Tuning PID Controllers for Unstable Systems with Dead Time Based on Dual-Input Describing Function Method

Abstract

Though various techniques have been studied as a way of adjusting PID parameters, no perfect method of determining parameters is available to date. Especially the design of PID controller for unstable processes with dead time (UPWDT) is even more difficult when the normalized dead time is quite large. In this paper, the Dual-Input Describing Function (DIDF) method is proposed, by which the performance and robustness of the closed-loop system can be improved. The method is based on moving the critical point (−1 + j0) of Nyquist’s stability to a new position arbitrarily selected on the complex plane. This can be done by determining appropriate coefficients of the DIDF. As a result, we can easily determine parameters of PID-type controller by using existing conventional tuning methods for stable or unstable systems. Simulation results are included to show the effectiveness of the proposed method.