Tuning of PID Controllers for First Order Plus Time Delay Unstable Systems

Abstract

The focus of the current study is to propose an improved Zeigler-Nichols method for tuning the PID controllers for unstable First Order plus Time Delay (FOPTD) systems. In the proposed method, the controller settings are obtained by solving the magnitude and phase angle criteria. The addition of the controller modifies the overall gain of the system, subsequently changing the values of the controller gain. A second iteration for calculating the updated controller gain is conducted by solving the system’s magnitude and the phase margin criteria, incorporating the Proportional-Derivative-Integral controller transfer function, with unity proportional gain, and with the values of reset time and derivative time. A number of FOPTD systems with varying time delay to time constant ratios are simulated by using the proposed method. A non-linear model of a bioreactor is also simulated to show the enhanced performance over the other methods present in literature. The proposed method significantly improves the performances for the servo and regulatory problems.