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A rational approximate method to fractional order systems

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  • Control Theory
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Abstract

This paper presents an approximate method for general fractional order dynamic systems. Firstly, a novel piecewise approximate method is proposed for fractional order integrator based on its frequency distributed mode. Based on the above method, an integer order approximation system is constructed to approximate a fractional order system. Theoretical analysis results show that the proposed method can achieve much better performance than the existing schemes for a given order in an interested frequency range. The advantage of the proposed method lies in that the resulting system are standard integer order system, which facilitates systematic stability analysis and controller synthesis in view of the well-developed linear or nonlinear system theory. Numerical simulations are presented to illustrate the effectiveness of the proposed approach in the end.

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Author information

Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, Anhui, China

    Yiheng Wei & Yong Wang

  2. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, 2600, Australia

    Qing Gao

  3. Department of Automation, North China Institute of Science and Technology, East Yanjiao, Beijing, China

    Cheng Peng

Authors
  1. Yiheng Wei
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  2. Qing Gao
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  3. Cheng Peng
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  4. Yong Wang
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Corresponding author

Correspondence to Yong Wang.

Additional information

Recommended by Associate Editor Guang-Hong Yang under the direction of Editor Zengqi Sun.

This work is supported by National Natural Science Foundation (NNSF) of China under Grants 61004017.

Yiheng Wei received his B. Eng. In Automation from Northeastern University in 2010. He is currently a Ph.D. student of Automation at the University of Science and Technology of China. His research interests include fractional order systems analysis and controller synthesis.

Qing Gao was born in Hubei province, China. He received his B. Eng. and Ph.D. degrees in Mechanical and Electrical Engineering from the University of Science and Technology of China, Hefei, China, in 2008 and 2013, respectively. He also received his Ph.D. degree in Mechatronics Engineering from the City University of Hong Kong, Kowloon, Hong Kong in 2013. Since 2014, he has been with the School of Engineering and Information Technology, University of New South Wales, Canberra at the Australian Defence Force Academy, as a postdoctoral research associate. His research interests include quantum control, intelligent systems & control, and variable structure control. Dr. Gao was the recipient of the Chinese Academy of Sciences Presidential Scholarship (Special Prize) and the Outstanding Research Thesis Award from City University of Hong Kong, both in 2013.

Cheng Peng received his Ph.D. from University of Science and Technology of China in 2007. He is now a lecture in the Department of Automation, North China Institute of Science and Technology. His research interests include vibration control, system identification.

Yong Wang received his B.S. from University of Science and Technology of China in 1982 and received his Ph.D. from Nanjing University of Aeronautics and Astronautics. Prof. Wang was the recipient of the Chinese Academy of Sciences Outstanding Instructor Scholarship in 2013. His research interests include fractional order systems and control, active vibration control and system identification.

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Wei, Y., Gao, Q., Peng, C. et al. A rational approximate method to fractional order systems. Int. J. Control Autom. Syst. 12, 1180–1186 (2014). https://doi.org/10.1007/s12555-013-0109-6

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  • DOI: https://doi.org/10.1007/s12555-013-0109-6

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