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RESEARCH PAPERS

The Application of Shifted Legendre Polynomials to Time-Delay Systems and Parameter Identification

[+] Author and Article Information
Rong-Yeu Chang, Maw-Ling Wang

Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC

J. Dyn. Sys., Meas., Control 107(1), 79-85 (Mar 01, 1985) (7 pages) doi:10.1115/1.3140711 History: Received June 29, 1983; Online July 21, 2009

Abstract

A linear time-delay state equation is solved by the proposed shifted Legendre polynomials method. The parameter identification of such a system with time delay is also studied. The system is partitioned into several time intervals. Within a certain time interval, the state and control functions are assumed to be expressed by the shifted Legendre polynomials series. Time-delay differential equations are transformed into a series of algebraic equations of expansion coefficients. An effective algorithm is proposed to solve the time-delay system problem and to estimate the system parameters. Only a small number of leading terms of expansion coefficients is enough to get accurate results. By using such an effective computational algorithm, the calculation procedures are greatly simplified. Thus much computer time is saved.

Copyright © 1985 by ASME
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