A Simple Graphical-Based Proportional-Integral-Derivative Tuning Method for Time-Delay Systems

Abstract

In this paper, a graphical-based proportional-integral-derivative (PID) tuning technique for time-delay systems is presented. The suggested tuning technique combines the stability boundary locus (SBL) method with the weighted geometrical center (WGC) concept. The plot of the stability region obtained by using real root boundary (RRB), infinite root boundary (IRB), and complex root boundary (CRB) in the parameter plane forms the basis of the proposed method. The tuning steps of the method can be expressed as follows. First, the stability region in (k(d), k(p)) -plane is obtained using the SBL for the fixed RRB line. Thus, the stability value range of the k(d) parameter is determined. Second, using these k(d) values, the entire set of stability regions in (k(p), k(i)) -plane is obtained. These regions constitute a three-dimensional global stability region in (k(p), k(i),k(d)) space. Finally, the WGC points of stability regions in each (k(p),k(i)) -plane are calculated. The center point having the best time domain performance among these WGC points is determined. This point gives the PID tuning parameters for the proposed method. The simulation results indicate that the presented tuning technique gives simple and reliable results and is useful in the stability analysis and the control of time-delay systems.