Auto-Tuning Method of Expanded PID Control for MIMO Systems

This paper is concerned with auto-tuning of the expanded PID control for general MIMO linear system (r-input, m-output, nth-order). The purpose is to give an adaptive law of time-varying PID parameter matrices so as to asymptotically stabilize the closed-loop system using expanded PID control for the regulation problem. The proposed method is derived from satisfying the Lyapunov's stability theorem. For its execution it is necessary for a certain hypothetical system to satisfy almost strictly positive real (ASPR) property. So we also propose the method letting its hypothetical system be ASPR. In our method, since it is not necessary for the controlled MIMO system to be stable and/or minimum phase, it is useful for large class systems. The effectiveness of the proposed method is confirmed with unstable MIMO system by numerical simulations