described
in Hanisch (1985, 1987a.b). Most of the other work
has not yet been published.
6. MODEL VALIDATION
Petri nets are a descriptive method for modelling
and design. Human errors are common and thus
models and designs must be validated before they are
implemented in a real-life process.
Commonly occurring errors can be divided into
two, not completely disjoint, classes:
1. Incorrect specification of the desired process
performance (technological errors).
2. Incorrect transformation of the technological
requirements into the formal Petri net model
(formal, logical errors).
It is one of the greatest advantages of Petri net theory
that it provides a variety of possibilities for proving
the correctness or detecting the incorrectness of a
given net. The most simple way to detect errors of the
first class is simulating the model by successive firing
Table 3. Process information of the net model of Fig. IO
m(P,o) Number of batches separated by filter system (2,3)
m(Pll) Number of batches to be separated by filter system (2.3) before the product is discharged
“(P&4) Number of batches separated by filter system (4, 5)
MP,J) Number of batches to be separated by filter system (4,s) before the product is discharged
PI7 Filter system (4, 5) does not contain liquid phase
PI8 Filter system (2, 3) does not contain liquid phase
P,.PI.Ps.P6.Pl.Ps.P13,P~6 are equal to the conditions c, of Table 2
f6>f7rG3, ‘15. 116are equal to the events c, of Table 2
a-a< are eoual to the activities (I. of Table 2
m(p,) denotes the number of tokens in pi

Coordinationcontrol modellingin batch productionsystems 9
25P3
. 02
Reach r Filter system (2,3 1 -a
Filter system 14,s 1 -0
Fig. 11. Pr/T net model.
enabled events or transitions and testing whether the
behaviour of the model corresponds to the desired
one or not.
A universal way to detect all errors of the second
class is to compute the reachability graph of the net.
The reachability graph contains all possible states
and all state transitions of the system [see Starke
(1990a)l.
Based on the reachability graph, all properties
known from Petri net theory such as:
-1iveness
-deadlocks
-conflicts
and many others can be tested. In terms of Petri net
theory, this is called net analysis. A comprehensive
description of formal properties and analysis tech-
niques is given in Starke (1990a).
The marked net models of the sample process
are live. Hence, no deadlocks can occur. The nets in
Figs 8, 10 and 11 are not free of conflicts.
A detailed description of the technological mean-
ing of such properties is given in Hanisch (1985,
Tabk 4. Process information of tlte net model of Fig. II
Pl Product is king separated by 6lter system x
PS Filter system x contains liquid phase to be cycled
p10 Filter system x doea not contain liquid phase
p12 Filter system x is empty
t, Separation by filter system x ends
tll Discharge of the reactor and separation by filter system x start
01 Transfer of liquid phase from filter system x into the reactor
03 Discharge of product from filter system x
p, ,p3.pJ. ps are equal to the conditions c<of Table 2
ts is equal to event es of Table 2
+ is equal to activity al of Table 2
1987a, b). The special role of conflicts for coordi-
nation control is shown in Hanisch (1990a,b; 1991a).
Only very simple models can be sketched and tested
by hand, for more complex ones computer-based
tools are required. At present the author uses the
program system PAN (PSI, 1989) for net analysis,
PETRINET (Hanisch, 1989) for simulation and per-
formance evaluation of C/E systems and P/T nets
and ATNA (Starke, 19QOb)for optimization of timed
net models. The program system PETRINET is
implemented on several 16-bit personal computers
and was used in three large chemical companies for
system modelling and simulation.
7. CONCLUSIONS
Some of the applications of Petri nets to batch
processes are shown in Table 5. At present Petri net
models are used in three different types of application
which are:
Design of a supervisory conrrolier-The technologi-
cal description ensures that all information necessary
to design a supervisory controller is given in the
model. This goal can only be achieved by teaming up
the chemical engineer responsible for the process
operation and the control engineer who designs the
supervisory controller based on Petri net theory.
The key to the design is the description of the
production process on the appropriate level using
Petri nets. Once a sufficiently complete description
has been established, the supervisory controller can
be designed and realized as shown in K&rig and
Quack ( 1988).
Place Product
Table 5. Survey of applications
Aim of modellina Net class Remarks
Bitterfeld Organic dye products, Description of the desired C/E systems Survey given in Han&h (1986)
catalysts and other mode of operation P/T nets
Pr/T nets
Leune Resin Analysis of bottbnaks and P/T nets, timed (Thiemicke and Hanisch, 1991)
disturbances
BUla
Berlin
Polyvinylchloride
Coal electrodes
Optimization of start P/T nets, rimed Continuous separation of the product,
scheduling of batch reactors not published
Description of the desired Pr/T nets, timed Not published
mode of operation, analysis
of disturbances
Saalfeld Chocolate Throughput optimization P/T nets, timed Continuous process, discretely controlled
(Schmidt, 1990)

10 H.-M. H
Performance evaluation-In order to apply Petri
nets for performance evaluation of the process, some
kinds of timed Petri nets must be used. Such concepts
are well known but they are beyond the scope of this
paper.
Timed Petri nets were applied to several batch
processes (see Table 5) to compute throughputs and
employment of limited resources. Some resultswill be
published in Thiemicke and Han&h (1991).
Process optimization-In the last 2yr, an analytic
method for determining optimal strategies for coordi-
nation control in batch processes based on timed
Petri nets was developed. The first simple approach
is published in Han&h (1990~). Improvements
and the mathematical formulation of the optimal
dynamic control problem are given in Hanisch
(199Ob,d,e). Based on these ideas, the analysis and
optimization tool ATNA (Starke, 1990b) was im-
plemented. A first experience of it is contained in
Hanisch (1991b).
Petri nets have shown to be an excellent tool
for improving the performance of batch processes.
The underlying mathematical theory of Petri nets
is well developed and provides powerful analytical
tools. This paper gives only an introduction with
the objective demonstrating the power of this
modelling and design method and the hope that more
and more chemical engineers will use this concept
to improve efficiency and also safety of batch
production systems.
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lemmer” Leuna-Merseburg (1989).
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ein diskontinuierliches &oduktionssystem. Drplomar-
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