an implementation of the matrix-based supervisory controller
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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 5, SEPTEMBER 2002 709
An Implementation of the Matrix-Based Supervisory Controllerof Flexible Manufacturing Systems
Stjepan Bogdan, Frank L. Lewis, Zdenko Kovacic, Ayla Grel, and Mario Stajdohar
AbstractThis paper deals with an implementation of a newmatrix-based supervisory controller of flexible manufacturingsystem (FMS). A design method is applied to the laboratory setupof a finite-buffer multiple reentrant flowline FMS which containsone 5-degree of freedom (DOF) robot, few transporters, pistons,and other elements (sensors, programmable logic controller, andpersonal computers). Control of the FMS is based on a matrixmodel approach which significantly reduces a computationaleffort and simplifies conversion of dispatching rules to the soft-ware program. The results obtained during experiments haveconfirmed effectiveness of the matrix-based FMS controller.
Index TermsDeadlock avoidance, discrete-event systems, flex-ible manufacturing systems (FMSs), supervisory controller.
I. INTRODUCTION
ANY MANUFACTURING process can be treated as agroup of jobs performed by someone or something inorder to get a product finished in a specific time. From the
control point of view, full automation requires controllability
and observability of all machine operations. Controllability is
provided by direct computer control of machine actuators at
the local level and by indirect computer control at the global
(shop or factory) level. Observability is ensured by processing
of data acquired from the suitably mounted sensors.
A swift change of production technology is an important
feature of flexible manufacturing systems (FMSs) which is
crucial in providing a quick output of medium series productswhich may undergo minor to major variations of shape, size,
and structure (material). Different scheduling rules can be
used to steer a manufacturing process depending whether it is
treated as a static or dynamic problem [1]. Failure to suitably
assign, or dispatch, resources can lead to system deadlock
[10]. When stability of finite-buffer automated manufacturing
systems is considered, then deadlock is found to be far more
critical issue than bounded-buffer stability [4].
Various concepts in Petri nets (PNs) [11] are extremely useful
for flexible manufacturing systems analysis and a great deal of
research has been done from the PN point of view [12][15],
[17], [18]. Though the PN framework offers rigorous ground
Manuscript received August 9, 2000; revised July 12, 2001. Manuscript re-ceived in final form January 7, 2002. Recommended by Associate Editor M.Lemmon.
S. Bogdan and Z. Kovacic are with the Faculty of Electrical Engineering andComputing, University of Zagreb, 10000 Zagreb, Croatia.
F. L. Lewis is with the Automation and Robotics Research Institute, Univer-sity of Texas at Arlington, Fort Worth, TX 76118-7115 USA.
A. Grel is with the Department of Electrical and Electronics Engineering,Eastern Mediterranean University, Famagusta, Turkey.
M. Stajdohar is with HEP, D.P. Elektra, 44000 Sisak, Croatia.Publisher Item Identifier 10.1109/TCST.2002.801876.
for theoretical analysis, it is very inconvenient for actual com-putational analysis of the practical FMS, introducing problems
of computational complexity (it is known that many problems
in scheduling, dispatching, and deadlock analysis are NP-hard
[16]). Matrix techniques that exploit the system structure can be
used to alleviate this.
In this paper, we are concerned with a practical implemen-
tation of a new matrix-based supervisory controller in order
to show its potential as a tool for very simple realization of
dispatching rules that are often used in the FMS. The phys-
ical model of an FMS has been built for testing of dispatching
algorithms. Namely, physical models are widely adopted as a
method for studying of FMS performance [3]. The FMS model
comprises few machines (transporters and pistons) and onearticulated robot arm. Various sensors are mounted in order to
get feedback data from the system. As the only shared resource
in the proposed FMS, the robot arm represents a potentialsource
of deadlock. In this sense, experiments have been organized to
illustrate those situations which may lead to system deadlock.
Prevention of deadlock may be accomplished by adequate FMS
control based on the usage offast logical matrix calculations in
a form of ladder diagram. In order to show efficiency of the pro-
posed controller two dispatching policies have been tested; last-
buffer-first-serve (LBFS) and improved first-buffer-first-serve
(FBFS) algorithm denoted as a stable FBFS policy [2].
This paper is organized as follows. In Section II, we give a
brief description of a matrix-based FMS controller according to
the concept described in [5] and [6]. Since the experiments ad-
dress the problem of deadlock free dispatching, a special em-
phasis has been put on determination of critical subsystems,
siphons, and traps [7], [8]. In Section III, we describe a structure
of an FMS laboratory setup. In Section IV, experimental results
obtained after applying dispatching algorithms prove theoretical
hypotheses and confirm effectiveness of the matrix-based FMS
controller. Final comments and discussion about future research
directives are given in Section V.
II. MATRIX MODEL OF AN FMS
The matrix model, which is described in more detail in [5]and [6], represents a set of logical rules that put in relation re-
sources, operations, control signals, and parts in an FMS. In
[8] it is shown that a matrix model is an efficient framework
for analysis of an FMS that offers a deep insight in the struc-
ture of the system and provides computational algorithms for
determination of control (i.e., dispatching) signals.
We make the following assumptions. 1) No preemption. A
resource cannot be removed from a job until it is complete; 2)
Mutual exclusion. A single resource can be used for only one job
at a time; 3) Hold while waiting. A process holds the resources
1063-6536/02$17.00 2002 IEEE
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Fig. 2. Experimental FMS setup.
III. FMS LABORATORY SETUP
In order to investigate performance of the matrix-based FMS
controller in a real environment a laboratory model of a flexible
manufacturing system has been built (Fig. 2). The laboratory
model contains a personal computer (PC),a programmable logic
controller (PLC), a robot driver, and machine shop that includes
a set of sensors, machines, and a 5-degree of freedom (DOF)
robot arm (Fig. 3).
The PC serves as an interface between the PLC and the robot
driver. It calculates joint velocities based on the difference be-
tween the next and the current robot arm position. In order to
reach the next position robot executes trajectories that are pre-
determined andsaved to file. Which trajectory will be performed
next depends on the code received from the PLC. Once received
by the PC the code is processed and information about motor
velocities is sent through the RS232 to the robot driver. Simul-
taneously the robot driver transfers data from motor encoders so
that the PC can calculate a current arm position.The PLC takes the highest control level in the FMS which
means that it bonds all parts of the system in one logical unit.
The main task of the PLC is to execute an FMS control al-
gorithm. The PLC picks sensors status and robot status (sig-
nals that form and ), sends onoff signals to the machines
(vectors and ) and makes decisions which trajectory robot
should terminate (components of dispatching vector ).
The PLC connection diagram is shown in Fig. 4. A very
simple 8-bit PLC is used in experiments. The matrix-based
FMS dispatching algorithm, in form of a ladder diagram, is
executed every 184 ms.
The machine shop includes one 5-DOF articulated robot
arm, three pneumatic double-acting cylinders which act astransporters, three pneumatic pistons for moving parts from
and to transporters, and one buffer. A modular nature of the
machine shop (all parts are movable and stand-alone) allows
the user to arrange different problems to be solved.
The structure of the machine shop used in experiments is
shown in Fig. 5 with a dotted line representing a part path.
As may be seen, the robot moves a part from an input place
to the transporter 1 ( ), which carries it to the piston 1 ( ).
The piston unloads the part from and moves it in front of
the second piston ( ). puts the part into the buffer ( ).
The robot lifts and carries it to transporter 2 ( ). The part ad-
vances through the line by moving along the transporter .
Fig. 3. Structure of the experimental FMS.
Once reaching the piston 3 ( ) the part is moved to the trans-
porter 3 ( ) which hauls it to the end of the line. Finally, the
part is removed from the line by the robot and dropped into the
output place.
A. Matrix Model of the Laboratory FMS
By using a system description (bill of materials, assembly
tree, heuristic design experience of the shop-floor engineer) one
can define the form of the matrices and vectors necessary for
generation of the matrix model which will consequentially lead
to set of rules.
As the first step of matrix model development we should
recognize and entitle all jobs (operations) in the FMS. In our
example one can resolve eight operations which are stated in
Table I. Even though from the mathematical point of view an
order of jobs is irrelevant when matrix model is carried out, a
causal ordering of operations has few merits. One is that in caseof causal ordering matrices and have a special, very con-
venient form that is important in proving the results on the FMS
structural properties [8].
Having this in mind and knowing the structure of the system,
we may write down a job vector and matrix :
(6)
Once having a job vector one should assign resources in the
FMS to the jobs, those providing a resource requirement matrix
. In the laboratory setup six resources are allocated in order
to perform operations defined with (6). Table II shows resource
assignment.
From Table II, it may be seen that robot RA has three tasks
and it is the only shared resource in the example. Also, one can
find that operation T3P is conducted by two physical resources
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Fig. 4. PLC connection diagram.
Fig. 5. Machine shop of the FMS laboratory setup.
that form one resource in the matrix model (T3A). Hence, the
forms of a resource vector and resource requirements matrix
are as follows:
(7)
One should notice that matrix has three 1s in the first
column. This column corresponds with robot (resource RA,
which is the first component of vector ) who has three jobs to
perform.
Causal ordering of jobs and resource assignment dictates the
shape of matrices and
(8)
To complete the matrix model we have to define matrices
and that describe part entering and leaving the line as well as
dispatching matrix . Since in our example we have one part
path, input vector and output vector become scalars (
PI and PO) which leads to vector-shaped and
(9)
As it is said earlier problem arises when conditions for two
or three jobs, performed by the robot, are met. In that case robot
is facing a conflict and introduction of a control vector is
necessary. Since matrix (7) has three 1s in the first column,
has to have three components,
and matrix has a form
(10)
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TABLE IOPERATIONS IN THE FMS EXAMPLE
TABLE IIRESOURCE ASSIGNMENT
The matrix model of the experimental FMS follows:
(11)
(12)
From vectors and matrices determined above, it is possible to
read FMS rules. For example, in order to start with operation
T2P rule has to be true (12), which means that operation
RP2 has to be done and resource T2A has to be idle (11). If we
associate a sensor (or group of sensors) with each operation, the
FMS controller can be written in a formof a PLC ladder diagramdirectly from the matrix model. The ladder diagram rung for the
rule has a form shown in Fig. 6.
It can be seen that completion of operation RP2 is assigned to
sensor S6, which is connected with input I0.5 (input word 0, bit
5). If the rule is satisfied, actuator connected with output O0.1
(output word 0, bit 1) starts operation T2P.
The matrix model could be easily understood by comparing
with a Petri net graph (Fig. 7) of the FMS laboratory setup.
It is clear that components of the logical state vector (rules)
correspond with Petri net transitions.
The matrix model can be used to simulate the system [6] or
to solve logical equations online, i.e., to control a system by
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Fig. 8. BP operation status during the LBFS dispatching: 1the buffer is full,0the buffer is empty.
Fig. 9. T1P operation status during the LBFS dispatching:1work-in-progress, 0idle.
Fig. 10. BP operation statusduring thestable FBFS dispatching: 1the bufferis full, 0the buffer is empty.
Fig. 11. T1P operation status during the stable FBFS dispatching:1work-in-progress, 0idle.
multiple reentrant flowline FMS was built. The matrix-based
FMS model was derived and thereafter used for the synthesis
of the matrix-based FMS controller. Deadlock prevention was
applied as a criterion for the controller design. The controller
was validated through implementation of two dispatching
policies, one was a well-known LBFS policy while the other
was a MAXWIP policy called also a stable FBFS. The matrix
techniques allowed effective and simple on-line control by
applying a set of discrete-event control signals.
Future work will be concerned with influence of operational
times on the stability and throughput of the manufacturing
system. Another issue will be an investigation of different FMS
topologies with shared resources and bottleneck machinesvarying in place.
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