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

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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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712 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 5, SEPTEMBER 2002

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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716 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 5, SEPTEMBER 2002

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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An Implementation of the Matrix-Based Supervisory Controller

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