An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Abstract

In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

“…Example The second example is a microthruster unit, which is taken from [10]. The model is expressed by the heat diffusion equation.…”

“…To solve these problems, model order reduction (MOR) techniques [1,4–7] have been developed to produce a low‐dimension model that approximates the input‐output behavior of the original large‐scale system with high fidelity. However, there are many large‐scale parametric systems in engineering applications [8–10] because of significant modifications to the systems, such as geometric or material properties variations and alterations in boundary or initial conditions. For the large‐scale parametric system, the goal is to obtain a reduced parametric system that can approximate the original parametric system for every parameter value in the parameter domain without repeating the reduction procedure.…”

Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction

“…Later, Imran et al [20] presented an improvement of [11] by considering a similar effect on the eigenvalues of symmetric matrices. Some recent developments on model reduction are appeared in [21][22][23][24][25].…”

Model reduction based on limited‐time interval impulse response Gramians

“…Recently, Haider et al [14] proposed the limited-time Gramians for large-scale descriptor systems. Some recent developments on frequency band related model reduction are appeared in [16][17][18][19][20][21][22][23].…”