Observer-Controllers forOutputRegulation: the InternalModelPrincipleRevisited

This paper addresses the design of observer-controllers that provide “robust” output regulation. By this we mean that regulation is achieved without knowledge of how the disturbances actually enter the system. While it would seem that this problem has already been settled by the internal model principle (IMP), it turns out that in its original formulation, the IMP is most directly applicable to the plant augmentation approach. In this approach, the dynamics required to achieve rejection (the “disturbance models”) are explicitly added to the plant outputs where rejection is required. Since the dynamics of the disturbance model can be measured directly, a reduced-order observer can be designed for the augmented plant, and then additional anti-windup techniques may be applied. In the alternative approach discussed in this paper, the outputs are not directly augmented with disturbance models, and in this case, the design of an output regulating observer-controller is less clear. This latter approach is based on disturbance accommodating control (DAC) and uses a disturbance model only in the observer, so that in many cases it has the same complexity as using output augmentation with a reduced-order observer. However, in the original formulation of DAC, output regulation was not guaranteed except in special cases. While formulations of the DAC approach exist that provide output regulation in the absence of modeling error, the requirements for “robust” regulation are not well known. In fact, there is some confusion surrounding the necessary multiplicity of the disturbance model when regulation is feasible at only a subset of the measurements used for control. In this paper, we provide an alternative, self-contained presentation of the internal model principle that clarifies the necessary requirements for designing DAC-type observer-controllers that achieve robust regulation. We also provide a method for constructing a DAC-type observer-controller that provides robust regulation whenever output regulation is feasible.