A simple tuning method of fractional order PI^λ-PD^μ controllers for time delay systems

In this paper, a practical tuning technique is presented to obtain all stabilizing fractional order PI^λ-PD^μ controller parameters ensuring stability for processes with time delay using the stability boundary locus and the weighted geometrical center (WGC) methods. The method is based on obtaining of stability regions plotted by using the stability boundary locus in the (k_d,k_f)-plane and (k_p,k_i)-plane, and then computing the weighted geometrical centers of these regions. After obtaining PD^μ controller parameters using the WGC method from the stability region, desired PI^λ controller parameters are computed by the same procedure. This paper provides a simple and efficient tuning method to obtain stabilizing parameters of PI^λ-PD^μ controller for time delay systems. The important advantages of the method are both calculating of controller parameters without using any complex solution methods and ensuring the stability of closed loop system. Illustrative examples are given to demonstrate the benefits and the simplicity of the proposed method.