Policy to cope with deadlocks and livelocks for flexible manufacturing systems using the max′‐controlled new smart siphons

Abstract

Both deadlocks and livelocks can result in the serious problems in running process of a flexible manufacturing system (FMS). This study proposes an iterative control policy for an FMS modelled with Petri nets on the basis of a combination of revised mixed integer programming and the concept of max -controlled siphon, which can not only solve the smart siphons associated with deadlocks and livelocks in Petri nets directly, but also make them max -controlled. Accordingly, an original Petri net system with deadlocks and livelocks can be turned into the live controlled one with a simple structure, and meanwhile no smart siphons can be found in it. It lays foundations for further analysis and control on deadlocks and livelocks. Compared with the existing methods in the literature, the proposed one is more general and effective. A theoretical analysis and several examples are given to demonstrate its efficiency and practical potentials.

Efficient optimal deadlock control of flexible manufacturing systems

“…Therefore, it should be an explicit guideline on designing efficient FMSs to avoid the presence of ‐resources. A new question is whether the concept of ‐resources can be extended to general FMSs, such as single‐type RASs [20]. This is the part of our current research agenda.…”

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

“…This section introduces some examples that belong to S 3 PR and ES 3 PR in the existing literature 20,22,25,29,41 to further exemplify Algorithm 1. Its control performance comparison with the existing approaches presented in the study of Ezpeleta et al 29 (denoted as ECM),…”

“…(denoted as HHJ + ), 3,44 (denoted as HJX + ), 22,23 (denoted as LZ), 38 (denoted as UZ), 25 (denoted as PCF), 7 (denoted as C1), 40 (denoted as C2) and Li et al 41 (denoted as LAW + ) is also carried out via some tables, where Ã, J, R, DS, and DFS denote maximally reachable state, MPB, the ratio of the number of reachable states of the live controlled system (N Ã , M Ã ) to MRN, deadlock states, and deadlock-free states of the corresponding Petri net system, respectively.…”

“…Tables 1-6 show solution of ESs, DSs, and their complementary sets, the addition of CPs and CTs to ESs, controllability test to DSs, the supplemental addition of CPs and CTs to ESs and the addition of CPs and CTs to DSs, a two-stage deadlock control process using Algorithm 1, and its control performance comparison with the existing approaches, respectively. Figure 3 shows a non-live marked ES 3 PR, where 41 We have jPj = jP 0 j + jP A j + jP R j = 16, jT j = 12, and two production routes PR m (m = 1, 2), respectively. Algorithm 1 is also applied to it.…”

Construct the closed-form solution of A-net of Petri nets by case study

“…The deadlock avoidance/prevention policy for PNs presently is to find critic first-met bad markings (FBMs) for maximally permissive control purpose which is the policy based on the net structure. [18][19][20][21][22][23] The structural analysis based deadlock prevention has been extensively studied by researchers, in which siphon computation and control play an essential role. [24][25][26][27][28][29][30] However, current advanced approaches such as those in Chen et al 31 produce maximally permissive supervisors while not being able to synthesize large controllers since reachability analysis of the PN must be employed; Chen et al 20 applied the methodology of interval inhibitor arcs to optimal supervisory control under resources containing multi-token circumstance while suffering from the exponential increment state explosion problem.…”