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Robust stabilizing regions of fractional-order PIλ controllers for fractional-order systems with time-delays

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Abstract

This study focuses on a graphical approach to determine the stabilizing regions of fractional-order PIλ(proportional integration) controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating methods of the real root boundary (RRB) curves, complex root boundary (CRB) curves and infinite root boundary (IRB) lines are investigated for a given stability degree. The stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.

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Authors and Affiliations

  1. College of Light Industry, Liaoning University, Shenyang, 110036, China

    Zhe Gao, Li-Rong Zhai & Yan-Dong Liu

  2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Li-Rong Zhai

Authors
  1. Zhe Gao
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  2. Li-Rong Zhai
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  3. Yan-Dong Liu
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Corresponding author

Correspondence to Zhe Gao.

Additional information

This work was supported by National Natural Science Foundation of China (No. 61304094).

Recommended by Associate Editor Min Wu

Zhe Gao received the B. Sc. degree from Shenyang Ligong University, China in 2006, the M. Sc. degree from Northeastern University, China in 2008, and the Ph.D. degree in control theory and control engineering from Beijing Institute of Technology, China in 2012. He is currently a lecturer at Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University, China.

His research interests include stability, control and realization for fractional-order systems.

ORCID iD: 0000-0002-7084-5426

Li-Rong Zhai received the B. Sc. degree from Dalian Polytechnic University, China in 1994, the M. Sc. degree from Northeastern University, China in 2005, and she is currently a Ph. D. degree candidate in control theory and control engineering from Northeastern University, China. She is currently a female lecturer at Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University, China.

Her main research interests include stability, control and the fault diagnosis of complex industry control systems.

Yan-Dong Liu graduated from Department of the Electrical Engineering and Automation, Liaoning University, China in 2010, and received the M. Sc. degree from Liaoning University in 2013. He is currently laboratory technician in control theory and control engineering laboratory at College of Light Industry, Liaoning University, China.

His research interests include identification and control for fractional-order systems.

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Gao, Z., Zhai, LR. & Liu, YD. Robust stabilizing regions of fractional-order PIλ controllers for fractional-order systems with time-delays. Int. J. Autom. Comput. 14, 340–349 (2017). https://doi.org/10.1007/s11633-015-0941-7

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  • DOI: https://doi.org/10.1007/s11633-015-0941-7

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