A convex optimization approach to multi-objective design of two-stage compensators for MIMO linear systems. (March 2023) - Supithak, Tanathorn; Banjerdpongchai, David
Abstract: The previous design of two-stage compensators with multi-objectives concerns the closed-loop stability, the low-sensitivity, and the satisfactory time-domain performance. However, the design only considers the single-input single-output system. This paper aims to present the design of two-stage compensators for multi-input multi-output (MIMO) linear systems which contain dynamical interaction between inputs and outputs. When Youla parameterization is applied to the MIMO linear system, the design criteria can be cast as a nonlinear optimization. In addition, the infinite dimension optimization problem is approximated to a finite dimension problem with Ritz approximation. The suitable form of design parameters is proposed to ensure the low sensitivity of the MIMO system. The two-stage compensator design is formulated as convex optimization which is efficiently solved using available solvers. Finally, the two-stage compensators are designed for Wood and Berry's model of binary distillation column. The numerical results indicate that all design objectives of frequency domain and time domain can be achieved by the two-stage compensators. Highlights: The design criteria include stability, low sensitivity, and transient response. The design is cast as convex optimization by Youla-parameterization and Ritz approx. Two-stage compensators are designed for distillation column to illustrate results.