Tuning of PID Controllers for First order Stable / Unstable Time Delay Systems with a Zero

PID controllers are designed for First order stable/unstable time delay systems with a zero by using IMC method. In this method first order Pade’s approximation is used while deriving PID controller parameters from IMC controller. Simple tuning rules for stable/ unstable First Order Plus Time Delay (FOPTD) system with a positive zero and unstable FOPTD system with a negative zero are given in terms of model parameters. The IMC filter time constant is a tuning parameter and is selected based on the maximum magnitude of the sensitivity function (Ms) value. Simulation results on various transfer function models and on the nonlinear model equations of continuous stirred tank reactor with nonideal mixing carrying out an enzymatic reaction (at two different operating points) are given to show the effectiveness of the proposed method. The proposed controller performs better than the controller designed by the recent literature methods in terms of ISE, IAE and ITAE.