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On ADRC for non-minimum phase systems: canonical form selection and stability conditions

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Abstract

Active disturbance rejection control (ADRC), as proposed by Prof. Jingqing Han, reduces first the plant dynamics to its canonical form, normally in the form of cascade integrators, for which the standard controller can be employed to meet the design specifications. This paper concerns with the selection of the canonical form for non-minimum phase systems. In particular, it is shown that, by employing the well known controllable canonical form, the uncertainties of such systems can be divided into two terms in the state space model, one in the control channel and the other in the output channel. The necessary and sufficient condition is obtained for the stability of the closed-loop system with the proposed canonical form and ADRC. Also, by showing the necessity of the detectability of the extended system as well as certain information of the system-s “zeros”, we present the fundamental guidelines of design ADRC for non-minimum phase uncertain systems.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wenchao Xue & Yi Huang

  2. Department of Electrical and Computer Engineering, Cleveland State University, Cleveland, Ohio, 44115, USA

    Zhiqiang Gao

Authors
  1. Wenchao Xue
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  2. Yi Huang
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  3. Zhiqiang Gao
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Corresponding author

Correspondence to Wenchao Xue.

Additional information

This work was supported by the National Basic Research Program of China (No. 2014CB845301) and the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences.

Wenchao XUE received the B.S. degree in Applied Mathematics from Nankai University, Tianjin, China, in 2007, and the Ph.D. degree in Control Theory from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, in 2012. He is now an assistant professor of Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include active disturbance rejection control, system stability, control and filter design for nonlinear uncertain systems. E-mail: wenchaoxue@amss.ac.cn.

Yi HUANG received the Ph.D. degree in Control Theory and Its Applications from Southeast University, Nanjing, in 1995. From 1995 to 1997, she worked as a postdoctoral fellow in the Institute of Systems Science, Chinese Academy of Sciences. From 1997, she has been at the Key Laboratory Systems and Control, Chinese Academy of Sciences as an assistant professor and then associate professor and professor. Her research work is concentrated on the estimation and control of nonlinear uncertain systems. E-mail: yhuang@amss.ac.cn.

Zhiqiang GAO received the Ph.D. degree in Electrical Engineering from University of Notre Dame in 1990. He is an associate professor and the director of Center for Advanced Control Technologies, Cleveland State University. His research is focused on the principles and practice of engineering cybernetics, particularly its manifestation in active disturbance rejection control. E-mail: z.gao@ieee.org.

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Xue, W., Huang, Y. & Gao, Z. On ADRC for non-minimum phase systems: canonical form selection and stability conditions. Control Theory Technol. 14, 199–208 (2016). https://doi.org/10.1007/s11768-016-6041-6

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  • DOI: https://doi.org/10.1007/s11768-016-6041-6

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