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    A new method for the redundancy analysis of Petri net-based liveness enforcing supervisors
    (Sage Publications Ltd, 2017) Gelen, Gokhan; Uzam, Murat; Li, ZhiWu
    The deadlock control of flexible manufacturing systems (FMSs) has been widely studied in the literature. Petri nets (PNs) are extensively used as a tool for modelling, analysis and controller synthesis of such systems. In general, Petri-net-based liveness enforcing supervisors (LESs) include control places (CPs) together with their input/output arcs. It is well known that the methods proposed for computing CPs may provide redundant and necessary CPs. In this paper, a new method is proposed for redundancy test of CPs by means of supervisory control theory (SCT). The proposed method is based on the idea that after the removal of a CP from an LES, if the controlled model is still live, then the removed CP is redundant. The proposed method makes use of the TCT implementation tool of SCT. It is applicable to a PN-based LES consisting of a set of CPs. The applicability of proposed method is demonstrated by means of examples from the relevant literature. For some examples, the redundancy test provides more permissive behaviour with structurally simpler supervisors.
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    Computation of the number of legal states for petri net-based deadlock prevention problems
    (Yildiz Technical Univ, 2023) Gelen, Gokhan; Uzam, Murat
    Petri net (PN) based prevention and control methods are widely studied in the literature to solve deadlock problems in flexible manufacturing systems (FMS). In PN models of FMS suffering from deadlocks, the reachability graph (RG) of the PN model can provide all reachable system states from the initial state, including all legal states, bad states, and deadlock states. A maximally permissive deadlock controller allows the system to reach all legal states exist within the live zone (LZ) that determines the optimal live behavior, while prohibits reaching bad and deadlock states exist within the dead zone. It is necessary to know the exact number of legal states that must be provided by a deadlock controller to determine the behavioral permissiveness of a control policy. Therefore, the number of legal states has been considered as a quality measure for deadlock prevention methods available in the literature. Unfortunately, to date for a given RG of a PN model of an FMS suffering from deadlocks, no study has been reported to provide the number of reachable legal states exist within the LZ of the given RG. In this paper, a method is proposed for the computation of the number of legal states that must be provided by an optimal deadlock prevention policy. The proposed method makes use of the reachability analysis of a given PN model of a deadlock-prone FMS together with the first strongly connected component (SCC) by using INA (Integrated Net Analyzer). The number of legal states computed from the first SCC that includes the initial marking represents the LZ of a RG. The proposed algorithm is implemented as an executable program. The number of legal states of a deadlock controller can easily and correctly be computed by using the proposed method and tool. Several well-known examples of FMS are considered to illustrate the applicability and the effectiveness of the proposed method.
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    On Deadlock/Livelock Studies Based on Reachability Graph of Petri Nets by Using TINA
    (Ieee-Inst Electrical Electronics Engineers Inc, 2024) Uzam, Murat; Liu, Ding; Berthomieu, Bernard; Gelen, Gokhan; Zhang, Zhaolong; Mostafa, Almetwally M.; Li, Zhiwu
    Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.
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    Think-globally-act-locally approach with weighted arcs to the synthesis of a liveness-enforcing supervisor for generalized Petri nets modeling FMSs
    (Elsevier Science Inc, 2016) Uzam, Murat; Gelen, Gökhan; Saleh, Tahir Lawan
    This paper proposes a general approach, called a think-globally-act-locally method with weighted arcs (TGALW), which can be used to compute a liveness-enforcing supervisor (LES) for the Petri net (PN) model of a flexible manufacturing system (FMS) prone to deadlocks. Compared with siphon-based deadlock prevention policies that are usually rather conservative, the method is especially effective for generalized PN classes such as (SR)-R-4 and (SPR)-P-4 and also leads to optimal or near optimal LESS while maintaining the necessary computations simple. An original PNM is first transformed into a net that is behaviorally equivalent to it. A global sink/source place (GP) is used temporarily in the design steps and is finally removed when the liveness of the system is achieved. At each iteration step, bad markings are identified and then controlled by monitors through an established place-invariant based method. A condition of the optimal controllability of a bad marking is proposed, i.e., if all bad markings are optimally controlled at each iteration step, the TGALW method can find an optimal LES. Redundancy of monitors is checked. Typical examples existing in the literature are used to demonstrate applicability and the effectiveness of the proposed method. (C) 2015 Elsevier Inc. All rights reserved.