Calculation of Stability Region of PID Controllers for a Class of Processes with Time Delay

For a class of process with time delay,a simple and accurate method to determine the stability regions of the PID controller is presented by calculating the stability boundaries in the PID controller parameter space and examining which side of each stability boundary has less unstable poles.As long as the control parameters are tuned in the resulting stability regions,the stability of the closed-loop system can always be guaranteed. This not only establishes the basis for the PID controller design but also provides a convenient approach for its tuning.The simulation examples demonstrate the validity of the proposed method.It is appropriate for both the unstable process with time delay and the non-minimum phase processes with time delay.