Decentralized QFT Controller Design Based on the Equivalent Subsystems Method

Abstract

Since the 1970s various decentralized control methodologies have been developed to deal with the challenge of controlling complex and/or spatially distributed systems with multiple inputs and multiple outputs (MIMO), e.g., chemical plants, power systems, water systems, etc. In general, the use of distributed information and control structures requires the synthesis of control laws in a constrained (decentralized) information structure. The article presents a novel frequency domain robust decentralized controller design method that is appropriate for uncertain dynamic MIMO systems with equal numbers of input and output variables, which consist of interconnected physical subsystems and are given as a set of square transfer function matrices. The main framework of the proposed method provides the Equivalent Subsystems Method (ESM), whereby the overall closed-loop system under a decentralized controller is stable if, and only if, all the individual closed-loop equivalent subsystems are stable. By generating equivalent subsystems for all transfer matrices, which describe the uncertain MIMO system, the individual uncertain equivalent subsystems are obtained as sets of respective frequency responses. Such representation allows the application of the QFT (quantitative feedback theory) approach to independently design local single-input single-output (SISO) robust controllers which constitute the resulting decentralized controller implemented in real subsystems. The designed controller ensures robust stability of the overall closed-loop system and the required performance as specified by the standard QFT performance specification types in both the equivalent subsystems and the overall closed-loop system. Compared to the existing method and references therein, the proposed method reduces the conservatism of the robust stability conditions and enables the exploitation of the benefits by the SISO QFT approach in the independent design of the robust decentralized controller. The developed design procedure is verified and illustrated in a case study on the robust decentralized level controller design of the quadruple tank process.