Dinamik durum geribeslemesi ile ayrık $H_infty$ model eşleme problemi

Özet

Bu çalışmada bir ön kontrolörün eşdeğeri olan dinamik durum geribeslemesi ile ayrık $H_infty$, model eşleme probleminin doğrusal matris eşitsizlikleri yaklaşımı ile çözümü amaçlanmıştır. Ayrık $H_infty$ model eşleme problemi, ayrık $H_infty$ optimal kontrol probleminin özel bir halidir. Bu nedenle ayrık $H_infty$ optimal kontrol probleminin doğrusal matris eşitsizlikleri ile elde edilen çözümü ayrık $H_infty$, model eşleme probleminin çözülmesi için kullanılabilir. Makalede ayrık $H_infty$ model eşleme probleminin dinamik durum geribeslemesi ile çözümünün tek doğrusal matris eşitsizliğine indirgenebildiği gösterilmiş ve kontrolör tasarımı için gereken sentez teoremi ve algoritma verilmiştir.

Abstract

The model matching problem is one of the most familiar problems in the control theory. Let $T_m(z)$ and T(z) be stable and proper transfer matrices. The discrete $H_infty$ model matching problem is to find a controller transfer matrix R(z) which is stable and causal, to minimize the $H_infty$ norm of $T_m(z)$-T(z)R(z). The interpretation is this: $T_m(z)$ and T(z) are given as the model and the given system transfer matrices, respectively. Thus, the closed-loop performance T(z)R(z) approximates the desired performance Tm(z). In this paper, we consider the discrete $H_infty$ model matching problem with dynamic state feedback in the sense of $H_infty$ optimality criterion by using linear matrix inequalities approach. The main contribution could briefly be explained as to reformulate the discrete $H_infty$ model matching problem as a special discrete Ha optimal control problem in the formulation of linear matrix inequality, to derive a solvability condition for this special case and to give a design procedure for the controller of the discrete $H_infty$ model matching problem. It may be noted that the linear matrix inequality based parameterization of the controller provides the best performance of the discrete $H_infty$ model matching problem in the sense of $H_infty$, and the controller can be determined through the solution of only one linear matrix inequality.