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Continuous integral-type sliding mode tracking control of under-actuated cranes: theory and experiments

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Abstract

We propose continuous integral-type sliding mode tracking control (CIT-SMTC) for a class of under-actuated gantry/bridge cranes. Compared to the available sliding-mode-based approaches for crane systems, the notable improvements of the proposed CIT-SMTC include: (i) the assurance of the soft start through the trajectory tracking control mode; (ii) the enhancement of system performance in terms of convergence time and control accuracy; (iii) the continuity of the control action; and (iv) the complete stability analysis of the overall closed-loop system. In the proposed control structure, an integral-type sliding surface is first designed such that during the sliding phase, the stability of the closed-loop system is guaranteed and the control performance of crane systems is enhanced. Then, by employing the introduced integral manifold and the super-twisting-like algorithm, the CIT-SMTC is proposed such that the states are restricted to the sliding surface in finite time and the continuous control signal is imposed. Rigorous analysis is provided to prove the stability of the overall closed-loop system. Finally, experimental results are shown to verify the superiority of the proposed CIT-SMTC.

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Data Availability

No data was used for the research in the article.

Notes

  1. We should mention that the dynamics and behaviors of gantry cranes, containing the special version known as container cranes, and bridge cranes, also referred to as overhead cranes, are mostly similar (see [3,4,5] for relevant discussions). In other words, the control structure proposed in this work can be straightforwardly implemented into gantry, bridge, overhead, or container cranes.

  2. In recent years, for under-actuated crane systems, considerable effort has been devoted to address the issues outlined in (I.i)–(I.iii) via the SMC (see [29,30,31,32,33,34,35]). However, the controllers in [29,30,31,32,33,34,35] can only partially resolve these issues and still persist several drawbacks. A detailed examination about the differences between the proposed CIT-SMTC and the works [29,30,31,32,33,34,35] is given in Remarks 8 and 9.

  3. The detailed derivation for the dynamics in (1) can be found in [3,4,5], which is omitted here to avoid the repetition.

  4. We note that further discussions regarding the remarkable features of the proposed control structure over the existing approaches can also be found in Sect. 3.4.

  5. We here note that other tracking sliding mode controllers for cranes in [30,31,32], as discussed in Remark 8, also exhibit a chattering phenomenon, due to the utilization of the discontinuous \(\textrm{sign}\) function. Hence, careful consideration is required for practical implementation with these controllers. Besides, the continuous sliding mode controllers for cranes in [33,34,35] cannot be implemented for comparison purposes since they do not allow cranes to operate in the trajectory tracking mode (see also Remark 9).

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Funding

This research was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A1A03040570), and in part by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (RS-2024-00422103).

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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 Electrical Engineering, Hanyang University, Seoul, South Korea

    Jun Moon

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Contributions

Conceptualization: N.P.N; Methodology: N.P.N; Formal analysis and investigation: N.P.N; Writing - original draft preparation: N.P.N; Writing - review and editing: H.O and J.M; Funding acquisition: H.O and J.M; Supervision: H.O and J.M; Validation: H.O and J.M.

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Correspondence to Hyondong Oh or Jun Moon.

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Nguyen, N.P., Oh, H. & Moon, J. Continuous integral-type sliding mode tracking control of under-actuated cranes: theory and experiments. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09891-3

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