Design, Tuning and Analysis of a Robust PID Controller for FOPTD Unstable Systems with Uncertainty in the Process Model Parameters

Abstract: In this paper, extensive simulations are performed on the FOPTD Unstable systems having uncertain process model parameters (i.e process gain (Kp), time constant ( τ ) and dead time (td), in order to design a robust PI/PID controller with better disturbance rejection and servo response, without compromising the robust performance (Robust stability) of the system. A simple PI/PID controller design and tuning method is described and compared from the point of view of the control system robustness for the First order plus time delay (FOPTD) process. For FOPTD Un-stable systems, the step responses obtained by the proposed method when uncertainty in the process model parameters exist, are compared to the responses obtained by Visioli [3], IMC(Wang/Hang)[5] and Huang-Chen [2] methods. The Proposed controller settings give a robust performance for uncertainty in model parameters. The performance of PID tuning techniques is analyzed and compared on basis of minimization of error and transient response specifications. A theoretical analysis of robustness and stability of the proposed controller is done using Kharitonov’s theorem (Barmish) [4] to validate the simulation results obtained using MATLAB/SIMULINK.

Keywords: PI/PID, FOPTD systems, Robustness, Uncertainty, Kharitonov’s theorem.