Petri Net Part 11 doc

Scheduling Analysis in FMS Using the Unfolding Time Petri nets, Mathematics and Computer in Simulation, Vol.70, pp.. Slice Analysis Method of Petri nets in FMS Using the Transitive Matri

M1 p4

p3

p1 p5

p5

M1 p4

p3

p1 p5

In this net, we can find the 6 processes of M1 are as follows (Fig 9):

Suf1 = t1 t5t3 (15), Suf2 = t5t1t3 (15), Suf3 = t1t3t5 (12),

Suf4 = t3t1t5 (12), Suf5 = t3t5t1 (15), Suf6 = t5t3t1 (15),

where () is an operation time of Sufi

temps

Suf5

Suf6

20 10

temps

Suf5

Suf6

20 10

Fig 9 Results of the permutations of BUC in M1

In M1, we can choose two schedules as transitions sequences: t3-t1-t5 and t1-t3-t5

2 Modeling of M2 and its unfolding nets

Machine M2 involved two tasks (OP1 and OP2) in three processes (t2, t4 and t6) (Fig 10,11)

M2’ p5

p1

M2’ p5

p3

p1

p3

Fig 11 Example of unfolding of M2

We can show the six processes like as follows (Fig 12) :

Suf1 = t2t4t6 (13), Suf2 = t2t6t4 (14), Suf3 = t4t6t2 (11), Suf4 = t4t2t6 (13), Suf5 = t6t4t2 (11), Suf6 = t6t2t4 (13)

temps

Suf5

Suf6

20 10

temps

Suf5

Suf6

20 10

Fig 12 Results of permutations of BUC in M2

In M2, we can find two solutions like as Suf3 and Suf5 Now, we apply the selected solutions

of BUC of M2: {Suf3 and Suf5} to obtain the solution BUC on M1: {Suf3 and Suf4}, then we obtained two solutions The optimal schedules of two cycles are in Fig 13 and 14

Bs1: A3A1B2 (M1) B3B1A2 (M2) Bs2: A1A3B2 (M1) B3B1A2 (M2)

timemachines

Fig 15 Linear schedule of Bs1

Finally, we get three pallets rather than two, which is lower bound WIP Indeed in this model, it is impossible to optimize CT with two pallets, as proved in (Camus,1997) So, we can say that this solution is best possible one(Fig 15,16)

6 Benchmark

6.1 Notations

In this section, one example taken from the literature is analyzed in order to apply three cyclic scheduling analysis methods such as Hillion (Hillion, 1987), Korbaa (Korbaa, 1997), and the previously presented approach The definitions and the assumptions for this work have been summarized (Korbaa,1997)

The formulations for our works, we can summarize as follows:

¦

J



J P

tt

) (

,the sum of all transition timings of J

M(J) (=Mo(J)), the (constant) number of tokens in J,

C(J) = P(J)/M(J), the cycle time of J,

Where J is a circuit

C* =Max(C(J)) for all circuits of the net,

CT the minimal cycle time associated to the maximal throughput of the system:

CT =Max(C(J)) for all resource circuits = C*

Let CT be the optimal cycle time based on the machines work, then WIP is (Korbaa,1997):

i

pe i pallets ty

i carried by

OS to be

time Operating

is 6 So the cycle time CT is 10 The minimization WIP is:

CT

OSofTimesperatingO

777

Also, the solutions of the proposed approach are quite similar to (a) and (c) in Fig 20 without the different position

2 Effect

It’s very difficult problem to solve a complexity value in the scheduling algorithm for evaluation In this works, an effect values was to be considered as the total sum of the numbers of permutation and of calculation in the scheduling algorithm to obtain a good solution An effected value of the proposed method is 744, i.e including all permutation available in each BUC, and selecting optimal solution for approach to next BUC An effect value to obtain a good solution is 95 in the Korbaa’s method; 9 times for partitions, 34 times

for regrouping, and 52 times for calculation cycle time In the Hillion’s method, an effected value is 260; 20 times for machine’s operation schedule and 240 times for the job’s operation schedule

Fig 21 Total relation graph

3 Time

Based on the three algorithms, we can get time results for obtaining the good solution Since this example model is simple, they need very small calculation times; 1 sec for the Korbaa’s approach and 1.30sec for both of the Hillion’s and the proposed approaches The Korbaa’s approach has minimum 1 minute and maximum 23 hours in the 9 machines and 7 operations case in Camus (Camus, 1997), while the proposed approach 3 minutes Meanwhile the Hillion’s and the Korbaa’s approaches belong to the number of the operation and the machines, the proposed method to the number of resource shares machines This means that the Hillion’s and the Korbaa’s approaches analyzing times are longer than the proposed one in the large model As the characteristic resultants of these approaches are shown in Fig 21, the Korbaa approach is found out to be good and the Hillion approach is

to be effectiveness in the time And on the effort point, the proposed approach is proved to

be good

7 Conclusion and future study

In this paper, we focused on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of WIP (Work In Process) Especially, this paper product ratio-driven FMS cyclic scheduling problem with each other products and ratios has been dealt We proposed a model that has two jobs and two machines And TPN slice and unfolding are applied to analyze this FMS model We can divide original system into subsystem using TPN slice and change iterated cycle module into acyclic module without any other behavior properties

Specially, we simulated our approach with IBM PC windows 2000 using Visual C++, then our approach is faster than Korbaa’s approach in the many resource shared This means that the new approach is more useful to the model that has many resource share machines in any case If the model has small resource share machines and short operation depths, then it’s useful to approach Korbaa’s

We are sure that proposed method is very useful to analyze all Petri net models This proposed method is available to apply to a complex computer simulation, a parallel computer design and analysis, and a distributed control system, etc

8 References

Best E., Cherkasova L., Desel J & Esparza J.(1990) Characterization of Home States in Free

Choice Systems, Hildesheimer Informatik-Berichte Vol.9/90, Universitat Hildesheim Carlier J & Chretienne P.(1988) Timed Petri nets Schedules, In: Advanced in PN, G

Rozenberg(Ed.), vol.340 of LNCS, pp.62-84, ISBN Verlag,Berlin, Germany

0-387-50580-6,Springer-Camus H.(1997) Conduite de Systèmes Flexibles de Production Manufacturière Par

Composition de Régimes Permanents Cycliques:Modélisation et Evaluation de Performances à l’Aide des Réseaux de Petri, Thèse doctorat USTL

Esparza J., Lomer S & Vogler W.(1996) An Improvement of McMillans unfolding

Algorithms, IN: LNCS 1055, pp.87-106

Hwang CH & Lee DI.(1997) A Concurrency Characteristic in Petri net Unfolding,”

Proceeding of SMC’97, pp 4266-4273

Hillion H., Proth J-M & Xie X-L.(1987) A Heuristic Algorithm for Scheduling and Sequence

Job-Shop problem, Proceeding of 26 th CDC 1987, pp.612-617

Julia S., Valette R & Tazza M.(1995) Computing a feasible Schedule Under A Set of Cyclic

Constraints, Proceeding of 2nd International Conference on Industrial Automation,

pp.141-146, Nancy 7-9, Juin, 1995

Kondratyev A., Kishinevsky M., Taubin A & Ten S.(1998) Analysis of Petri nets by

Ordering Relations in Reduced Unfolding, Formal Methods in System Design, Vol 12,

No.1, pp 5-38

Korbaa O., Camus H & Gentina J-C.(1997) FMS Cyclic Scheduling with Overlapping

production cycles, Proceeding of ICATPN’97, pp.35-52

Lee DY & DiCesare F.(1995) Petri Net-based heuristic Scheduling for Flexible

Manufacturing, In: Petri Nets in Flexible and Agile Automation, Zhou MC.(Ed.),

pp.149-187, Kluwer Aca Pub., USA

Lee J.K & Korbaa O (2006) Scheduling Analysis in FMS Using the Unfolding Time Petri

nets, Mathematics and Computer in Simulation, Vol.70, pp 419-432,

Lee J.K., Korbaa O., & Gentina J-C.(2001) Slice Analysis Method of Petri nets in FMS Using

the Transitive Matrix, Proceeding of INCOM01, 8,Vienna,Austria,Control Problem in Manufacturing, Elsevier Science

ISBN:0-08-043246-Lee J.K & Korbaa O (2004) Modeling and analysis of radio-driven FMS using unfolding

time Petri Nets , Computer Ind Eng.(CIE), Vol.46,No.4, pp 639-653

Liu J., Itoh Y., Miyazawa I & Seikiguchi T.(1999) A Research on Petri nets Properties using

Transitive matrix”, Proceeding of IEEE SMC99, pp.888-893,

Murata T.(1989) Petri Nets: Properties, Analysis an Applications, Proceedings of the IEEE, vol

77, No 4, April 1989, pp 541-580

McMillan K.(1995) A technique of state space search based on unfolding, Formal Methods in

System Design Vol 6, No.1, pp 45-65

Ohl H., Camus H., Castelain E & Gentina JC.(1995) Petri nets Modeling of Ratio-driven

FMS and Implication on the WIP for Cyclic Schedules, Proceeding of SMC’95,

pp.3081-3086

Richard P.(1998) Scheduling timed marked graphs with resources : a serial method,

Proceeding of INCOM’98

Taubin A., Kondratyev A & Kishnevsky M.(1997) Application of Petri Nets unfolding to

Asynchronous Design, Proceeding of IEEE-SMC 1997, pp.4279-4284

Valentin C.(1994) Modeling and Analysis methods for a class of Hybrid Dynamic Systems”,

Zuberek W., Kubiah W.(1993) Throughput Analysis of Manufacturing Cells Using Timed

Petri nets, Proceeding of ICSYMC 1993, pp.1328-1333

Error Recovery in Production Systems:

A Petri Net Based Intelligent System Approach

Nicholas G Odrey

Department of Industrial and Systems Engineering, Lehigh University

USA

1 Introduction

Leading-edge companies require flexible, reliable and robust systems with capabilities

to adapt quickly to changes and/or disturbances In order to be adaptable a flexible manufacturing systems must possess the ability to (i) reconfigure the existing shop floor and (ii) automatically recover from expected and unexpected errors One of the major problems in flexible manufacturing systems is how to effectively recover from such anticipated and unanticipated faults Traditional techniques have addressed the error recovery problem from the point of view of defining a set of actions for a pre-specified set of errors The main disadvantage of this approach is that not only a huge amount of coding is required but also that two undesirable situations still may occur: (i) some errors may not occur in a prespecified set during the lifetime of the system and (ii) there may be errors that cannot be anticipated Pre-enumerating a large number of error occurrences will not guarantee that the system will not encounter a new error situation Our intent here is to show the genesis of work into intelligent control of discrete event dynamic systems to overcome (ii) as exemplified by a Petri Net based model for large scale production systems Petri Nets have been successfully used for modeling and controlling the dynamics of flexible manufacturing systems (Hilton & Proth, 1989; Zhou & DiCesare, 1993) Generally, in a Petri net, the operations required on a part are modeled with combinations of places and transitions The movement of tokens throughout the net models the execution of the required operations The content of this chapter is multi-faceted Topics include Petri Net modeling, state space representation and associated solution techniques, hierarchical decomposition and control, hybrid modeling, multiple agent systems, and, in general, issues pertaining to our work on intelligent control of manufacturing systems

Our focus here is on the characteristics of physical error occurrences which impose difficult challenges to discrete event control The majority of our effort has been on workstation/cell control within the hierarchical system originally proposed by the National Institute of Standards and Technology (NIST) e.g (Albus, 1997) The controller must first handle simultaneously production and recovery activities, and second, treat unexpected errors in real-time to avoid a dramatic decrease in the performance of the system In the following sections we follow the modeling approach previously presented by (Odrey& Ma, 1995) which had its origins in the work of (Liu,

1993) This previous work included modeling, optimization, and control within the framework of hierarchical systems In particular, the research was focused on efforts towards the foundations of a multilevel multi-layer hierarchical system for manufacturing control The Petri Net formalism can handle the complexities of the highly detailed activities of a manufacturing workstation such as parallel machines, buffers of finite capacity, dual resources (multiple resources required simultaneously

on one operation), alternative routings, and material handling devices to name a few Details on the mathematical structure and definitions pertaining to Petri nets can be found in numerous sources e.g., (Zhou & Dicesare, 1993; Murata, 1989) The reader is referred to this literature for detailed underlying mathematical models A further thrust of our work has been to enhance a multilevel multi-layer model by the incorporation of intelligent agents with the purpose of adding flexibility and agility Thus, one objective of our effort is to determine whether it is possible to integrate Petri Nets constructs with object-oriented formalisms and have an “all in one” modeling and implementation tool for intelligent agent-based manufacturing systems Several researchers have attempted to combine these techniques One of the first approaches was Object Oriented Petri Nets (Lee and Park, 1993)

More recent work pertains to addressing the issue of monitoring, diagnostics, and error recovery within the context of a hierarchical multi-agent system (Odrey & Mejia, 2003) The system consists of production, mediator, and error recovery agents Production agents contain both planner and control agents to optimize tasks and direct material flow, respectively Here we address the error recovery agent within a hierarchical system at the workstation level in more detail It is assumed that raw sensory information has been processed and is available When an error is detected, the control agent requests the action of a recovery agent through a mediator agent In return, the recovery agent devises a plan to bring the system out of the error state Such an error recovery plan consists of a trajectory having the detailed recovery steps that are incorporated into the logic of the control agent In the context of Petri Nets, a recovery trajectory corresponds to a Petri subnet which models the sequence of steps required to reinstate the system back to a normal state After being generated, the recovery subnet is incorporated into the workstation activities net (the Petri Net of the multi-agent system environment) In this research, we follow the designation of others (Zhou & DiCesare, 1993) and denote the incorporation of a recovery subnet into the activities net as net augmentation The terms “original net” or “activities net” refer to the Petri Net representing the workstation activities (within a multi-agent environment) during the normal operation of the system The net augmentation brings several problems that require careful handling to avoid undesirable situations such as the occurrence of state explosions or deadlocks Intelligent agents seem to be a promising approach to deal with the unpredictable nature of errors due to their inherent ability to react to unexpected situations Research on intelligent agents in the context of manufacturing have been mostly concentrated on the “production activities” e.g scheduling, planning, processing and material handling (Gou, et al., 1998; Sousa & Ramos, 1999; Sun, et al., 1999) However the activities related to exception handling such as diagnostics and error recovery have received little attention Our research aims

to provide some evidence as to how the performance of a manufacturing system can be improved by using intelligent agents modeled with Petri Nets

1.1 Statement of the problem

The focus in this chapter is on physical error occurrences and is directed towards supporting effective procedures for error recovery in an attempt to arrive at a reconfigurable, adaptive, and “intelligent “manufacturing system As such, a hybridization of Petri Nets and intelligent agents seem to be a promising approach to deal with the unpredictable nature of errors due to their inherent ability to react to unexpected situations Within this context, we investigate system learning with a hybrid Petri net-neural net structure The following sections of this chapter first discuss the background on architectures for reconfigurable and adaptable manufacturing control Subsequent discussions will be based on the genesis of work at Lehigh University on Petri nets from initial modeling and solution approaches to more recent work on embedding intelligent agents with Petri Nets A hybrid nets consisting

of a Petri Net with a Neural Net approach for the purpose of intelligent control is also discussed

2 Architectures

Even though our focus in this chapter is on Petri Net modeling and error recovery , we would be remiss to not mention the underlying architecture of the systems being investigated, While some performance tests (Brennan, 2000; Van Brussel, et al.,1998) suggest that intelligent agent architectures for manufacturing systems outperform other architectures, the lack of standards on design methodologies, communication protocols and task distribution among the agents makes difficult their introduction to real-life applications Opposed to intelligent agent-based architectures, hierarchical architectures have been conceived with the standardization issues in mind A hierarchical architecture groups the elements of the manufacturing system into hierarchical levels, e.g enterprise, factory, shop, cell, manufacturing workstation and equipment levels, with the purpose of coping with complexity The major drawback of hierarchical architectures is that their structure is overly rigid and consequently difficult to adapt to unanticipated disturbances (Van Brussel, et al., 1998) To increase the functionality of the system, components at the same level may be linked The purpose was to loosen the strict master-slave relationship of the proper hierarchical form This resulted in the so termed, modified hierarchical form Higher flexibility was reported with this architecture; however some problems arose in the communication links between entities of the same level mostly caused by the lack of development of the technology available at that time (Dilts et al., 1991)

To overcome the difficulties of the hierarchical architectures a heterarchical (distributed) form was proposed (Duffie et al., 1988) In this architecture a single entity did not exist at the top level as in the hierarchical scheme In this architecture there existed a number of parts or components which “negotiate” the utilization of scarce resources As such, a feedback signal did not have to go one level up in the hierarchy to find a response and a corrective action A system failure in the context of this architecture meant “lack of communication” between two entities As one communication link failed other resources were capable of establishing the linkage There was not a single information source as the information was distributed throughout the system Ideally the system would have been very flexible and adaptable as new elements (software or hardware) could have been “attached” to the existing ones without major disruptions The heterarchical control architectures coped very well with disturbances and reacted quickly to changes but the lack of hierarchy led to unpredictability

in the system Consequently global optimization was almost impossible because there was