A multiple controller structure and design strategy with stability analysis

Abstract

This paper proposes a multi-controller structure for a plant and develops associated stability results. The main theoretical result of the paper is a quite simple necessary and sufficient condition for the closed-loop stability of the scheme. The result also specializes as a multi-controller generalization of the single controller Youla-Kucera theory for the class of all stabilizing controllers for a plant, and to known results concerning simultaneous stabilization. The plants considered are recursively expressed in terms of a set of approximations of frequency-shaped plant-model errors. The controllers in successive loops can be designed based on increasing refinement in model approximation, perhaps via on-line identification. An advantage of the proposed multi-controller strategy is that a number of various controller design techniques can be employed to achieve performance objectives which are not conveniently achievable by any one technique. A design example is included with first an LQG design applied for stabilization of a crude nominal model, and then an H ∞ optimal design, and finally an H 2 optimal design. The latter two designs are aimed at enhancing H ∞ H 2 performances. There could even be a further adaptive loop for on-line performance enhancement.