On internal model compensation for general regulator problems

The paper studies a general regulator problem with an internal model in a subset of measurement channels. It proposes a procedure to reduce the stabilization problem for an augmented system (the plant plus internal model) to an equivalent one based on a process without the internal model and having the complexity of the plant. A key idea is to introduce stable internal model compensation (IMC) elements to the controller, which are, in a sense, dual to the dead-time compensators used in the control of delay systems. Closed-form state-space expressions for such IMC elements and the resulted equivalent plant are derived. It is shown that the complexity of the resulted overall controller is lower than in approaches based on the augmented plant.