Multivariable Stable PID Controller Design with Parallel Feedforward Compensator

In this paper, a new design method of multivariable PID controller is proposed. The method utilizes the characteristics of almost strict positive realness (ASPR) of the plant so that the stability of the multivariable PID control system is guaranteed by the use of K-Y lemma and Lyapunov´s stability theorem. An application of the proposed design concept to a practical design of tracking PID control system is also discussed. Usually the ASPRness of the controlled plant is attained by introducing an auxiliary subsystem called parallel feedforward compensator (PFC). Up to this time, the design of above-stated multivariable PFC has contained a very troublesome procedure. To improve such a situation, a very simple and effective PFC design method based on the approximate plant model is proposed. The effectiveness and robustness of the proposed method is examined through numerical simulations