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Stability Analysis of a Nonlinear PID Controller

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  • Control Theory and Applications
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Abstract

In our previous work, the authors presented an effective nonlinear proportional-integral-derivative (PID) controller by incorporating a nonlinear function. The proposed controller is based on a conventional PID control architecture, wherein a nonlinear gain is coupled in series with the integral action to scale the error. Three new tuning rules for processes represented as the first-order plus time delay (FOPTD) model were obtained by solving an optimization problem formulated to minimize three performance indices. The main feature of the proposed controller is that it preserves the numbers of tuning gains even though nonlinearity is introduced and remains easy implementation in real applications. However, due to the introduction of a nonlinear element, the stability problem of the proposed controller may be raised. This paper presents one sufficient condition in the frequency domain for the absolute stability of the nonlinear PID controller, based on circle stability theory. It is proved that the nonlinear gain used is in the sector [0, 1]. The condition of the linear block F(s) is derived for the overall feedback system to be stable. Checking the stability and the effectiveness and robustness of the feedback system for setpoint tracking are demonstrated through a set of simulation works on three processes with uncertainty.

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Authors and Affiliations

  1. Department of Mechanical Facility Control Engineering, Korea University of Technology and Education, 1600 Chungjeol-ro, Dongnam-gu, Cheonan-si, Chungcheongnam-do, Korea

    Yung-Deug Son

  2. Department of Mechatronics Engineering, Graduate School, Korea University of Technology and Education, 1600 Chungjeol-ro, Dongnam-gu, Cheonan, Chungnam, 31253, Korea

    Sang-Do Bin

  3. Department of Electrical Power and Control Engineering, Adama Science and Technology University, P.O. Box 1888, Adama, Ethiopia

    Gang-Gyoo Jin

Authors
  1. Yung-Deug Son
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  2. Sang-Do Bin
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  3. Gang-Gyoo Jin
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Correspondence to Gang-Gyoo Jin.

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This paper was supported by Education and Research promotion program of KOREATECH in 2021.

Yung-Deug Son received his B.S. degree in control and instrumentation engineering from Korea Maritime University in 1997. He was a student researcher with Tokyo Institute of Technology, Japan, in 1998, and received an M.S. degree in from Kobe University of Mercantile Ocean Electro- Mechanical, Japan, in 2001, and a Ph.D. degree from the Department of Electrical Engineering, from Pusan National University, Busan, Korea, in 2015, respectively. From 2001 to 2009, he was a Senior Research Engineer with Hyundai Heavy Industries Co., Ltd. He has been with the School of Mechanical Facility Control Engineering, Korea University of Technology and Education (KOREATECH), where he is currently an assistant professor. His research interests include power conversion, electric machine drives and intelligent control.

Sang-Do Bin received his B.S. and M.S degrees in marine engineering from Korea Maritime University, in 1983 and 2013, respectively. He is currently working toward a Ph.D. degree in the Department of Mechatronics Engineering, Korea University of Technology and Education (KOREATECH). His research interests include intelligent control and optimization using generalized predictive control algorithms.

Gang-Gyoo Jin received his B.S. degree in marine engineering from Korea Maritime University and an M.S. degree in electrical, electronic and computer engineering from Florida Institute of Technology and a Ph.D. degree in electrical, electronic and system engineering from University of Wales Cardiff, in 1977, 1985, and 1996, respectively. His research interests include intelligent control, fractal technique, and optimization using genetic algorithms.

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Son, YD., Bin, SD. & Jin, GG. Stability Analysis of a Nonlinear PID Controller. Int. J. Control Autom. Syst. 19, 3400–3408 (2021). https://doi.org/10.1007/s12555-020-0599-y

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  • DOI: https://doi.org/10.1007/s12555-020-0599-y

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