Evaluation and tuning of robust PID controllers

Based on a general controller evaluation method, taking both performance and robustness in different frequency regions into account, an analytical PID design method is presented. It is related to the well known and often used lambda tuning approach, which is based on internal model control (IMC) for a specific second-order non-minimum phase plant model. The analytical method introduced in this paper includes two tuning parameters, one that guarantees a specified stability margin for the given model, and one that is also able to adjust the control activity to a desired level. The suggested method, called robust IMC, gives the user the important freedom to control both mid- and high-frequency robustness. An extended evaluation procedure also illustrates how efficiently PI and PID controllers including a Smith predictor (SP) can control time delayed plants. More specifically, it is shown to be more profitable to provide a PI controller with derivative action than with a SP for plants with long time delays.