Exact observer-based structures for arbitrary compensators

Abstract

In this paper, some new techniques for determining the observer-based or LQG form of any compensator with arbitrary order are discussed. The practical appeal of such techniques is that they allow for a simplified implementation and reduced memory storage of general controllers and offer additional flexibility for handling gain-scheduling and input saturation constraints as compensator states become meaningful variables. The derived observed-based controllers are input–output equivalent to the original controller but with an explicit separated estimation/control structure. Such structures involve both static control and estimation gains with an extra Youla parameter that can be either static or dynamic. The proposed techniques are applicable both in continuous and discrete time, to full-order controllers, that is, controllers whose order is the same as the plant's order but also to augmented- and reduced-order controllers whose orders are greater or smaller, respectively. Necessary conditions to apply this general controller equivalence principle are derived. The interest and practicality of such techniques are then investigated with regards to the LQG implementation of H∞ and μ controllers, classes or controllers that do not generally enjoy ease of implementations. Copyright © 1999 John Wiley & Sons, Ltd.