Stability analysis uncertain system with time delay based on stability margin

When the PID controller parameters are given, and the controlled object model parameters change in the process, it is necessary to make sure the range of parameters to keep uncertain model process robust stability. Based on the analytical form of dual-locus method, this paper has given the necessary and sufficient conditions for robust stability of time delay system under the PID control order inertia plus pure delay, and accurate the lag time τ of robust stability domain when the steady-state gain parameter k and time constant T are given. Then combined with the amplitude - phase test methods, it gives the stability domain of lag time τ which can satisfy the amplitude margin and phase margin requirements.