1. Computation of Minimal Siphons for a Class of Generalized Petri Nets
Mowafak Hassan Abdul-Hussin
Department of Communication Engineering,
University of Technology, Baghdad, IRAQ.

2. Abstract - Siphons are well suited to analyze and control deadlocks in Petri Nets (PN). A formal specification is presented to enable us to exert control to prevent the occurrence of deadlock problems. The approach adopted is Simple Sequential Processes with Resourses SSPR and drives us to distinguish deadlock states with insufficiently marked siphons. Depending on siphon control, a class of Petri nets is applied to calculate minimal siphons with high modelled power and can be modelled to become a focus of the resource circuits of the system. Deadlock prevention is achieved through the utilization of a method proposed to make elementary siphons maximally controlled by adding Control Places (CPs). The simulation PN toolbox is used with MATLAB as a tool to find minimal siphons and simulate the multipurpose manufacturing resources problem to illustrate the reachability graph of a deadlock system. For this purpose, the application system net is used in the analysis and control of the siphons. Finally, two examples are presented to demonstrate how the method works with siphons effect.

3. II. PRELIMINAIRS

4. III. Generalized Petri Net
Example 1. As an example, consider the following event set in the S4PR net representing RAS consists of three resources types, (see Fig. 1) and it contains deadlock, with capacities 5, 2, 1, and supporting two types of Job: J_1 and J_2.
Figure 1. Example of An S4PR net

5. The effectiveness of the control policy is depicted in Fig
The effectiveness of the control policy is depicted in Fig. 2, and reachability graph has shown the deadlock states marking that occurred at M7 and M12 in the red colored.
Figure. 2. The reachability tree of PN of Figure 1, used MATLAB [13]

6. Fig. 3, liveness reachability graph, and Fig. 4 is running on MATLAB
Figure 3. Controlled system of S4PR of Fig. 1
Figure 4. Coverability tree in MATLAB when adding three controls pleases VS1 VS3 is live.

7. Figure 5. Layout of FMS cell
Example 2. In this example, the manufacturing cell of Figure 5 is representing FMS. Figure 5, the layout of a manufacturing system including two machines (M1, M2), and two assembly robots (R1, R2).
Figure 5. Layout of FMS cell

8. A Petri net model of Figure 5
Figure. 6. A Petri net model of Figure 5

9. Fig. 7. A live-controlled an S4PR net with two monitors test in MATLAB
Figure. 7. Liveness system with two monitors VS1 and VS2

10. Figure 8. Shows reachability graph results of Figure 7. In Fig
Figure 8. Shows reachability graph results of Figure 7. In Fig. 8, a Petri net is liveness and has 16 states reachable marking.
Figure. 8.

11. CONCLUSIONS
A siphon’s-based model is related to the ‘liveness’ of a Petri net model of FMS. To an elementary siphon we add a monitor to the plant model such that the siphon is invariant-controlled.
The reachability graph of a PN contains all the necessary information to make decisions.
The highlight significance of results is liveness of S4PR-net where the S4PR class uses siphons
Thank you