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A divide-and-conquer-method for the synthesis of liveness enforcing supervisors for flexible manufacturing systems

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Abstract

In this paper a divide-and-conquer-method for the synthesis of liveness enforcing supervisors (LES) for flexible manufacturing systems (FMS) is proposed. Given the Petri net model (PNM) of an FMS prone to deadlocks, it aims to synthesize a live controlled Petri net system. For complex systems, the use of reachability graph (RG) based deadlock prevention methods is a challenging problem, as the RG of a PNM easily becomes unmanageable. To obtain the LESs from a large PNM is usually intractable. In this paper, to ease this problem the PNM of a system is divided into small connected subnets. Each connected subnet prone to deadlocks is then used to compute the LES for the original PNM. Starting from the simplest subnet prone to deadlocks to make the subnet live, monitors (control places) are computed. The RG of each subnet is considered and split into a dead-zone (DZ) and a live-zone. All states in the DZ are prevented from being reached by means of a well-established invariant-based control method. Next, the computation of monitors is followed for bigger subnets. Previously computed monitors are included within the bigger subnets based on a criterion. This process keeps the DZ of the bigger subnets smaller compared with the original uncontrolled subnets. When all subnets are live we obtain a set of monitors that are included within the PNM to obtain a partially controlled PNM (pCPNM). A new set of monitors is also computed for the pCPNM. Finally, a live controlled Petri net system is obtained. The proposed method is generally applicable, easy to use, effective and straightforward although its off-line computation is of exponential complexity in theory. Its use for FMS control guarantees deadlock-free operation and high performance in terms of resource utilization and system throughput. Two FMS deadlock problems from the literature are used to illustrate the applicability and the effectiveness of the proposed method.

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Acknowledgments

This work was in part supported by the research grant of The Scientific and Technological Research Council of Turkey (Türkiye Bilimsel ve Teknolojik Araştırma Kurumu - TÜBİTAK) under the project number TÜBİTAK-112M229, in part by the National Natural Science Foundation of China under Grant No. 61374068, and in part by the Science and Technology Development Fund, MSAR, under Grant 066/2012/A2.

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Authors and Affiliations

  1. Elektrik-Elektronik Mühendisliği Bölümü, Meliksah Universitesi Muhendislik-Mimarlik Fakultesi, 38280 , Talas, Kayseri, Turkey

    Murat Uzam & Rabiu Saleh Zakariyya

  2. Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau

    ZhiWu Li

  3. School of Electro-Mechanical Engineering, Xidian University, Xi’an,  710071, Shaanxi, China

    ZhiWu Li

  4. Mekatronik Mühendisliği Bölümü, Muhendislik ve Doga Bilimleri Fakultesi, Gaziosmanpasa Universitesi, 60150, Tokat, Turkey

    Gökhan Gelen

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  1. Murat Uzam
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Correspondence to Gökhan Gelen.

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Uzam, M., Li, Z., Gelen, G. et al. A divide-and-conquer-method for the synthesis of liveness enforcing supervisors for flexible manufacturing systems. J Intell Manuf 27, 1111–1129 (2016). https://doi.org/10.1007/s10845-014-0938-z

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