Liveness Analysis and Deadlock Control for Automated Manufacturing Systems With Multiple Resource Requirements
本文针对多资源需求的自动化制造系统，用一类广义Petri网建模，提出通过控制完美资源变迁回路来防止死锁，并设计结构简单的控制器，适合制造系统工程师参考。
This paper focuses on the liveness analysis and deadlock control for automated manufacturing systems (AMSs) with multiple resource requirements. Such an AMS is modeled by a class of generalized Petri nets called systems of simple sequential processes with multiple resources (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR). It is shown that a deadlock of the considered AMSs can be characterized by the saturation of a structural object in S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR, called perfect resource transition-circuit (PRT-circuit). As a consequence, an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PMR is live if and only if no PRT-circuit is saturated at any reachable marking. To ensure the system liveness, one has to prevent all PRT-circuits from being saturated at all reachable markings. To develop a structurally simple Petri net deadlock controller, we present the concept of an effective transition cover, which is a special subset of PRT-circuits that may be saturated. Then by designing a control place with a proper control variable for each PRT-circuit in an effective transition cover, we obtain a deadlock controller for the system. The needed control variables are determined by an integer linear program. Since the number of PRT-circuits in an effective transition cover is much less than that of all PRT-circuits that need to control, our controller is of small structural size. For an AMS with saturable PRTcircuits, there exists at least a transition cover. An algorithm is presented for checking the effectiveness of transition covers, and transforming noneffective transition covers into effective ones. Finally, some examples are used to illustrate the proposed method.