2132. Study on a fractional-order controllers based on best rational approximation of fractional calculus operators

Huimin Zhao1, Wu Deng2, Xinhua Yang3, Yu Xue4

1, 2, 3Software Institute, Dalian Jiaotong University, Dalian 116028, China

1, 2The State Key Laboratory of Mechanical Transmissions, Chongqing University,
Chongqing 400044, China

1, 2Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031, China

1, 2, 3Dalian Key Laboratory of Welded Structures and Its Intelligent Manufacturing Technology(IMT) of Rail Transportation Equipment, Dalian Jiaotong University, Dalian 116028, China

4Nanjing University of Information Science and Technology, Nanjing, 210044, China

2Corresponding author

E-mail: 1hm_zhao1977@126.com, 2dw7689@163.com, 312634293@qq.com, 4fukaifang@yeah.net

Received 12 March 2016; received in revised form 16 June 2016; accepted 14 July 2016

DOI https://doi.org/10.21595/jve.2016.16966

Abstract. This paper presents a rational approximation method for fractional calculus operators in the given frequency range and the error, which is based on the best rational approximation definition. The fractional integral operator is selected as an example to describe the construction of the rational approximation functions. An application case () is used to illustrate the effectiveness of the proposed method. The obtained approximation function in the frequency domain is a best rational approximation function, which can further improve the accuracy of the approximation without increasing the orders. On the basis of the presented rational approximation method, a rational approximation equation of a fractional-order PID controller is obtained. Finally, the method for analyzing the optimization and frequency characteristics of the fractional‑order controller is implemented to demonstrate the good frequency characteristic and best structure. The results from theoretical analysis and experimental verification show that the proposed method provides a new design idea for the effective application of the fractional-order PID controller in engineering.

Keywords: best rational approximation definition, fractional calculus operators, fractional‑order PID controller, model optimization.

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Cite this article

Zhao Huimin, Deng Wu, Yang Xinhua, Xue Yu Study on a fractional‑order controllers based on best rational approximation of fractional calculus operators. Journal of Vibroengineering, Vol. 18, Issue 5, 2016, p. 3412‑3424.

 

Š JVE International Ltd. Journal of Vibroengineering. Aug 2016, Vol. 18, Issue 5. ISSN 1392-8716