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Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.

A Petri net Approach for Dynamic Control Reconfiguration of Manufacturing Systems with Consideration of Resource Changes. Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D. Outline. Introduction. Research motive and purpose.

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Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.

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  1. A Petri net Approach for Dynamic Control Reconfiguration of Manufacturing Systems with Consideration of Resource Changes Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.

  2. Outline

  3. Introduction

  4. Research motive and purpose • In the manufacturing process,the manufacturing system may occur unexpected events, that will result changes of the available resource’s amount. • After resources changes, according to the original control rules will cause a lack of system resources. • The purpose of this research is the manufacturing system return to normal in the situation of resource changes. • Both of adjusting control rules and assigning the other department’s resources are the ways of troubleshooting.

  5. Research process

  6. Literature review

  7. Reconfig- uration Petri Net RMS Deadlock

  8. RMS • A kinds of manufacturing Systems, that can revise and adjust its structure.Itcan promise customized flexibility in a short time.(Mehrabi, et al. [2000]) • Reconfiguration can mainly divide into two classes: • Reconfiguration in plan stage • Reconfiguration in control stage • Reconfiguration can be classified in terms of two levels: • Hardware: Reconfiguration of resources • Software: Reconfiguration of control rules (Bi, et al. [2008]、Koren, et al. [1999]、Malhotra, et al. [2009])

  9. Petri Net(1/5) • Petri net are useful graphical tool for modeling the manufacturing systems. • Petri net are an appropriate tool for the study of discrete-event dynamical systems because of their modeling power and flexibility. (Yamalidou, et al. [1996]) (Reddy, et al. [1993])

  10. Petri Net(2/5) • Petri net includes four basic elements: Token、Place、Transition、Arc • Petri net is a five tuple:

  11. Petri Net(3/5) • The analysis method of Petri net. • Reachability analysis method • Reachability tree • Reachability graph • Invariant analysis method • P-invariant • T-invariant

  12. Petri Net(4/5) • P-invariant • one can find subsets of place over which the sum of the tokens remains unchanged • T-invariant • one can find that a transition firing sequence bring s the marking back to the same one. →Define the posive integer solution x of CTx=0 →Multiplying XTto both sides →Since CTx=0, thus xTC=0 → then x is a P-invariant →Cu=0 , then u is a T-invariant

  13. Petri Net(5/5) • Literature Review about using Petri net on RMS

  14. Reconfiguration(1/2) • Reconfiguration • Control rules of the manufacturing system are used to handle the systems. • Reconfiguration have to reach two points: • To safety the resources constraints • To avoid the systems deadlocks

  15. Reconfiguration(2/2) • Literature review about reconfiguration：

  16. Deadlock(1/2) • The deadlock situation lead to the manufacturing system can not operate. • Deadlock situations are as a result of inappropriate resource allocation policies or exhaustive use of some or all resources. • These researches about solving deadlock can be divided into three groups: • Schedule • Circuit & Cycle • Controller

  17. Deadlock(2/2) • Literature review about deadlock of manufacturing system.

  18. Summary

  19. Research methods

  20. This research proposed a example about Reconfigurable manufacturing system(RMS). • Machine1: 3 • Machine2: 2 • Machine3: 3 • Machine4: 2 • AGV: 4 • Part A：CI→AGV→mc1→AGV→mc3→AGV→mc4→CO. • Part B：CI→AGV→mc3→AGV→mc2→AGV→mc1→CO. Example Operating • Machine1: 3 →1 • Machine2: 2 →1 • Machine3: 3 →2 • Machine4: 2 →2 • AGV: 4 →3 Resource changes

  21. Because the lack of system resources, it have to reconfigure the system. • This research considers the reconfigure methods, including adjust control rules and assign the other department’s resources. • Petri net • P-invariant • T-invariant & Reachability analysis • This research totally using five petri net model: • Flow Petri Net(FPN) • Resource Petri Net Controller(RPNC) • Original Petri Net(OPN) • Deadlock free Petri Net Controller(DPNC) • Deadlock free Petri Net(DPN) Research methods

  22. Methods process

  23. Establish the Original Petri net. Modeling(1/8)

  24. Step1:Establish the Flow Petri Net(FPN) Modeling(2/8)

  25. Step2:List the resource constraints. • Resource constraints: Modeling(3/8) Petri net places ‘s tokens Numbers of limit resources Parameter of limit resources

  26. Step3:Establish Resources Petri netController based on the P-invariant. Modeling(4/8) mc1

  27. The places of RPNC. • P-invariant: Modeling(5/8) Satisfy Resource constraints Place of Petri net Controller

  28. The arc of RPNC • P-invariant: Modeling(6/8)

  29. Step4:Establish Original Petri net(OPN). • OPN is consisted of FPN and RPNC. Modeling(7/8)

  30. Step5:Test and verify the deadlock of OPN • Matlab Petri Net toolbox. • Reduction of OPN Modeling(8/8)

  31. The procedure of reconfiguring system: • Step1:Decide the dynamic state of the resource changes. • Step2:According number of resources toupdate the resource constraints.(B →B*). • Step3:According B* to reconfigure the resource controller’s token. • Step4:Reconfigure the firing sequence. Reconfiguration(1/5)

  32. The procedure of Step3 & Step4. • Ⅰ : Reconfigure the resources controller’s token • Ⅱ : Determine the value of the om(Rpi) • Ⅲ : If the om(Rpi)≦0, to solve the reconfigure firing vector f. • Ⅳ : Determine whether the solution is feasible. • Ⅴ : If the solution is unfeasible, to revise the lb. • Ⅵ : Execute f , to adjust manufacturing systems. • Ⅶ : Reconfigure finish. Reconfiguration(2/5)

  33. The reconfiguration of firing sequence . • The transition of adjusting control rules. • The transition of assigning the other department’s resources. Reconfiguration(3/5)

  34. The costs of the firing transition, this research list three scenarios, we try to find the lowest cost of these scenarios: • Scenario 1: The costs of assign resources is very expensive. • Scenario 2: The costs of adjust control rules is slightly cheaper than assign the other department’s resources. • Scenario3: The costs of adjust the control rules is equal to assign the other department’s resources. Reconfiguration(4/5)

  35. Mathematical modelsof solving the objective marking omobj and transition firing vector f Reconfiguration(5/5) Firing vector Cost Correlation matrix of assign resource Correlation matrix of OPN Firing rule of Petri net: Objective function Integer and non-negative constraints Cost low bound

  36. If deadlock occur, it must add Deadlock free Petri net controller(DPNC) to establish Deadlock free petri net(DPN). • Deadlock free Petri Net Controller(DPNC) Deadlock(1/3)

  37. Mathematical modelsof solving the Deadlock free Petri Net Controller: Deadlock(2/3) • Nonreachability restrictions Circulation restrictions Reachability restrictions

  38. The procedure of Minimum controller search method (Yun-Yi Wang [2011]) Deadlock(3/3)

  39. Expected results

  40. The expected results of this research hope that it can resolve the problems about system’s resource changes by reconfiguring the manufacturing system and avoiding deadlock. Expected results

  41. Thanks for your listening

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