A Numerical PID Tuning Approach for LTI Systems

Abstract

This paper presents a novel PID tuning approach for nth-order LTI systems. It is a purely time-domain approach which determines the controller gains kP , kI , and kD by utilizing the characteristic polynomial of closed-loop output dynamics. Using the fact that the value of discriminant of the characteristic
polynomial of output dynamics is representative of critically-, under- or over-damped transient response, the proposed numerical approach computationally searches for those sets of controller gains which yield the desired transient response. Furthermore, the computational search can be refined by considering step response attributes such as rise time, settling time, overshoot and etc. Simulation results are included to show the efficacy of the proposition.