PID Tuning Based on Output Matching in Frequency Domain

This paper presents a PID gain tuning method based on model matching to desired reference models for closed-loop systems with PID controllers. The features of the proposed method are as follows. Even if the plant transfer function model is unknown, if its frequency characteristics can be obtained, the PID gain can be tuned, and the stability margin and time responses of the closed-loop system after tuning can be estimated. Furthermore, by newly introducing an approximate model matching error, the least squares method can be applied to obtain the PID gain, and an appropriate reference model that satisfies the desired stability margin can be efficiently searched for. The usefulness of the proposed method is demonstrated through numerical examples.