Realization of PID Controller Parameter Stable Regions for Time Delay Systems

Based on generalization of the Hermite-Biehler theorem, the stable regions of proportional gain of PID Controller can be determined by the inverse Nyquist plot of the time delay plant. In the integral and differential gain plane, an anti-clockwise rule of judgment method is proposed for more than a boundary line. It may quickly determine the parameter stable regions in this two-dimensional plane. Thus a new approach is given to determine the stable regions of PID controller parameter space for time delay systems. The given algorithm is suitable for software realization. The simulation examples demonstrate the validity of the proposed algorithm.