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Super-twisting disturbance-observer-based nonlinear control of the overhead crane system

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Abstract

In this paper, we consider the application of the disturbance observer technique and interconnection and damping assignment passivity-based control to the disturbance estimation and regulation control of underactuated overhead crane systems. In particular, based on the super-twisting sliding mode control technology, a finite time disturbance estimator is presented, which can identify uncertain disturbances exactly in finite time. Next, we obtain an equivalent system and an auxiliary control input in terms of the partial feedback linearization methodology, and a desired storage function with assigned characteristics is established. On the basis of the matching conditions, we derive the desired storage function by solving two ordinary differential equations, without necessity of solving partial differential equations. Subsequently, a novel disturbance-observer-based nonlinear controller is derived, and rigorous theoretical analysis is given to prove that all of the states of the closed-loop system asymptotically converge to the origin. Experimental tests are carried out to illustrate the disturbance estimation and regulation performance of the presented control law. In addition, to demonstrate the excellent robustness of the presented controller, a comparison study is included as well.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. Recalling that \(\frac{\partial V_d}{\partial {\varvec{q}}}=\left[ \frac{\partial V_d}{\partial q_1} ~~ \frac{\partial V_d}{\partial q_2} \right] ^{\mathrm T}\) in this paper.

  2. The lemma is the core of the forthcoming energy shaping, which obviates the need for solving the PDE of (32).

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Funding

This work was supported by the Natural Science Foundation of Zhejiang Province (LY22F030014) and the National Natural Science Foundation of China (61803339).

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  1. School of Information Science and Engineering, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Meizhen Lei, Xianqing Wu, Yibo Zhang & Liuting Ke

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  1. Meizhen Lei
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  2. Xianqing Wu
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Correspondence to Xianqing Wu.

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Lei, M., Wu, X., Zhang, Y. et al. Super-twisting disturbance-observer-based nonlinear control of the overhead crane system. Nonlinear Dyn 111, 14015–14025 (2023). https://doi.org/10.1007/s11071-023-08596-3

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  • DOI: https://doi.org/10.1007/s11071-023-08596-3

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