Stability regions of H-infinity PID parameters for model uncertainty system with time delay

In this paper a method is introduced for finding all proportional integral differential (PID) controllers that satisfy a robust performance constraint for a given transfer function of any order with time-delay by using the frequency response. The H-infinity index of additive weight uncertainty on the basis of robustness stability condition of closed loop system is first got by small gain theorem. Then, based on the boundary crossing theorem, the parameter boundaries with the expected decay ratio index of PID controller are derived. PID control method that simultaneously stabilize the system and robustly meet the performance requirements by choosing PID controllers parameter in the stability region. The proposed method avoids the complexity of stability regions of PID parameters, the closed-loop system has strong robustness for any order time-delay system with no accurate model. The simulation results demonstrate the validity of this method.