PID Tuning for Optimal Closed-Loop Performance With Specified Gain and Phase Margins

A new robust proportional-integrative-derivative (PID) tuning method based on nonlinear optimization is developed. The closed-loop bandwidth is maximized for specified gain and phase margins (GPM) with constraint on overshoot ratio, so that criteria of closed-loop performance and robustness are both satisfied. The equations of open-loop amplitude ratio and phase change are derived based on frequency analysis for the first-order plus time delay system with a PID controller in parallel form. The equation of closed-loop amplitude ratio is also explicitly given. The formulated optimization problem from the tuning method based on GPM with constraint on closed-loop amplitude ratio is further given. The method is demonstrated in simulation examples and compared with previous work on this topic.