Design of Optimal Petri Net Supervisors for Flexible Manufacturing Systems via Weighted Inhibitor Arcs

Abstract

This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.

Intelligent Colored Token Petri Nets for Modeling, Control, and Validation of Dynamic Changes in Reconfigurable Manufacturing Systems

“…Traditional Petri nets are popularly used to model, simulate, control, and analyze automated manufacturing systems (AMSs). Existing traditional Petri net studies assumed one or more of the following: (1) the system configuration is recognized and does not change throughout the operation, (2) there is no addition of new machines and no removal of old machines, and machine failures are not addressed, (3) rework is not required, and (4) products to be manufactured are identified, their process routes are specified, and the addition of new products is not applicable [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. This means that traditional Petri net models do not undergo dynamic configurations, such as processing failures and rework, machine breakdowns, addition of new machines, addition of new products, removal of old machines, or change processing routes induced by the competitive global market.…”

Deadlock and Blockage Control of Automated Manufacturing Systems with an Unreliable Resource

“…1. The parts in p 33 and p 34 require r 2 while the part in p 13 does not. Suppose that all parts in p 34 are unfinished.…”

“…If r 2 fails, then the part in p 33 cannot be moved into r 2 since all buffer spaces of r 2 are occupied and cannot be freed. Also the part in p 13 cannot be moved into r 3 since r 3 is occupied by the part in p 33 . Thus, we need to constrain the number of parts requiring r u .…”

“…As a mathematical formalism and graphical tool, a Petri net (PN) has been used for modeling, analyzing, and designing discrete event systems, including AMSs. To cope with deadlocks for AMSs, researchers have presented a variety of control policies [1,5,6,13,16,[18][19][20][24][25][26][27][28][29][30][31][32][33][34][35]. Ezpeleta et al [5] define a class of PNs called system of simple sequential processes with resources (S 3 PR).…”

Single Controller-Based Colored Petri Nets for Deadlock Control in Automated Manufacturing Systems

“…In this process, all first-met bad markings can be prevented by using iterations [14]. Several policies have been developed to prevent deadlock states, including iterative methods, the theory of region, and siphon control [10,[13][14][15][16][17][18][19]. The weakness of the reachability graph analysis is that the size of a reachability graph of a Petri net grows quickly and, in the worst case, grows exponentially with respect to the net size and its initial marking, and the net can easily reach an unmanageable level.…”