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Super Twisting Algorithm for Robust Geometric Control of a Helicopter

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Abstract

In this paper (A preliminary version of the submitted paper appeared in the Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS’20), Athens, Greece*), a robust attitude controller is proposed for a small-scale helicopter based on Multi-Variable Super Twisting Algorithm. An interconnected hybrid model of a helicopter is considered consisting of fuselage and rotor which are modeled as a single rigid body and a disc, respectively. For designing a globally defined controller, we consider that attitude dynamics evolves on non-Euclidean space. We assume that the rotor is subjected to unknown disturbances and exact information of the helicopter parameters are unavailable due to parametric uncertainty. A attitude tracking controller using Super Twisting Algorithm based on Second-Order sliding mode technique is proposed to ensure robustness in the presence of both unknown disturbance and parameter variation. A family of strong Lyapunov functions is used to show that the proposed controller drives the closed loop system to the sliding manifold in finite time. For the suitable choice of gain matrices, the reduced order error dynamics becomes almost globally asymptotically stable. We further show that the reduced order error dynamics is almost semi-globally exponentially stable if its trajectories starts from a specific subset. The rate of convergence can be adjusted as required by tuning the controller gains. Numerical simulations are carried out by comparing the proposed controller with the state-of-the art controllers available in the literature.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, India

    Akhil B. Krishna & Mangal Kothari

  2. Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, India

    Arijit Sen

Authors
  1. Akhil B. Krishna
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  2. Arijit Sen
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  3. Mangal Kothari
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Contributions

Akhil B Krishna provided the research ideas and theoretical analysis, wrote the code and the paper. Arijit Sen and Mangal Kothari worked to improve the mathematical analysis, results, and manuscript of the paper. All authors have read and agreed to publish this version of the manuscript.

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Correspondence to Akhil B. Krishna.

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Krishna, A.B., Sen, A. & Kothari, M. Super Twisting Algorithm for Robust Geometric Control of a Helicopter. J Intell Robot Syst 102, 61 (2021). https://doi.org/10.1007/s10846-021-01366-6

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  • DOI: https://doi.org/10.1007/s10846-021-01366-6

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