Multi criteria H∞ optimal PID controllers from an undergraduate perspective

A simple design method for robust PID controllers is presented. It is based on a multi criteria H∞ optimal control formulation, which is shown to be easily solved by a few lines of MATLAB code. This optimal solution for PID controllers including low pass filtering, is complemented by a simple paper and pen solution that can be used to obtain nearly optimal solutions. The presented approach is shown to give significantly better results compared to ordinary text book solutions based on frequency domain loop shaping. The paper also includes a discussion on how to best formulate PID controllers for design, and how additional filtering may easily improve high frequency robustness.