Stability Analysis on Iterative PID Control Design Algorithm for Maximizing Proportional Gain

This paper deals with an iterative proportional-integral-derivative (PID) gain tuning algorithm to maximize the proportional (P) gain while guaranteeing the stability of the closed-loop system. Indeed, by increasing P-gain, the performance of the closed-loop system, such as the steady-state error, disturbance rejection, and transient response, is improved. However, increasing P-gain alone generally destabilizes the closed-loop system, and thus, the control designer also needs to increase the derivative (D) gain. To improve the control performance and guarantee stability simultaneously, P- and D-gains are sequentially increased in an iterative manner. Furthermore, if necessary, the integral (I) gain is selected to achieve the desired steady-state performance with the pre-designed PD controller. With its strong control performance, the proposed algorithm makes it easy to design PID gains and can be applicable to the fine-tuning of PID gains selected by other PID gain tuning algorithms. In addition, the stability conditions of designing PID gains are presented for linear time-invariant systems. Thus, the stability of the closed-loop system is guaranteed while separately increasing each P-, I-, and D-gain. To validate the effectiveness of the proposed algorithm, simulations for a single-link flexible robot manipulator system have been conducted.