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Boundary control of a Timoshenko beam with prescribed performance

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Abstract

This paper focuses on the boundary control of a Timoshenko beam with a tip mass in space. Compared with an Euler–Bernoulli beam model, the coupling of the Timoshenko beam’s transverse vibration and its cross-sectional rotation makes it difficult to develop the controller. The Timoshenko beam is essentially a distributed parameter system, the motion of which can be described using partial differential equations. A prescribed performance function is introduced to the boundary control strategy to guarantee the transient and steady tracking errors. By applying the proposed controller, the outputs are ultimately restricted within a small residual set, which is arbitrarily predefined, and the minimum convergence rate can be ensured. The stability of the boundary control is analyzed using the LaSalle’s invariance principle and the theoretical solutions of the Timoshenko beam model. Finally, the performance of the presented boundary controller is verified by numerical case studies.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11832005, 11772150 and 11902145) and the National Science Foundation of Jiangsu Province of China (Grant No. BK20190390).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing, 210016, Jiangsu, China

    Junteng Ma, Zhengtao Wei, Hao Wen & Dongping Jin

  2. Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing, 210014, Jiangsu, China

    Junteng Ma

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  1. Junteng Ma
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  2. Zhengtao Wei
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Correspondence to Hao Wen.

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Ma, J., Wei, Z., Wen, H. et al. Boundary control of a Timoshenko beam with prescribed performance. Acta Mech 231, 3219–3234 (2020). https://doi.org/10.1007/s00707-020-02701-y

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  • DOI: https://doi.org/10.1007/s00707-020-02701-y

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