460
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
Multiagent Supervisory Control for
Antifault Propagation in Serial
Production Systems
Kwang-Hyun Cho, Associate Member, IEEE, and Jong-Tae Lim, Member, IEEE
Abstract—In this paper, a multiagent supervisory control
methodology is proposed for antifault propagation in serial
production systems by incorporating the idea of multiagent
control within the fault-tolerant supervisory control scheme.
Especially, the concept of antifault propagation between cascaded
processes is established and the synthesis of agent supervisors is
investigated based on this concept. A case study of a polypropylene
polymerization process in the petrochemical industry is provided
to illustrate the proposed control policy.
Index Terms—Antifault propagation, discrete-event dynamic
systems, multiagent control, polypropylene polymerization
process, supervisory control.
aug-event
recognizer
for
NOMENCLATURE
[
]
[
]
Plant model (or generator) of an automaton
where
is the set of
states , is the set of events ,
is the transition function,
is the initial state, and
is the set
of marker states.
Closed behavior of
or language of the
and
is deplant
fined .
Marker behavior of
and
.
Behavior of the supervised plant
.
.
Starting state of the event
[string ]
leading to (domain of [ ] leading to ).
Ending state of the event [string ] from
(range of [ ] from )—
[
] is
[
]
to be used instead of
is the initial state of the auwhere
tomaton.
for each
with
where is the state set and
is the prefix closure of —
is to be
.
used instead of
Manuscript received January 18, 2000; revised October 30, 2000. Abstract
published on the Internet December 18, 2000. This work was supported by the
Korea Research Foundation uder Grant KRF-99-003-E00420.
K.-H. Cho is with the Division of Electronic Engineering, School of Electrical Engineering and Automation, University of Ulsan, Ulsan 680-749, Korea
(e-mail: ckh@uou.ulsan.ac.kr).
J.-T. Lim is with the Department of Electrical Engineering, Korea Advanced
Institute of Science and Technology, Taejon 305-701, Korea.
Publisher Item Identifier S 0278-0046(01)02645-4.
controllable
language
controllable
sublanguage
of
Range of the language (
for each
where is a kind
of string , especially an element of the
language )—in this case, always
.
Event augmented with its originating state
with
].
[
Set of events which constitute the string .
Number of events comprising the string
(length of the string ).
Generator such that
.
or
Recognizer automaton for
.
such that
where
is the set of uncontrollable
events of .
and
is
controllable .
I. INTRODUCTION
D
ISCRETE-EVENT dynamic systems (DEDSs) have attracted much attention in the area of systems modeling
and control-law synthesis [1]–[3]. Within this framework, the
diagnostic issues over various fields have been studied up to the
present: the fault detection and isolation problems are dealt with
in [4]–[6] and the failure analysis with the corresponding system
controller design is addressed in [7], [8]. In particular, in [8],
the abnormal status in the behavior of the DEDS was quantitatively analyzed upon a discrete-event model (DEM) [9] and
the synthesis of fault-tolerant supervisor was introduced based
on the failure analysis. However, the approach in [8] becomes
intractable for large complex systems such as serial production
systems which are common in most of the production industries, due to the state explosion in the DEMs. Moreover, the synthesis of decentralized supervisor [10]–[13] (which is the most
promising way to reduce the complexity) still needs many complicated steps in the design stage to guarantee the same optimal
behavior as the centralized supervisor and cannot deal with the
problem of fault propagation between unit processes (i.e., local
plants). To resolve these problems, it is required to consider
a new concept of fault-tolerant supervisory control which independently supervises each unit process and shares the least
0278–0046/01$10.00 © 2001 IEEE
CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION
amount of information just needed to prevent the fault-propagation between unit processes. Therefore, in this paper, we propose a multiagent supervisory control methodology for antifault
propagation in serial production systems by incorporating the
concept of multiagent control [14]–[16] with the fault-tolerant
supervisory control scheme. This is an integrated action of cooperative agent supervisors endowed with high autonomy and
the least common information for the fault-propagation control.
The present state-of-the-art of related works involves: 1) artificial intelligence techniques; 2) a model-based approach; and
3) DEDS methods based on state machines, Petri nets, etc. The
fault diagnosis using artificial intelligence techniques [18]–[20]
is computationally expensive and impractical for large systems.
The model-based approach to fault diagnosis [21]–[23] is extremely slow due to the expensive use of functional simulation
thus is not appropriate for fault diagnosis in large-scale systems.
The recent DEDS method for fault diagnosis and the system
design based on state machines in [6] and [7] cannot still be
applied for large-scale systems because of the use of simulation and the computational complexity of constructing the diagnosers. The Petri-net-based method [24]–[26] shows substantial
reduction of complexity in the model description; however, the
simulation-based analysis and design of it are still complex and
hard to be generalized. On the other hand, the approach to be
developed in this paper deals with the state explosion problem
by making use of the structural properties of serial production
systems, i.e., it divides the overall processes into the unit processes with the corresponding information function and then applies the fault diagnosis and the antifault-propagation supervisory control policy to the unit processes via the agent supervisors. The emphasis is to be on the antifault-propagation supervisory control between unit processes which has never been
considered in the decentralized supervisory control and other literature, and on the formulation of the overall analytical framework based on multiagent system concepts. Throughout the remainder of this paper, it is assumed that each agent supervisor
can record all the state transitions and events generated by each
unit process modeled by a deterministic automaton.
The paper is organized as follows. In Section II, we present
the definition of multiagent supervisory control, the property of
antifault propagation, and the framework of multiagent supervisory control for antifault propagation. In Section III, the synthesis of agent supervisors for multiagent supervisory control
for antifault propagation is described. In Section IV, the case
study of a polypropylene polymerization process in the petrochemical industry is provided. Finally, the conclusions are formulated in Section V.
II. MULTIAGENT SUPERVISORY CONTROL
ANTIFAULT PROPAGATION
FOR
In [14]–[16], multiagent systems are understood as
distributed computational systems in which several semi-autonomous agents interact or work together to perform some
set of tasks or satisfy some set of goals. The agent is an entity
with goals, actions, and domain knowledge, situated in an
environment. It can maintain autonomy while still contributing
to overall system effectiveness. Motivated from these ideas, we
Fig. 1.
461
Multiagent supervisory control of serial production systems.
introduce a concept of multiagent supervisory control in this
section.
Consider the serial production systems composed of unit
in tandem. The supervisor
of each
process ,
is to be called an agent supervisor and the correunit process
sponding integrated action of control is to be called multiagent
supervisory control. In other words, multiagent supervisory
control is a cooperative integration of agent supervisors with
high autonomy and the least common information for the
overall control objectives. The configuration of multiagent
supervisory control for serial production systems is illustrated
controls
through
in Fig. 1, where an agent supervisor
and transfers the coded information
the feedback map
of an actually occurred sequence
after supervision
, and then gets the feedback information
from
to
. Based on
,
determines whether it keeps
controlling or stops the current process and starts diagnosis.
where
represents the normal
Note that
the fault mode, implying some possible abnormal
mode and
can be designed based on the legal
status in the operation.
such that
[1] as usual if
language
is achievable, i.e., controllable and observable. Since
is
becomes achievable if we choose
assumed to be observable,
[2]. However, in the closed-loop operation,
where
shows the abnormal operation due to some failures. In [8],
the abnormal status in the behavior of the DEDS was quantitatively analyzed upon a DEM such as a “fault” representing a
rather tolerable malfunction and a “failure” denoting a complete
breakdown of the overall system operation. Furthermore, when
some abnormal events occur during operation, if we can still
find another event sequence which can reach the marker state
or if we can eliminate the path to the abnormal events, then the
work procedure was called “fault tolerable” and the synthesis of
fault-tolerant supervisor was introduced based on the tolerable
fault event sequences. The previous concepts were basically
formulated for a unit process. However, these can be extended
to supervision of multiprocesses such as multiagent supervisory
control. In this case, the failures for one process can be further
classified into failures that propagate to the subsequent process
and can be compensated by the corresponding supervisor,
and failures that propagate but cannot be compensated by any
measure or do not propagate and leads to breakdown of the
current process. In view of multiagent supervisory control, the
former ones can also be treated as “faults” on the extended
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
concepts of tolerable fault event sequences. If we call the
fault-tolerance concept within the unit process internal fault
tolerance, we can consider the fault-tolerance concept between
the subsequent unit processes as antifault propagation.
Definition 1: The multiagent supervisory control system
and
is antifault propagative between
and
over
if any fault propagation from
into
can be
.
eliminated by the subsequent agent supervisor
This concept of antifault propagation means the capability
of compensating any propagated faults by certain complementary measures. Furthermore, the multiagent supervisory control
is called an antifault-propagative
system over ,
.
system if it is antifault propagative for all
Definition 2: Multiagent supervisory control for antifault
propagation is a kind of multiagent supervisory control resulting in the antifault-propagative system over the closed-loop
operation.
Assume that the total set of events of , can be partitioned
as
where
is the set of controllable events of ,
is the set
is the set of normal events
of uncontrollable events of ,
is the set of abnormal events of ,
is the
of ,
, and
is the set of unset of compensable events of
. Let
be a fault-tolerant
compensable events of
where denotes the composupervisor of
.
sition of two DEMs [9], and
implies that there exists a comIn the foregoing,
such that
plementary measure
for some
and
where
is the set of complementary measures in
,
,
,
, and
. Hence, we can
achieve the overall control objective without interrupting the
via the corresponding agent supervisor
current process
in this case. Based on this concept, we consider
action on
the following domain of antifault propagation.
,
Definition 3: The domain of antifault propagation of
is the set of states of
, from which any postlanguages
could be supplemented to meet the antifault propagation beand
by the subsequent agent supervisor
.
tween
Physically, the domain of antifault propagation corresponds
to the endurable status at the end of the job, capable of
continuing the current process in spite of the occurrence
of some faults. Along with the previous definitions about
, we know
where
.
be the actually occurred sequence over
Let
then we can examine the existence of
satisfying the antifault propagation between
and
in
the following.
such
Theorem 1: There exists an achievable
if and only if
that
.
Proof:
Sufficient Condition: If
then it becomes trivially true. If
then
from
and
following Definition 3. Assume
occurs, then choose
where
and
, resulting in
(where
)
(for some
)
.
due to the structural
Hence
and
property following the definitions of
.
Necessary Condition: Assume
then
and
resulting in
such that
. Therefore, if
such
then
that
.
Theorem 1 implies that whenever the range of the actually oclies within the domain of antifault
curred sequence of
, we can make
and
propagation of
antifault propagative since
is reconfigurable based on the
. The synthesis of
recognizer automaton of the achievable
the corresponding agent supervisors and the implementation of
the supervised system are to be developed in the following section.
Note that if the existence condition of Theorem 1 is not sat, then we cannot achieve the anisfied for certain
. Physically, this situation cortifault propagation by any
responds to the cases when some uncompensable event occurs
or the complementary measure of
is not included in
in
due to the operational restriction of the process. In
addition, the proposed approach is not applicable if we cannot
identify the occurrence of abnormal events for the uncertainty
embedded in the system.
Remark 1: Here we considered only the case of two-tier fault
propagation (i.e., a fault propagation between the subsequent
two processes among those s connected in series). However,
the proposed approach is also applicable to the cases of any kind
of multi-tier fault propagation by considering the fault propagated from just the prior tier composed of unit processes hitherto undergone and by using the proposed approach in the same
way, consecutively.
and
III. SYNTHESIS OF AGENT SUPERVISORS
ANTIFAULT PROPAGATION
FOR
A. Synthesis Procedures
In this section, we consider the synthesis of agent supervisors
in multiagent supervisory control for antifault propagation when
the condition of Theorem 1 is satisfied such that an achievable
exists. Let, for each
,
and
be defined such that
CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION
for the corresponding
where
means
such as 2s complement in
the mathematical complement of
case of a binary number. These could be listed in the complementary measures table (CMT) at the outset. Let
be defined for each
and
be a function composed of a sequence of , for
. Furthermore, let
a certain coded information of
be a function representing the orderly information of
for the successive events comprising
. Based
such that
on these, we choose a function
where
1) if
, for
with
for some
,
with
, and
, implies
then
where
with
;
.
2) otherwise,
Here, we employ the coding scheme to ensure the least common
information between agent supervisors for the autonomy and
of
encapsulation. In particular, the orderly information
is utilized to transfer the information about the occurrence
and is further used for constructing
of abnormal events via
through
based on
and
.
is also capable of providing the
On the other hand,
to
such that it can determine
feedback information
or stops and starts diagnosis.
whether it keeps controlling
is defined as
The feedback information
if
otherwise.
is interpreted as “keep controlling” and 0 “stop and
. This transfers the information regarding the
diagnose” by
condition of Theorem 1.
is achievable, we can synthesize
as
Since
(1)
where
and
ognizer automaton for
is the feedback map defined as
if
otherwise
is a rec-
and
, and
.
in which
then the agent
Theorem 2: If
for
in (1) meets the antifault propagation
supervisor
and
.
between
occurred after
Proof: Assume
such that
[i.e.,
] anymore due to
where
. Then
should be
from
and
such that
. These are mapped into
through
and the corresponding agent supervisor
463
in (1) over
(where
subsequent to
generate
and
)
for some
and
from Theorem 1. Therefore, any fault
in this way, which
propagated from can be eliminated by
.
results in the antifault propagation between and
Based on the transferred coded information
, Theorem 2
in (1) makes
and
anshows that
exists under Thetifault propagative if the corresponding
orem 1.
Remark 2: As it follows from Theorems 1 and 2, in order to
achieve the antifault propagation in the multiagent supervisory
control of serial production systems, the minimal information
we need within the proposed framework is the coded information of the compensable events and the corresponding complementary measures in the CMT.
B. Comments on Implementation
For the implementation of the foregoing supervisory control
policy, we can make use of either the command response model
introduced in [27] or the extended process model proposed in
[28].
According to the semantics of [27], we can implement the
supervised control system via the three-layered structure: the
supervisor/controller, the implementation interface composed of
command/response interpreter and equipment drivers, and the
plant. The supervisor/controller module schedules and generates
commands in the form of allowed languages for the plant based
on the reported responses. Then, the command/response interpreter converts commands from the supervisor in lower level
commands for the equipment drivers such as discrete actions,
continuous actions, or changes in software execution according
to the attributes of the plant. On the other side, it supplies the
supervisor with logical responses that reflect the information
provided by the sensor measurements such as discrete-state
changes or continuous-state changes, and the software execution
messages. The plant is operated by the actuators activated by the
equipment drivers and also produces the responses via sensor
measurements or program execution messages.
In the framework of [28], the process coupled with the
controller is regarded as the extended process which generates
events spontaneously. Then the inputs of the supervisor are the
outputs of the extended process and the supervisor confines the
behavior of the extended process by prohibiting some of the
generated events.
IV. A CASE STUDY OF A POLYPROPYLENE
POLYMERIZATION PROCESS
In this section, we consider the utilization of multiagent supervisory control for antifault propagation through a case study
of a polypropylene polymerization process based on a pilot plant
in the petrochemical industry. The polypropylene polymerization process is a kind of petrochemical process producing the
polypropylene [17] from the propylene by polymerization and
composed of several unit processes such as a prepolymerization process, a polymerization process, and posterior processes
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
Fig. 2. Overall schematic diagram of a polypropylene polymerization process.
TABLE I
NOMINAL REACTION CONDITIONS AT LR1 AND LR2
connected in serial as illustrated in Fig. 2. The propylene and
MUD/TEAL/Donor mixture are fed into the prepolymerization
reactor and then transferred to the polymerization reactors together with the hydrogen, propylene, ethylene, and Butene-1.
Polymers are formed in the polymerization process under specific reaction conditions and the polypropylene is finally produced after several posterior processes. In the following, we
consider the polymerization process which comprises two loop
reactors (LRs) connected in tandem to elevate the productivity
over unit volume and to reduce the residence time in the reactors. The specific nominal reaction conditions at each LR are
described in Table I, in the case of terpolymer polymerization.
The material feed rates are controlled by flow controllers (FCs).
Suppose that the FC of LR1 is subject to abnormal events which
be the aucause deviation from the nominal set values. Let
1 or 2) in view of flow
tomaton of the process in LRi (
and
.
control. Fig. 3 illustrates the component DEMs of
(“set to nominal value”),
(“reset to initial
In Fig. 3,
(“adjust to higher value”),
(“reset to nominal
value”),
(“adjust to lower value”),
(“reset to nominal
value”),
value”) are the normal controllable events of , where represents one of (“Hydrogen”), (“Propylene”), (“Ethylene”),
Fig. 3. Component DEMs of
(ethylene); (Butene-1)].
b
and
G
and
G [m: h (hydrogen); p (propylene); e
(“Butene-1”).
is also subject to abnormal events of
(“stuck to higher value”) and
(“stuck to lower value”).
are composed of
(Initial Value of
The states of
in
),
(Nominal Value of
in
),
(Higher
in
),
(Stuck to Higher Value of
in
Value of
),
(Lower Value of
in
), and
(Stuck to
has similarly the normal controlLower Value of in ).
and its states comprise
lable events of
. Therefore, we know that
CHO AND LIM: MULTIAGENT SUPERVISORY CONTROL FOR ANTIFAULT PROPAGATION
TABLE II
CMT FOR 6
AND 6
465
TABLE III
STATES DEFINITION FOR PARTS OF DEMS OF
G
AND
G
and
For the action enforcement in the implementation, the interface is needed to interpret the commands corresponding to the
events and to act on the physical system as mentioned in Section III-B. The commands given to the interface carry implicitly
continuous attributes in this case and initiate a continuous control action of the FC. For example, the command corresponding
causes the FC of LR1 to control the propylene feed rate
to
to LR1 at the higher value than the nominal feed rate until the
next control action. Hence, in this case, the equipment driver is
responsible for the real-time dynamic control of the continuous
subsystem, e.g., FC.
Note that the deviation from the nominal values in LR1 can
be compensated by adjusting the corresponding material feed
rate in LR2 accordingly for propylene, ethylene, and Butene-1
in view of overall polymerization process conditions. However,
if hydrogen is stuck to a higher value, then the transfer line
becomes plugged before the reaction mixture transfers to LR2
since hydrogen controls the intrinsic viscosity of polymers in
the mixture, which cannot be adjusted in LR2. Hence, we know
From these and Definition 3, the domain of fault tolerance of
becomes
for all
where
represents the state of the component DEM of
with
. Let the complebe defined for
and
mentary measure function
as appeared in the CMT of Table II where the binary
. Under normal
number is used such that
,
is chosen to be
to
operating conditions of
satisfy the nominal reaction conditions. However, suppose
and
occur such that
due to
. In this case,
and
are faults and
on which
can be reconfigured to
there exists
and
since
meet the antifault propagation between
from Theorem 1. Therefore, the
returns 1 to expefeedback information
dite the current process without interruption. In view of
, it can be synthesized as follows. Let
reconfiguration of
be defined as
for
and
with the binary number
where
, and
such that
in case of no duplication between the occurwith
rence of events. Moreover, let
where
for
, and
be defined as
in
carries the orderly
the binary representation. In this case,
via the ascending binary value relationinformation of
, let, e.g.,
,
ship. From
,
,
,
,
,
,
,
,
,
,
,
,
,
,
where
and
are
described in Table III. Then,
and we know
with
and
with
. The occurrence of abnormal events is identified by the transferred coded
in this way. Furthermore, we can formulate
information
such that
as
since
and
from the CMT.
Therefore, it becomes
which assures the antifault propagation between
and
in
accordance with Theorem 2.
occurs such that
On the other hand, if
due to
then
becomes a failure since
as presumed
returns 0 which
by Theorem 1. Therefore,
to stop the current process and do failure diagrequires
physically causes the
nosis. This is because the failure event
transfer line plugged, which cannot be complemented by any
.
measure of
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
V. CONCLUSIONS
We have studied the multiagent supervisory control methodology for antifault propagation in serial production systems. The
major characteristic of the proposed scheme lies in the fact that it
allows as much autonomy as possible for each agent supervisor
and the least shared information between agent supervisors cooperating for overall goals in view of antifault propagation. The
main contribution of this paper can be summarized as follows.
1) The idea of multiagent control is introduced for supervisory control of serial production systems in view of
fault-propagation prevention.
2) The concept of antifault propagation between cascaded
processes is established.
3) The synthesis of each agent supervisor satisfying the antifault propagation, the coded information for the actually
occurred sequence of the closed-loop operation in the prior
process, and the feedback information from the posterior
process are proposed and developed in a concrete form.
4) The analytical framework of multiagent supervisory control systems for antifault propagation is established.
5) The case study of a polypropylene polymerization
process in the petrochemical industry is provided to
illustrate the proposed control policy.
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Kwang-Hyun Cho (S’94–A’00) received the B.S.,
M.S., and Ph.D. degrees in electrical engineering
from Korea Advanced Institute of Science and
Technology (KAIST), Taejon, Korea, in 1993, 1995,
and 1998, respectively.
From September 1998 to February 1999, he was a
Research Associate in the Department of Electrical
Engineering, KAIST. In 1999, he joined the School
of Electrical Engineering and Automation, University of Ulsan, Ulsan, Korea, where he is currently
an Assistant Professor. His research interests include
analysis and supervisory control of discrete-event dynamic systems, nonlinear
systems, hybrid systems, and application of system and control theory to communication networks and bioelectronics.
Prof. Cho is a member of the Institute of Electronics Engineers of Korea and
Institute of Control, Automation and Systems Engineers.
Jong-Tae Lim (M’88) received the B.S.E.E. degree
from Yonsei University, Seoul, Korea, the M.S.E.E.
degree from Illinois Institute of Technology,
Chicago, and the Ph.D. degree in computer, information, and control engineering from the University
of Michigan, Ann Arbor, in 1975, 1983, and 1986,
respectively.
From 1975 to 1981, he was an Engineer with
Korea Electric Company. From 1987 to 1988, he was
a Research Fellow in the Department of Electrical
Engineering and Computer Science, University of
Michigan. In 1988, he joined the Department of Electrical Engineering, Korea
Advanced Institute of Science and Technology, Taejon, Korea, as an Assistant
Professor. He is currently a Professor. His research interests are in the areas
of system and control theory, communications networks, and manufacturing
systems.
Prof. Lim is a member of the Institute of Control, Automation and Systems
Engineers, Korean Institute of Electrical Engineers, and Institute of Electronics
Engineers of Korea.