Second-order Time Delay System Stable Regions of PID Controller Parameter Based on Stability Margins

Based on the generalization of Hermite-Biehler theorem,the stable regions of proportional gain of PID(proportion integration differentiation) controller can be determined by inverse Nyquist curve of second-order object with time delay.The parameter stable regions can be determined by inequalities in the integral and differential gain plane.Thus a new approach is given to determine PID controller parameter stable regions of second-order time delay system.On this basis,for performance of stability margins,the corresponding approach of PID controller parameter stable regions is also given.The simulation examples demonstrate the validity of the proposed approach.