Structural Design of Supreme Controller with Uncontrollable Transitions

Abstract

In the framework of Petri net (PN), the structural supervisory control of discrete event system (DES) is an exciting method to design controller in the presence of uncontrollable transitions. Especially, this method addresses the controllability problem existing in the desired functioning PN. The controllability condition defined by uncontrollable synchronization can be expressed as constraints (GMEC). This leads to design place invariant-based controller, implemented through control places connected to plant transitions. The controller is maximally permissive if the transitions are controllable. Implying that the controller insures that the constraints are never violated directly or may be violated through the firing of uncontrollable transitions. But, if one control place is connected to uncontrollable transition, then the controller is non-admissible, since it cannot prevent such transition. The common idea is to transform the constraints or to displace the controller arcs. Unfortunately, the constraints transformation is computationally complex and not structural, while the arcs displacement approach is unsystematic. Our idea consists to iterate the structural supervisory control method to ensure a systematic displacement of controller arcs, so that no control place is input place of uncontrollable transition. This approach focuses on structural design of a less restrictive and admissible controller, namely the supreme controller