A GRAPH-THEORETIC APPROACH TO INTEGRATED PROCESS AND CONTROL SYSTEM SYNTHESIS

Abstract A graph-theoretic method for integration of process and control system (IPCS) syntheses has been proposed in the present paper. The foundation of this integration is a well-established, graph-theoretic approach to process synthesis in conjunction with the analysis of structural controllability based on digraph-type process models. A directed bipartite graph, the CP-graph, has been introduced for unambiguous representation of an IPCS structure. The notion of CP-graph has given rise to a set of axioms for describing the combinatorially feasible and controllable structures. The maximal controllable structure of an IPCS synthesis problem has been defined as the union of combinatorially feasible and controllable IPCS structures; obviously, the optimal IPCS structure must be a substructure of this maximal controllable structure. Thus, the mathematical programming model, e.g., MINLP model, of an IPCS synthesis problem should be derived from the maximal controllable structure. The fundamental combinatorial algorithm of IPCS synthesis, i.e., algorithm CMSG, for identifying this maximal controllable structure has been formulated. The complexity of this algorithm has been proved to be polynomial on the size of the problem; its efficacy is illustrated with a relatively simple example. The resultant IPCS structures are compared with the structures synthesized without considering their control systems.