Fast Synthesis of Optimal and Structurally Simple Supervisors for Automated Manufacturing Systems

For automated manufacturing systems (AMSs), this paper presents a Petri net based deadlock prevention method to efficiently obtain an optimal supervisor with a compressed structure in terms of control places and added arcs. The optimal supervisor can be achieved by forbidding all first-met bad markings (FBMs) and permitting all legal markings. An iterative method for a lexicographic multiobjective integer linear program (LMILP) is formulated to design such a supervisor with a simple structure. At each iteration, a place invariant is designed to obtain an optimal control place by solving an LMILP whose objectives are first to forbid as many FBMs as possible, second to minimize the number of added arcs, and third to simplify coefficients of the place invariants. Instead of a single sizable linear program, several much smaller LMILPs are formulated, which can be solved much faster. Finally, a benchmark example is used to show the efficiency and effectiveness of the approach.