An Iterative Synthesis Approach to Petri Net-Based Deadlock Prevention Policy for Flexible Manufacturing Systems

Abstract

A deadlock prevention approach for flexible manufacturing systems (FMS) with uncontrollable transitions in their Petri net models (PNM) was proposed in [1]. A few examples were considered to show the applicability of the proposed approach. Fig. 1 depicts the PNM of an FMS considered in [1]. This is a well-known FMS example widely used in the Petri-net based deadlock prevention literature to demonstrate a variety of design methods of liveness-enforcing supervisors [2][3][4][5][6][7][8][9]. In the literature, generally all the transitions of this PNM are assumed to be controllable, but in [1] it is assumed that transitions t1, t2, t7, t11, t15, and t16 are controllable and other transitions are uncontrollable. The PNM shown in Fig. 1 suffers from a deadlock problem and, therefore, to enforce the liveness on this PNM it is necessary to introduce a liveness enforcing mechanism. Consequently, by using the approach proposed in [1] seven monitors (control places) shown in Fig. 2 were computed to enforce liveness on the PNM shown in Fig. 1. However, as it will be shown in the next section, the closed loop system containing the PNM shown in Fig. 1 and the LES shown in Fig. 2 does not provide a live system.The controlled PNM consists of the PNM shown in Fig. 1 and of seven monitors depicted in Fig. 2. In order to analyse the controlled PNM, a Petri net analysis software tool called INA [10] was used. The controlled PNM is obtained as an INA file as shown in Fig. 3. Analysis results for the controlled PNM by using INA is obtained as shown in Fig. 4. It can be seen from Fig. 4 that the controlled PNM is not live. In order to analyse Petri-net-based monitors, a recently proposed method [11] can also be used.This paper has shown that the liveness enforcing supervisor containing seven monitors computed in [1] does not provide a live behaviour.

A Computationally Improved Optimal Solution for Deadlocked Problems of Flexible Manufacturing Systems Using Theory of Regions

“…Two FMS examples are used to evaluate our deadlock prevention policy [12][13][14][15][16][17][18][19][20][21][22][23] . Example I: An FMS is shown in Figure 10 12 .…”

“…Uzam and Zhou propose an iterative control policy of liveness enforcement for PNs based on the theory of regions 17 . Less computation is required to obtain a controller.…”

Theory of Regions for Control Synthesis without Computing Reachability Graph

“…Compared with most of traditional global-conquer methods of Uzam and Zhou [15,16], the computational efficiency of PN supervisors is improved. Nevertheless, as the number of shared resources in uncontrolled systems has increased, too many subsystems should be disposed.…”

Development of Critical-Siphon Theory to Fastest Deadlock Controller for Flexible Manufacturing Systems and Computer-Integrated Manufacturing

“…Deadlock prevention has been popular to avoid deadlocks in FMS and CIM since it runs fast and statically to avoid run-time detection and computation. Classical approaches either suffer from adding too many monitors or reaching too few states [1,2,3]. Recently, maximally permissive process control policies [4,5,6] with little redundancy have emerged.…”

“…In the context of FMS the number of good states in a Petri net model of an FMS, which can be provided under the deadlock prevention or liveness-enforcing policies, has been regarded as a "quality measure . In terms of the practical implementation of these policies, this quality measure implies high efficiency, throughput, and flexibility [3]. The highest quality can be provided by the maximally permissive (optimal) control policies.…”