Constrained Optimal Pade´ Model Reduction

A frequency-domain multipoint Pade´ approximation method is given that produces optimal reduced order models, in the least integral square error sense, which are constrained to match the initial time response values of the full and reduced systems for impulse or step inputs. It is seen to overcome a perceived drawback of the unconstrained optimal models, i.e., that they do not guarantee a proper rational reduced order transfer function for a step input. The method is easy to implement when compared to existing constrained optimal methods, and consists of solving only linear sets of equations in an iterative process. It is also seen to be a natural extension of an existing optimal method. Numerical examples are given to illustrate its application.

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Transfer Function Reduction

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1976_190_068_02 ◽

1976 ◽

Vol 190 (1) ◽

pp. 643-651 ◽

Cited By ~ 1

Author(s):

R. Whalley

Keyword(s):

Transfer Function ◽

Series Expansion ◽

Laurent Series ◽

Hankel Matrix ◽

Rational Functions ◽

Reduced Form ◽

Reduced Order Models ◽

Minimum Phase ◽

Reduced Order

SYNOPSIS A method of generating reduced order models from the Laurent series expansion of a transfer function is examined by means of the Hankel Matrix and its correspondence to the field of rational functions. The approach enables particularly simple results to be derived regarding the composition of the reduced form and the avoidance of non minimum phase characteristics therein.

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Order Reduction of Discrete-Time System Via Bilinear Routh Approximation

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2896138 ◽

1990 ◽

Vol 112 (2) ◽

pp. 292-297 ◽

Cited By ~ 16

Author(s):

Chyi Hwang ◽

Ching-Shieh Hsieh

Keyword(s):

Transfer Function ◽

Approximation Method ◽

Order Reduction ◽

Reduced Order Models ◽

Discrete Time System ◽

Initial Value ◽

Time System ◽

Bilinear Transformation ◽

Reduced Order ◽

Canonical Expansion

In this paper, a method of combining the Routh approximation method with the bilinear transformation is presented for deriving stable reduced-order models of a strictly proper z-transfer function Gn(z). It is based on applying the bilinear transformation to the (z+1)Gn(z), and then deriving a new bilinear Routh γ − δ canonical expansion for Gn(z). The proposed bilinear Routh approximation method has all the advantages of the Routh approximation method [5] while without having initial-value problem caused by the bilinear transformation. A numerical example is included to illustrate the procedure.

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