Regular Papers

International Journal of Control, Automation and Systems 2016; 14(1): 181-187

Published online February 11, 2016

https://doi.org/10.1007/s12555-013-0240-4

© The International Journal of Control, Automation, and Systems

A Generalized Padé Approximation of Time Delay Operator

Yiheng Wei, Yangsheng Hu, Yi Dai, and Yong Wang*

University of Science and Technology of China, Hefei

Abstract

This paper addresses the problem of fractional order Padé approximation for the time delay operator. Based on optimization method, a fitting polynomial with basic order a is constructed to approximate the time delay operator. This makes for two generalized Padé approximations in the form of normal and symmetric approximation, respectively. The advantage of the proposed method lies in the fact that the resulting approximate model is in the standard transform function form of any commensurate order a, making all of the existing stability analysis methods and control design tools for such systems amenable to the fractional order time delay systems. Some numerical examples are given to demonstrate the effectiveness of the proposed method."

Keywords Fractional order systems, Padé approximations, polynomial fitting, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2016; 14(1): 181-187

Published online February 1, 2016 https://doi.org/10.1007/s12555-013-0240-4

Copyright © The International Journal of Control, Automation, and Systems.

A Generalized Padé Approximation of Time Delay Operator

Yiheng Wei, Yangsheng Hu, Yi Dai, and Yong Wang*

University of Science and Technology of China, Hefei

Abstract

This paper addresses the problem of fractional order Padé approximation for the time delay operator. Based on optimization method, a fitting polynomial with basic order a is constructed to approximate the time delay operator. This makes for two generalized Padé approximations in the form of normal and symmetric approximation, respectively. The advantage of the proposed method lies in the fact that the resulting approximate model is in the standard transform function form of any commensurate order a, making all of the existing stability analysis methods and control design tools for such systems amenable to the fractional order time delay systems. Some numerical examples are given to demonstrate the effectiveness of the proposed method."

Keywords: Fractional order systems, Padé, approximations, polynomial fitting, time delay.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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