On the model matching approach to PID design: Analytical perspective for robust Servo/Regulator tradeoff tuning

This communication addresses the robust tuning of a One-Degree-Of-Freedom (1DOF) PID controller for both acceptable load disturbance attenuation (Regulator mode) and setpoint tracking (Servo mode) of step signals based on a First Order Plus Time Delay (FOPTD) model. This problem arises naturally from the fact that sometimes a simple PID has to deal with setpoint changes and load disturbances in the same proportion. Hence, some kind of Servo/Regulator tradeoff tuning is necessary to minimize the overall performance degradation. Based on the well-established min-max model matching theory, two different analytical approaches are compared, determining when and why they outperform one another. First, a recent design which accomplishes the tradeoff tuning by means of considering the inherent behaviour of each operating mode is revisited. Second, an IMC-like design which looks at the Servo/Regulator tradeoff problem from a Robustness/Performance point of view is presented. Simulation examples clarify the discussion and confirm the effectiveness (and the limits) of the IMC-like design.