1 / 15

Modeling with ordinary Petri Nets

Modeling with ordinary Petri Nets. Events : Actions that take place in the system The occurrence of these events is controlled by the state of the system. The state of the system is described as a set of conditions . A condition : a predicate or logical description of the state

clare-ware
Download Presentation

Modeling with ordinary Petri Nets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modeling with ordinary Petri Nets Events: Actions that take place in the system The occurrence of these events is controlled by the state of the system. The state of the system is described as a set of conditions. A condition: a predicate or logical description of the state of the system. Events may occur. Occurrence of an event may require some conditions to hold (preconditions). Occurrence of events may cause some preconditions to cease and may cause other conditions (postconditions) to become true.

  2. Conditions The machine shop is waiting. An order is arrived and is waiting. The machine shop is working on the order. The order is complete. Events An order arrives. The machine shop starts on the order. The machine shop finishes the order. The order is sent for delivery. Modeling - machine shop example (1)

  3. Modeling - machine shop example (2)

  4. Feedback control - Assembly cell (1)

  5. Feedback control - Assembly cell (2) Constraints: Each robot shall perform a task at a time: m2 + m3 1 m4 + m5 + m6 + m7  1 M-1 robot does not interrupt S-380 robot: m1 + m2 + m3 + m5 + m6 + m7  1 <<<Resources to be taken care of>>>: A piston rod shall be ready at P3 : m3  1 A pulling tool is required in P4 and P5 : m4 + m5  1 A cap is required in P6: m6  1 Two nuts are required in P7: m7  1

  6. Feedback control - Assembly cell (3) Uncontrollability conditions: Operation of M-1 robot not be interrupted from the point that it pulls the piston rod into the engine block until it has completed fastening the cap on the piston rod.  T6, T7, T8 uncontrollable. 1- Check L.Wuc 2- Find R1 and R2 so that R1. Wuc + R2L. Wuc 0 L´= R1 + R2L. R2 = I, find R1 by row operation.

  7. Feedback control - Assembly cell (4) Uncontrollability conditions

  8. Feedback control - Assembly cell (5) Vision system used in M-1 robot has been obscured: Starting and completing the task can be observed, but tracking the robot’s performance in between is not possible  T5, T6, T7 unobservable. 1- Check L´.Wuc 2- Find R1 and R2 so that R1. Wuo + R2L”. Wuo 0 L”= R1 + R2L’. R2 = I, find R1 by row operation.

  9. Feedback control - Assembly cell (6) Uncontrollable and unobservable conditions

  10. Concepts in Petri Net (1) Autonomous PN: Neither time nor external synchronization are involved in the model. Boundedness: For every reachable marking, the number of tokens in every place is bounded. Safeness: The marking of every place is either 0 or 1 (Boolean marking). Liveness: Regardless of the evolution, no transition will become unfireable on a permanent basis. Invariants: P-invariants and T-invariants. Concurrency: Firing of transitions are causally independent (I.e. concurrent, they may occur in any order). Synchronization: ….

  11. Concepts in Petri Net (2) Source transition: without input place. Sink transition: without output place. Deadlock: no transition is enabled. Conflict: between transitions. Conservation: A PN is conservative if it does not lose or gain tokens but merely moves them around.

  12. Petri net classes (1)

  13. Petri net classes (2) • Three main classes: • Ordinary PNs: All arcs have weight 1, one kind of tokens, infinite capacity • for places, no time involved. • Abbreviations: Simplified representations (useful graphical representations), • can be mapped to an ordinary PN. • Extensions: Some functioning rules are added, to enrich the initial model.

  14. Applications • Modeling: • - Communication protocols in computer systems; • (concurrency, synchronization, and resource sharing). • - Manufacturing systems; • concurrency (two machines working independently) • synchronization (a machine is free and a part is ready • to be processed by it). • Resource sharing (a robot is assigned to handle parts • in two machines but not at the same time). • - Hybrid Systems (continuous + discrete parts); • ex. batch production processes in biotechnological • industry, manufacturing systems.

  15. Analysis • PNs exhibit how a system work. • Analysis of a PN consists of seeking properties of the • constructed model such as liveness, boundedness, deadlock, …. • (they show whether the specifications are fulfilled). • Main categories of methods for seeking these properties: • Drawing the graph of marking and coverability tree. • Using linear algebra. • Reducing the PNs.

More Related