Adaptive PID Control for Servo Problem of MIMO Systems

Abstract

This paper is concerned with an adaptive PID control for the servo problem of MIMO systems {A, B, C} whoseA, B, Care unknown matrices in the presence of the constant disturbance. We propose the new adaptive two-degree of freedom PID controller that has the both constant matrices gain and adjusting gain matrices. The proposed design method is derived from satisfying Lyapunov's stability theorem under some assumptions that the controlled system's zero-dynamics is asymptotically stable, some rank conditions concerning the controlled system and the reference model matrices andCB=0,CAB>0 orCB>0. In our method, the asymptotic output tracking can be guaranteed even if there exist unknown system parameters and unknown constant disturbances. Finally, the effectiveness of the proposed method is confirmed with the simulation results for the 8-state, 2-input and 2-output system.