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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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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.
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.
Reconfig- uration Petri Net RMS Deadlock
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])
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])
Petri Net(2/5) • Petri net includes four basic elements: Token、Place、Transition、Arc • Petri net is a five tuple:
Petri Net(3/5) • The analysis method of Petri net. • Reachability analysis method • Reachability tree • Reachability graph • Invariant analysis method • P-invariant • T-invariant
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
Petri Net(5/5) • Literature Review about using Petri net on RMS
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
Reconfiguration(2/2) • Literature review about reconfiguration:
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
Deadlock(2/2) • Literature review about deadlock of manufacturing system.
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
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
Establish the Original Petri net. Modeling(1/8)
Step1:Establish the Flow Petri Net(FPN) Modeling(2/8)
Step2:List the resource constraints. • Resource constraints: Modeling(3/8) Petri net places ‘s tokens Numbers of limit resources Parameter of limit resources
Step3:Establish Resources Petri netController based on the P-invariant. Modeling(4/8) mc1
The places of RPNC. • P-invariant: Modeling(5/8) Satisfy Resource constraints Place of Petri net Controller
The arc of RPNC • P-invariant: Modeling(6/8)
Step4:Establish Original Petri net(OPN). • OPN is consisted of FPN and RPNC. Modeling(7/8)
Step5:Test and verify the deadlock of OPN • Matlab Petri Net toolbox. • Reduction of OPN Modeling(8/8)
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)
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)
The reconfiguration of firing sequence . • The transition of adjusting control rules. • The transition of assigning the other department’s resources. Reconfiguration(3/5)
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)
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
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)
Mathematical modelsof solving the Deadlock free Petri Net Controller: Deadlock(2/3) • Nonreachability restrictions Circulation restrictions Reachability restrictions
The procedure of Minimum controller search method (Yun-Yi Wang [2011]) Deadlock(3/3)
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