On compensating internal models in regulator problems

This article 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 compensation of internal model (CIM) 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 CIM elements and the resulting equivalent plant are derived for both finite-dimensional and repetitive internal models. The complexity of the design of stabilizers is then substantially lower than in approaches based on system augmentation.