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A frequency-domain method for solving linear time delay systems with constant coefficients

A frequency-domain method for solving linear time delay systems with constant coefficients Abstract In an active control system, time delay will occur due to processes such as signal acquisition and transmission, calculation, and actuation. Time delay systems are usually described by delay differential equations (DDEs). Since it is hard to obtain an analytical solution to a DDE, numerical solution is of necessity. This paper presents a frequency-domain method that uses a truncated transfer function to solve a class of DDEs. The theoretical transfer function is the sum of infinite items expressed in terms of poles and residues. The basic idea is to select the dominant poles and residues to truncate the transfer function, thus ensuring the validity of the solution while improving the efficiency of calculation. Meanwhile, the guideline of selecting these poles and residues is provided. Numerical simulations of both stable and unstable delayed systems are given to verify the proposed method, and the results are presented and analysed in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

A frequency-domain method for solving linear time delay systems with constant coefficients

Jin, Mengshi; Chen, Wei; Song, Hanwen; Xu, Jian
"Acta Mechanica Sinica" , Volume 34 (4): 11 – Aug 1, 2018
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References (22)

Publisher
Springer Journals
Copyright
2018 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-018-0760-5
Publisher site
See Article on Publisher Site

Abstract

Abstract In an active control system, time delay will occur due to processes such as signal acquisition and transmission, calculation, and actuation. Time delay systems are usually described by delay differential equations (DDEs). Since it is hard to obtain an analytical solution to a DDE, numerical solution is of necessity. This paper presents a frequency-domain method that uses a truncated transfer function to solve a class of DDEs. The theoretical transfer function is the sum of infinite items expressed in terms of poles and residues. The basic idea is to select the dominant poles and residues to truncate the transfer function, thus ensuring the validity of the solution while improving the efficiency of calculation. Meanwhile, the guideline of selecting these poles and residues is provided. Numerical simulations of both stable and unstable delayed systems are given to verify the proposed method, and the results are presented and analysed in detail.

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Aug 1, 2018

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