scholarly journals Gram matrix of a Laguerre model: application to model reduction of irrational transfer function

2005 ◽  
Vol 85 (3) ◽  
pp. 651-655 ◽  
Author(s):  
N. Tanguy ◽  
P. Bréhonnet ◽  
P. Vilbé ◽  
L.C. Calvez
Keyword(s):  
Transfer Function ◽  
Model Reduction ◽  
Gram Matrix ◽  
Model Application ◽  
Irrational Transfer Function

A Method of Model Reduction

1986 ◽  
Vol 108 (4) ◽  
pp. 368-371 ◽  
Author(s):  
Jium-Ming Lin ◽  
Kuang-Wei Han
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Model Reduction ◽  
Control Systems ◽  
Response Curve ◽  
Nonlinear Control Systems ◽  
Frequency Response Curve ◽  
Stability Boundaries ◽  
Parameter Variations ◽  
The Stability

In this brief note, the effects of model reduction on the stability boundaries of control systems with parameter variations, and the limit-cycle characteristics of nonlinear control systems are investigated. In order to reduce these effects, a method of model reduction is used which can approximate the original transfer function at S=0, S=∞, and also match some selected points on the frequency response curve of the original transfer function. Examples are given, and comparisons with the methods given in current literature are made.

A Innovation Identification Approach of Control System by Irrational (Fractional) Transfer

2016 ◽  
Vol 3 (2) ◽  
pp. 336
Author(s):  
Nguyen Quang Dung ◽  
Tran Hoang Quang Minh
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Interpolation Method ◽  
Distributed Parameter ◽  
Computationally Efficient ◽  
Transient Responses ◽  
Adaptive Controllers ◽  
Real Interpolation Method ◽  
Identification Approach ◽  
Irrational Transfer Function

<p>In this paper, an innovative algorithm of identification of control system, described by irrational transfer function with distributed parameter characteristics - with irrational components, is proposed. Algorithm is based on real interpolation method (RIM). Parameters of irrational transfer function can be identified by its experimental transient responses. Each of them can be represented by an analytic expression, table or graph. The proposed method is computationally efficient, simple and practical, as is illustrated by numerical examples. In the furure, the method can be used for tuning the controller and for direct application construction of adaptive controllers, working on the identification principle.</p>

Model Reduction of Transfer Functions Using a Dominant Root Method

1990 ◽  
Vol 112 (3) ◽  
pp. 547-554 ◽  
Author(s):  
J. E. Seem ◽  
S. A. Klein ◽  
W. A. Beckman ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Padé Approximation ◽  
Computational Effort ◽  
Pade Approximation ◽  
Bilinear Transformation ◽  
Transfer Problems

Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.

Tracking Via Feedback for Systems with Irrational Transfer Function

1971 ◽  
Vol 9 (3) ◽  
pp. 317-338 ◽  
Author(s):  
M. I. Freedman ◽  
R. Glassey
Keyword(s):  
Transfer Function ◽  
Irrational Transfer Function

scholarly journals Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

2007 ◽  
Vol 17 (4) ◽  
pp. 455-462 ◽  
Author(s):  
Abdelbaki Djouambi ◽  
Abdelfatah Charef ◽  
Alina Besançon
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Analog Circuit ◽  
Phase Error ◽  
Optimal Approximation ◽  
Fractional Systems ◽  
Systems And Control ◽  
And Control ◽  
Simple Analog ◽  
Irrational Transfer Function

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.

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