PI/PID controller design based on IMC and percentage overshoot specification to controller setpoint change

In this work, the normalized Internal Model Control (IMC) filter time constant is designed to achieve a specified value of the maximum sensitivity for stable first and second order plus time delay process models, respectively. Since a particular value of the maximum sensitivity results in an almost constant percentage overshoot to controller setpoint change, an empirical relationship between the normalized IMC filter time constant and percentage overshoot is presented. The main advantage of the proposed method is that only a user-defined overshoot is required to design a PI/PID controller. Simulation examples are given to demonstrate the value of the proposed method.