Steady-State Gain Identification and Control of Multivariable Unstable Systems

A method is presented to identify the steady-state gain matrix of a multivariable (SSGM) unstable system under closed-loop control. Effects of disturbances and measurement noise on the identification of SSGM were also studied. Davison's method (Davison, 1976) was modified to design single-stage multivariable PI controllers using only the steady-state gain matrix of the system. Since the overshoots in the responses are larger, a two-stage P-PI control system is proposed. Based on the SSGM, a simple proportional controller matrix was designed by the modified Davison's method (1976) to stabilize the system. Based on the gain matrix of the stabilized system, diagonal PI controllers were designed. The performance of the two-stage control system was evaluated and compared with that of single-stage multivariable controllers. Simulation results on two examples show the effectiveness of the proposed methods for both servo and regulatory problems.