Two-Degree-of-Freedom Control Scheme for Robust Centralized PI/PID Controller Design Using Constrained Optimization

Abstract

For a two-input two-output distillation column with heavy interactions and long dead times, a two-by-two PI/PID controller is designed. The design objectives are good setpoint regulation and appropriate load disturbance rejection. The constraints are on degree of robust stability, control effort as well as peaks of the maximum singular value of sensitivity and complementary sensitivity matrices. As this set of design objectives and constraints is often conflicting, a more flexible control structure, a two-degree-of-freedom scheme, is proposed. The design problem is formulated as a constrained optimization problem and is solved by a powerful random-search optimization technique, the so-called vector-based swarm optimization. Next, the performance of the proposed method in controlling a Wood and Berry distillation column is evaluated and compared with that of several well-known design techniques. Because of using a flexible control structure, a powerful optimization algorithm and a comprehensive set of design requirements, the proposed control strategy performs well in coping with conflicting design objectives.