Robust Control for Single Unit Resource Allocation Systems

Supervisory control for deadlock-free resource allocation has been an active area of manufacturing systems research. Most work, however, assumes that allocated resources do not fail. Little research has addressed allocating resources that may fail. Automated manufacturing systems have many types of components that may fail unexpectedly. We develop robust controllers for single unit resource allocation systems with unreliable resources (Chew et al., 2008; Chew et al., 2011; Chew & Lawley, 2006; Lawley, 2002; Lawley & Sulistyono, 2002; Wang et al., 2008; Wang et al., 2009). These controllers guarantee that when unreliable resources fail, parts requiring failed resources do not block the production of parts not requiring failed resources. Further, while resources are down, the system is controlled so that when repair events occur, the system is in a safe and admissible state. There is little manufacturing research literature on robust supervision. Reveliotis (1999) considers the case where parts requiring a failed resource can be re-routed or removed from the system through human intervention. Park & Lim (1999) address existence questions for robust supervisors. Hsieh (2004) develops methods that determine the feasibility of production given a set of resource failures modelled as the extraction of tokens from a Petri net. In contrast, our work models the failure of the workstation server while assuming that buffer space remains accessible after the failure event. We assume that when the server of a workstation fails, we can continue allocating its buffer space up to capacity, but that none of the waiting parts can be processed and thus cannot proceed along their routes until the server is repaired. We further assume that server failure does not prevent finished parts occupying the workstation’s buffer space from being moved away from the workstation and proceeding along their routes. Finally, we assume that server failure does not damage or destroy the part being processed and that failure can only occur when the server is working. The last two assumptions are made for notational efficiency and presentation clarity. They can be easily relaxed by adding appropriate events and state variables to our treatment. Our objective is to control the system so that failure of an unreliable resource does not prevent processing of parts not requiring the failed resource. When a resource fails, all parts in the system requiring the failed resource for future processing are unable to complete until the failed resource is repaired. Because these parts occupy buffer space, they can block production of parts not requiring the failed resource. Thus, we want to assure that, when unreliable resources fail, the buffer space allocation can evolve under normal operation so