Supervisor Computation and Representation: A Case Study

Abstract

When supervisory control theory is applied to industrial problems the need for a more expressive modeling formalism than plain event based automata is crucial. The models are typically built in a bottom-up structure where multiple sub-plant and sub-specifications together compose the full plant and specification, respectively. Typically, the enabling of an event in a sub-model may depend on the state of other sub-models. The standard approach is to synchronize on shared events. However, to build models of large industrial problems with complex constraints between sub-models are beyond many engineers abilities. One attempt to deal with this problem is to extend the plain automata with variables and allow guard conditions and action functions to be associated with transitions. This paper discusses the strengths and weaknesses of one such formulation that fits well together with the standard supervisory control theory. A related problem is how to represent the result after the synthesis procedure, i.e., the supervisor. In this paper we present an approach where the supervisor may be represented as extended guard conditions on the original sub-models. This allows an efficient and comprehensible representation of complex supervisors. Hence, it is preferable both from a user, as well as an implementation perspective. Both the modeling formalism based on extended finite automata and the way to represent the supervisor as extended guard conditions have been implemented in a supervisory control tool.