A new model order reduction method for the design of compensator by using moment matching algorithm

Abstract

The aim of this paper is the construction of a new model reduction technique for large scale stable linear dynamic systems. It is principally focused on the dominant modes and time moments retention. This reduction implicates the translation of the overall important features confined in the large scale complete order model into the lower order system, allowing the computation of approximant denominator by using generalized pole clustering method. The approximant numerator is obtained by means of the factor division algorithm. As a result, a lower order system is obtained. To demonstrate its effectiveness, to highlight some fundamental of its features, and to accomplish its accuracy, a comparative study is done. Two standard numerical examples are taken, where approximant model computed by the proposed method is compared with the reduced order models computed from the recently proposed methods as well as well-known model reduction schemes. The paper is also emphasized on the design of compensator by using moment matching algorithm with the help of the reduced model. The design of compensator is validated and illustrated with the help of a standard numerical example taken from the literature.

Development of Frequency Weighted Model Order Reduction Techniques for Discrete-Time One-Dimensional and Two-Dimensional Linear Systems With Error Bounds

“…The fictitious matrices are created by square-rooting eigenvalues that have identical effects on each eigenvalue of 1-D and 2-D discrete-time input and output matrices to construct stable ROMs with low truncation errors at specified frequency weights. Decomposition is performed first for the discrete-time 2-D weighted system using the minimal rankdecomposition condition as illustrated in (11,16); then, the controllability and the observability Gramians are computed based on modified associated input and output matrices for decomposed 1-D sub-systems. The proposed scheme also provides an a priori error bound expressions by using the BT and an optimal Hankel norm approximation approaches, respectively, for the 1-D and 2-D discrete-time frequency weighted systems.…”

“…The algorithms use greedy iterations to choose expansion locations and interpolate the transfer function. Similarly, another interpolation-based approach is presented in [11]. It focuses on dominated and temporal moment retention.…”

Design of suboptimal model-matching controllers using squared magnitude function for MIMO linear systems

“…The methodology in [11] applies to unstable plant TFs. Model order reduction reduce the complexity of implementation of higher integer-order systems [12,13]. A model-order reduction method has been applied to closed-loop systems with parameter variations [14].…”

A Novel Approach for Model Order Reduction in Discrete Time System

“…The Pade approximation is also adopted to get the numerator polynomial coefficient to the proposed model. Prajapati and Prasad [28] proposed a new approach based on generalized pole clustering for computing the reduced model denominator. The technique of factor division is efficient to extract the numerator polynomial value.…”