Synthesis of Petri Net Controller Based on Constraints Matrix

Abstract

A new method for constructing a Petri net feedback controller based on constraints matrix is presented for a discrete event system modeled by a Petri net, which enforces linear inequality constraints involving the place marking and the firing transition. The controller is constructed based on the concepts of place invariants and the structural conflicts of Petri net theory, and the controller introduced is maximally permissive. Firstly, local incident matrix of constrained places is constructed based on part design and Petri net reduction technique, and then constraints matrix is constructed based on the local incident matrix. The constraints matrix eases the design of controller and holds remarkable advantages especially for systems with large scale, because it considers part of the plant only, not the entire plant, and it only concludes two rows. Finally, the method is proved to be simple and efficient through some examples.