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Technical Brief

Sliding mode control of vibration in single-degree-of-freedom fractional oscillators

[+] Author and Article Information
Jian Yuan

Institute of System Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, 264001, P.R.China
yuanjianscar@gmail.com

Youan Zhang

Institute of Technology, Yantai Nanshan University, Yantai, 265713, P.R.China
zhangya63@sina.com

Jingmao Liu

Shandong Nanshan International Flight Co., LTD, Yantai, 265713, P.R.China
liujingmao@nanshan.com.cn

Bao Shi

Institute of System Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, 264001, P.R.China
baoshi781@sohu.com

1Corresponding author.

ASME doi:10.1115/1.4036665 History: Received April 12, 2016; Revised April 02, 2017

Abstract

This paper proposes sliding mode control of vibration in three types of single-degree-of-freedom fractional oscillators: the Kelvin-Voigt type, the modified Kelvin-Voigt type and the Duffing type. The dynamical behaviors are all described by second-order differential equations involving fractional derivatives. By introducing state variables of physical significance, the differential equations of motion are transformed into non-commensurate fractional-order state equations. Fractional sliding mode surfaces are constructed and the stability of the sliding mode dynamics is proved by means of the diffusive representation and Lyapunov stability theory. Then, sliding mode control laws are designed for fractional oscillators respectively in cases where the bound of the external exciting force is known or unknown. Furthermore, sliding mode control laws for nonzero initialization case are designed. Finally, numerical simulations are carried out to validate the above control designs.

Copyright (c) 2017 by ASME
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