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 Davison , E. J. ( 1976 ). Multivariable tuning regulators: The feed-forward and robust control of general servo-mechanism problem , IEEE Trans. Automat. Contr. , 21 , 35 – 47 .[Crossref], [Web of Science ®] , [Google Scholar]) 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 Davison , E. J. ( 1976 ). Multivariable tuning regulators: The feed-forward and robust control of general servo-mechanism problem , IEEE Trans. Automat. Contr. , 21 , 35 – 47 .[Crossref], [Web of Science ®] , [Google Scholar]) 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.