Time-Varying Automated Manufacturing Systems and Their Invariant-Based Control: A Petri Net Approach

In the context of automated manufacturing systems, we propose a class of time-varying systems which enable different working modes at different time intervals. This paper provides a comprehensive and comparative study on invariant-based linear constraints in supervisory control of time-varying systems. First, generalized linear constraints (GLCs) which contain both marking and firing vectors are used to prevent the illegal event from firing at the critical good marking, so as not to reach any deadlock. Supervisor simplification on GLCs is presented in order to remove the dependent ones while retaining the independent ones. Then, weight coefficients are introduced to linear constraints to enhance our specifications' expressivity capability in these iterative approaches. It shows that such specifications have an obvious advantage in improving permissiveness for the systems whose processes can accommodate more tokens. Above linear constraints can be implemented via place invariants in Petri net, and solve the forbidden state problem and event/state separation problem. The experimental studies illustrate the application of time-varying systems and the effectiveness of invariant-based control methods.