petri nets 07

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II Sem M.Tech F M S05 MCM 22

Chapter 5: Modeling and Analysis of FMSPetri Nets

Petri net is a graphical and mathematical tool, which provides a uniform environment for modeling, formal analysis and design of discrete event systems particularly in flexible and agilemanufacturing systems. Petri nets were named after Carl A. Petri who created it in 1962. It is a netlike mathematical tool for the study of communication with automata. It can also be used to model

properties such as process synchronization, asynchronous events, sequential operations, concurrentoperations and conflicts and resource sharing.

As a graphical tool it provides a powerful communication medium between the user and thecustomer. As a mathematical tool it can be described by a set of linear algebraic equations or other mathematical models reflecting the behavior of the system. In the manufacturing area Petri nets areused to represent production lines with buffers, automated assembly systems, machine shops, FMS,JIT, and KANBAN systems. Petri nets also have applications in a number of different disciplinesincluding engineering, manufacturing, business, chemistry, mathematics, and even within the

judicial systemA Petri net may be identified as a particular kind of bipartite directed graphs populated by

three types of objects. These objects are places, transitions and directed arcs connecting these placesto transitions and transitions to places.

These nets have two types of components: places and transitions (places = factors, transitions = processes). Places are depicted as circles and transitions are by bars or boxes. A place may be aninput position or output position to a transition depending on direction of the arc

Example of a Petri net

The dynamics of a Petri net is a sequence of transition "firing". When a transition is fired then twothings happen. First, tokens are taken away from places which have arrows going from these placesto the transition considered. If more than one arrow goes from place to transition, then the number of tokens removed from that place is equal to the number of arrows. Second, new tokens are placedon places indicated by arrows that originate from the transition. The number of tokens placedcorresponds again to the number of arrows (in the case of multiple arrows). Input places mayrepresent the availability of resources, transition their utilization and output places the release of resources. For example, in the figure above, when transition t 1 is fired, then one token is removedfrom place p 1, one token is removed from place p 2, place p 1 and place p 2 are now input places for DEVADATTA. V R Asst. Professor P E SC E Mandya 1


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transition t 1 and one token is added on place p 3. Now place p 3 is output place for transition t 1. Whentransition t 2 is fired, then one token is removed from place p 3, and one token is added on place p 2.Transition t 1 can be interpreted as feeding and growth, and transition t 2 as reproduction.

In this example, a token in p1 and p2 means a component and a robot available, respectively. Thenumber of tokens in the place indicates the number of available resources.

A specific process in an automated manufacturing consists of a variety of components

ranging from robots, machines, raw materials, sensors, computers and accessories. At the modeling

DEVADATTA. V R Asst. Professor P E SC E Mandya 2

P1Componentsavailable

t1Picking up

P3Robot handling acomponent

t2Placing

P2Robot ready


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stage it is necessary to focus on the major operations and their relationship in the process. The basicrelationships among the operations are sequential, concurrent, conflicting, cyclic and mutuallyexclusive. Sequential: - One operation follows the other, the Petri nets are as shown in the figure

Concurrent: - If two operations are initiated by an event, they form parallel structure starting witha transition, i.e. two positions are out puts of the same transition.

Conflicting: - If two operations can follow a single source, then two transitions will be two outputsfrom a single place.

Cyclic: - If a sequence of operations can follow one after the other and completion of the last oneinitiate the first one, then the cyclic structure is formed among these operations.

Mutually exclusive: - Two processes are mutually exclusive if they cannot be performed at thesame time due to constraints on the usage of shared resources. A structure to realize this is through a



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common place marked with one token plus multiple output and input arcs to activate these processes. For example, a robot may be shared by two machines for loading and unloading

Method of modeling: -1. Identification of operations and resources.2. Identification of relations between operations and resources..3. Petri net design.4. Petri net modification.

Example:- An automatic production line consists of two machines M1, M2, two robots R1, R2 andtwo conveyors. Each machine is served by a dedicated robot which perform load and unload tasks,robot takes 1 time unit for each task. One conveyor is used to transport empty pallets and the other is to transport work pieces, a maximum of two at a time. There are only three pallets available in thesystem. Each workpiece is machined first in M1 and later in M2, the machining time in M1 is 10time units and in M2 is 16 time units. The conveyors transportation time is negligible. Design aPetri net for this production line.

1. Identification of operations and resources:-

Major operations Resources

R1 loadingM1 processingR1 unloadingR2 loadingM2 processingR2 unloading

Raw material with palletsConveyorsM1, M2R1, R2

2. Identification of relations between operations and resources:-The relations among the above mentioned operations form a strict sequential sequence for

products. All the resources are dedicated. The dedicated resource features with single input andsingle output arcs.

3. Petri net design



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There are four transitions:R1 Loading R1 UnloadingR2 Loading R2 Unloading

Three places:Two places for M1, M2 operations, one place for intermediate parts ready in conveyor for M2.

Because of sequential relationship between the operations places and transitions are connected bydirected arc as shown in figure.

4. Petri net modificationDesignate places for availability of raw material and availability of R1 and R2. Also availability

of M1 and M2, availability of conveyor in a proper sequence - totally six places. Add these six places suitably to the above diagram and allocate place numbers. Finally indicate delays of placesand transitions


M1- Process parts ready M2 - process

R1 Load R1 Unload R2 Load R2 Unload

Slots in theConveyor Available

P2

M1- Process Parts ready M2 - processR1 Load

R1 UnloadR2 Load R2 Unload

P3 P4

P1

P6P5

P8

P7

P9

t 4t3t2t1Raw material &Pallets available

R1Available R2

Available

M1Available

M1Available

M2Available


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The complete Petri net is shown in the above figure and the timing information is shown below

Places Interpretation Time DelayP1 Work pieces and Raw material available 0P2 M1 processing a workpiece 10P3 Work piece is available for processing at M2 0P4 M2 processing a workpiece 16P5 M1 available 0P6 Conveyor slots available 0P7 M2 available 0P8 R1 available 0P9 R2 available 0

Transitionst1 R1 loads the workpiece to M1 1t2 R1 unloads the workpiece from M1 to conveyor 1t3 R2 loads a workpiece to M2 1t4 R2 unloads the finished workpiece from M2 1

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