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A parameter formula connecting PID and ADRC

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Abstract

This paper presents a parameter formula connecting the well-known proportional-integral-derivative (PID) control and the active disturbance rejection control (ADRC). On the one hand, this formula gives a quantitative lower bound to the bandwidth of the extended state observer (ESO) used in ADRC, implying that the ESO is not necessarily of high gain. On the other hand, enlightened by the design of ADRC, a new PID tuning rule is provided, which can guarantee both strong robustness and nice tracking performance of the closed-loop systems under the PID control. Moreover, it is proved that the ESO can be rewritten as a suitable linear combination of the three terms in PID, which can give a better estimate for the system uncertainty than the single integral term in the PID controller. Theoretical results are verified also by simulations in the paper.

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Acknowledgements

This work was supported by National Key R&D Program of China (Grant No. 2018YFA0703800), National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, and National Natural Science Foundation of China (Grant No. 11688101).

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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

    Sheng Zhong, Yi Huang & Lei Guo

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Sheng Zhong, Yi Huang & Lei Guo

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  1. Sheng Zhong
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  2. Yi Huang
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  3. Lei Guo
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Correspondence to Yi Huang.

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Zhong, S., Huang, Y. & Guo, L. A parameter formula connecting PID and ADRC. Sci. China Inf. Sci. 63, 192203 (2020). https://doi.org/10.1007/s11432-019-2712-7

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  • DOI: https://doi.org/10.1007/s11432-019-2712-7

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