Dualization of the internal model principle in compensator and observer theory with application to repetitive and learning control

This paper reconsiders the concepts of servo compensator and disturbance observer. Both concepts make use of an internal model representing general persistent disturbances. Although the use of such a model has been well recognized to be necessary within the servo compensator concept, its role has been less understood disturbance observers. In this paper necessary and sufficient conditions for proper use of both concepts will be derived by reformulating the servo compensator and disturbance observer problem in a general standard plant. Moreover, it is shown that a robust servo compensator, stabilized by an observer-based controller using output feedback, is dual to a disturbance observer in combination with state feedback and disturbance compensation. As an illustration, the presented theory is applied to the concepts of repetitive and learning control, which turn out to be dual concepts for accommodating arbitrary periodic signals.