Robust proportional-integral control

In this paper, the classical porportional-integral controller is derived by using an on-line uncertainty estimation approach. The crucial role of integral action in linearization-based controller design for uncertain and externally disturbed systems is highlighted. Specifically, the integral action is interpreted as a modeling error compensator, which induces certain robustness capabilities against external disturbances, uncertain parameters, and nonlinearities. Our approach leads to a parametrization of the controller gain and the integral time in terms of estimation and nominal closed-loop time constants. As a consequence of our results, the role of the integral time in the robustness of the closed-loop system is clarified.