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A Practical Guideline for Designing and Tuning Adaptive Backstepping Controllers for a Class of Second-Order Systems based on PID Similarity

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Abstract

This work proposes a practical guideline for designing and tuning adaptive backstepping control systems by leveraging the similarity with PID control laws for a class of second-order nonlinear systems. A complete set of mathematical formulations, visual aids, and a well-structured algorithm are provided to exploit the benefits of the established link. This aims at facilitating the adoption of advanced nonlinear control laws in more real-life and industrial applications while benefiting from the legacy of PID tuning rules. Furthermore, the proposed guideline allows for upgrading primitive PID controllers to more advanced nonlinear control system. The adaptive backstepping control law is formulated as a two degrees-of-freedom control law that combines the sum of a feedback PID control component and a feedforward model compensation component. The relationship between backstepping and PID gains is provided in the form of a third-order polynomial, and a simplified second-order one, with practical design algorithm and tuning guidelines. The proposed control law and tuning methodology are validated on a quadrotor unmanned aerial vehicle (UAV) system in both simulation and experimentally.

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Funding

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Ahmad Kourani and Naseem Daher. The first draft of the manuscript was written by Ahmad Kourani and all authors commented on subsequent versions of the manuscript. All authors read and approved the final manuscript.

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Authors and Affiliations

  1. Department of Mechanical Engineering, American University of Beirut, Riad El-Solh, Beirut, 1107 2020, Beirut, Lebanon

    Ahmad Kourani

  2. Department of Electrical and Computer Engineering, American University of Beirut, Riad El-Solh, Beirut, 1107 2020, Beirut, Lebanon

    Naseem Daher

Authors
  1. Ahmad Kourani
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  2. Naseem Daher
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Correspondence to Naseem Daher.

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Code availability

A related code on the implementation of the methodology presented in this work is publicly available at github.com/AUBVRL/Tune-Backstepping-Like-PID. The code is available as a MATLAB/Simulink project.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Kourani, A., Daher, N. A Practical Guideline for Designing and Tuning Adaptive Backstepping Controllers for a Class of Second-Order Systems based on PID Similarity. Int. J. Dynam. Control 10, 1829–1846 (2022). https://doi.org/10.1007/s40435-022-00922-8

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  • DOI: https://doi.org/10.1007/s40435-022-00922-8

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