Open-Loop Control by Model-Matching

Abstract

The model-matching problem consists in assigning the transfer matrix of a system. Many control problems reduce to model-matching and several approaches have been developed. The model-matching can be exact when a given transfer matrix is assigned or approximate when the design is such that the transfer matrix of the controlled system gets a specified structure (as is the case for decoupling control) or gets as close as possible to a reference transfer matrix. In the latter case, the distance between the two transfers is expressed in terms of a chosen norm of the difference between the two transfer matrices like, e.g., the ||.||_∞ norm for the H_∞ control. The exact model-matching (EMM) consists in precisely assigning all entries of the transfer matrix to given transfer functions. It can be done by feedforward (pre or postcompensation) or by feedback (static or dynamic).