New approach to the realization of PID Controller parameter stable regions

Based on Generalization of Hermite-Biehler theorem, the stable regions of PID Controller proportional gain can be determined by inverse Nyquist plot of a given plant. In the plane of integral and differential gains, an anti-clockwise rule is proposed as a method to judge stability boundary lines. This method can quickly determine the parameter stable regions in this two-dimensional plane. Thus new approach can be applied to determine the stable regions of PID controller parameter space. The simulation examples demonstrate the validity of the proposed approach. The approach can automatically give the stable regions of the proportional gain and the three-dimensional space of the parameter stable region of the PID controller.