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A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum

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Abstract

In this paper, we propose a new class nonlinear hybrid controller (NHC) for swinging-up and stabilizing the (under-actuated) rotary inverted pendulum system. First, the swing-up controller, which drives the pendulum up towards the desired upright position, is designed based on the feedback linearization and energy control methods. Then, the modified super-twisting sliding mode control is proposed based on the new sliding surface to stabilize both the fully-actuated (the rotary arm) and under-actuated (the pendulum) state variables. In the proposed NHC, around the upright position, the stabilization controller is applied, and in different circumstances aside from the upright position, the swing-up controller is used. We show that with the proposed NHC: (i) in the swing-up stage, the pendulum is able to reach the desired upright position; and (ii) in the stabilization stage, the closed-loop rotary inverted pendulum is asymptotically stable. We demonstrate the effectiveness of the proposed NHC through extensive experiments. In particular, (i) the faster swing-up under the similar control effort is obtained, compared with the existing fuzzy logic swing-up controller; (ii) the better stabilization control performance for the convergence of the angular positions of the rotary arm and pendulum is attained and the chattering is alleviated, compared with the existing sliding mode stabilization controllers; (iii) the better stabilization control accuracy with the faster convergence time and lower peak overshoot is accomplished, compared with the existing Fuzzy-LQR controller; and (iv) the good robustness against sudden external disturbances is achieved.

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Notes

  1. For the sake of readability, we denote \(f_{\theta } := f_{\theta } \big ( \alpha ,{\dot{\alpha }},{\dot{\theta }} \big ), g_{\theta } := g_{\theta }(\alpha )\).

  2. https://drive.google.com/file/d/1UhKIVLicHaclpRv3T7ZtWOj87ozG4s6c/view.

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Acknowledgements

The authors are very grateful for the professional suggestions and comments from all reviewers, which have improved the quality of the paper.

Funding

This research was supported in part by the National Research Foundation of Korea Grant funded by the Ministry of Science and ICT (NRF-2017R1A5A1015311) and in part by Basic Science Research Program through the National Research Foundation of Korea Grant funded by the Ministry of Education (2020R1A6A1A03040570).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, South Korea

    Ngo Phong Nguyen & Hyondong Oh

  2. Department of Aerospace and Software Engineering, Gyeongsang National University, Jinju, 52828, South Korea

    Yoonsoo Kim

  3. Department of Electrical Engineering, Hanyang University, Seoul, South Korea

    Jun Moon

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  1. Ngo Phong Nguyen
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  2. Hyondong Oh
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Correspondence to Hyondong Oh or Jun Moon.

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Nguyen, N.P., Oh, H., Kim, Y. et al. A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum. Nonlinear Dyn 104, 1117–1137 (2021). https://doi.org/10.1007/s11071-021-06317-2

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