Robust Stability Regions of PID Parameters for Uncertainty Systems with Time Delay Using D-partition Technique ⋆

In this paper, a method is introduced for finding gains for all proportional integral derivation (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 robust stability condition of closed loop system is first get 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. The system can be stabilized 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 robust for any order time-delay system with no accurate model. The simulation results demonstrate the validity of this method.