Coprime factorization controller reduction using a new set of invariants

Abstract

A new controller reduction scheme using a new set of similarity invariants is proposed for LQG controller. The new set of invariants is defined by modifying the existing ones with two real constants. A modified balanced realization is suggested as a basic algorithm. Through case studies according to the two real constants, it is shown that a reduced-order controller which has good performance can be obtained by appropriately selecting only one constant. Reasonable bound for the constant is also given. The stability and performance of the closed-loop system with the reduced-order controller obtained by the proposed method are investigated. Some examples show that the proposed method is very attractive in terms both of stability and of accuracy of the closed-loop approximation. The new LQG-controller reduction scheme is extended to general types of coprime factorization controller reduction problem : non-weighted coprime factor controller reduction, constant-weighted coprime factor controller reduction, stability-weighted coprime factor controller reduction, and robustness-preserving coprime factor controller reduction. For the robustness-preserving controller reduction, robust stability conditions of the closed-loop system with a reduced-order controller are newly derived. Through a example, it is shown that the proposed coprime factor controller reduction methods using the new set of invariants yield reduced-order controllers which have both good closed-loop stability and good robustness. For general robustness problems, the relations between coprime factor perturbation and general types of structural perturbations are also derived.