Fundamentals of Internal-Model-Based Control Theory

Abstract

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic rejection of disturbances is a central problem in control theory. There are essentially three different possibilities to approach the problem: tracking by dynamic inversion, adaptive tracking, tracking via internal models. Tracking by dynamic inversion consists in computing a precise initial state and a precise control input (or equivalently a reference trajectory of the state), such that, if the system is accordingly initialized and driven, its output exactly reproduces the reference signal. The computation of such control input, however, requires “perfect knowledge” of the entire trajectory which is to be tracked as well as “perfect knowledge” of the model of the plant to be controlled. Thus, this type of approach is not suitable in the presence of large uncertainties on plant parameters as well as on the reference signal. Adaptive tracking consists in tuning the parameters of a control input computed via dynamic inversion in such a way as to guarantee asymptotic convergence to zero of a tracking error. This method can successfully handle parameter uncertainties, but still presupposes the knowledge of the entire trajectory which is to be tracked (to be used in the design of the adaptation algorithm) and therefore an approach of this kind is not suited to the problem of tracking unknown trajectories. Of course, one might consider the problem of tracking a slowly