Adaptive Stable PID Controller with Parallel Feedforward Compensator

In this paper, a new design method of adaptive PID controller is proposed. The method utilizes the characteristics of almost strict positive realness (ASPR) of the plant so that the stability of the adaptive 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 PFC has contained a very troublesome procedure. To improve such a situation, a very simple and effective PFC design method is proposed here. The effectiveness and robustness of the proposed method is examined through simulations by comparing it with other conventional PID controller parameter tuning rules based on the first order with time delay process model