An approximation method and PID controller tuning for systems having integer order and non-integer order delay

Abstract

In this study, an algebraic approximation method is proposed to investigate the stability analysis and time domain response of non-integer order delay systems. Besides, stabilizing Proportional Integral Derivative (PID) controllers are computed in the (kp,ki) plane for the fixed value of kd and a simple PID controller tuning method for the systems with integer order delay and non-integer order delay is presented. For this purpose, to obtain stable PID controller parameters in the (kp,ki) plane, the necessary equations are obtained using the stability region concept. A new design technique is proposed that facilitates the selection of the controller parameters from this region. This design technique is compared with the weighted geometrical center method (WGC). Both methods are used for the first time to the systems with non-integer order delay. Comparisons are also made with some other tuning methods in the literature. Considering the reasonable results obtained, the proposed method can be seen as a very advantageous design technique. Moreover, it provides an easy design procedure without any performance criteria restrictions such as gain margin, phase margin, maximum overshoot, etc. The only criterion here is to obtain the stability region. The simulation results include a detailed comparison of the WGC and the proposed method. Although the WGC seems to be superior in terms of performance, the computational load is considerably higher than the proposed method, which makes the proposed method quite sufficient for a simple and acceptable start.