A general PID controller tuning method based on state space pole placement

Abstract

This paper presents a universally applicable analytic tuning method for PID control. The method begins with a second-order dead time model derived from step response analysis. Optimal poles are determined using a Linear Quadratic (LQ) regulator. State feedback for a non-zero setpoint and load disturbance, combined with a reduced-order observer, results in a two-degree-of-freedom PID structure with a first-order filter. Using the poles from state feedback, PID controller parameters are calculated via pole placement. A robust PID controller is achieved with M constraint optimal integral gain (MIGO) through the optimal selection of the LQ weighting factor and observer pole for load disturbance. Benchmark examples demonstrate the method's applicability, providing both good regulation and servo behaviour.