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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Notes
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.
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.
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.
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).
References
Moreno-Valenzuela, J., Aguilar-Avelar, C.: Motion Control of Underactuated Mechanical Systems. Springer, Berlin (2018)
Wu, J., Zhang, P., Meng, Q., Wang, Y.: Control of Underactuated Manipulators: Design and Optimization. Springer Nature, Berlin (2023)
Ramli, L., Mohamed, Z., Abdullahi, A.M., Jaafar, H.I., Lazim, I.M.: Control strategies for crane systems: a comprehensive review. Mech. Syst. Signal Process. 95, 1–23 (2017)
Hong, K.S., Shah, U.H.: Dynamics and Control of Industrial Cranes. Springer, Berlin (2019)
Mojallizadeh, M.R., Brogliato, B., Prieur, C.: Modeling and control of overhead cranes: a tutorial overview and perspectives. Annu. Rev. Control. 56, 100877 (2023)
Fang, Y.: Lyapunov-based control for mechanical and vision-based systems. Ph.D. thesis, Clemson University, United States (2002)
Ngo, Q.H.: Modeling and control of an container crane. Ph.D. thesis, Pusan National University, Republic of Korea (2012)
Wang, D., He, H., Liu, D.: Intelligent optimal control with critic learning for a nonlinear overhead crane system. IEEE Trans. Ind. Informat. 14(7), 2932–2940 (2018)
Ma, L., Lou, X., Wu, W., Huang, X.: Neural network-based boundary control of a gantry crane system subject to input deadzone and external disturbance. Nonlinear Dyn. 108(4), 3449–3466 (2022)
Tuan, L.A.: Neural observer and adaptive fractional-order backstep** fast-terminal sliding-mode control of RTG cranes. IEEE Trans. Ind. Electron. 68(1), 434–442 (2021)
Wen, Y., Lou, X., Wu, W., Cui, B.: Backstep** boundary control for a class of gantry crane systems. IEEE Trans. Cybern. 53(9), 5802–5814 (2023)
Huang, J., Wang, W., Zhou, J.: Adaptive control design for underactuated cranes with guaranteed transient performance: Theoretical design and experimental verification. IEEE Trans. Ind. Electron. 69(3), 2822–2832 (2022)
Zhang, S., He, X., Zhu, H.: Barrier function-based adaptive antisway control for underactuated overhead cranes. Nonlinear Dyn. 111(19), 18077–18093 (2023)
Vázquez, C., Collado, J., Fridman, L.: Control of a parametrically excited crane: a vector Lyapunov approach. IEEE Trans. Control Syst. Technol. 21(6), 2332–2340 (2013)
Qian, Y.Z., Fang, Y.C., Yang, T.: An energy-based nonlinear coupling control for offshore ship-mounted cranes. Int. J. Autom. Comput. 15(5), 570–581 (2018)
Miranda-Colorado, R.: Robust observer-based anti-swing control of 2D-crane systems with load hoisting-lowering. Nonlinear Dyn. 104(4), 3581–3596 (2021)
Lei, M., Wu, X., Zhang, Y., Ke, L.: Super-twisting disturbance-observer-based nonlinear control of the overhead crane system. Nonlinear Dyn. 111, 14015–14025 (2023)
Bartolini, G., Pisano, A., Usai, E.: Second-order sliding-mode control of container cranes. Automatica 38(10), 1783–1790 (2002)
Lee, H.H.: A new design approach for the anti-swing trajectory control of overhead cranes with high-speed hoisting. Int. J. Control 77(10), 931–940 (2004)
Ngo, Q.H., Hong, K.S.: Adaptive sliding mode control of container cranes. IET Control Theory Appl. 6(5), 662–668 (2012)
Piao, M., Kim, G.H., Shah, U.H., Hong, K.S.: Adaptive sliding mode control of a mobile harbor system. In: Proceedings of the 37th Chinese Control Conference (CCC), pp. 507–512. IEEE (2018)
Wang, T., Tan, N., Qiu, J., Yu, Y., Zhang, X., Zhai, Y., Labati, R.D., Piuri, V., Scotti, F.: Global-equivalent sliding mode control method for bridge crane. IEEE Access 9, 160372–160382 (2021)
Wang, T., Tan, N., Zhang, X., Li, G., Su, S., Zhou, J., Qiu, J., Wu, Z., Zhai, Y., Labati, R.D., Piuri, V., Scotti, F.: A time-varying sliding mode control method for distributed-mass double pendulum bridge crane with variable parameters. IEEE Access 9, 75981–75992 (2021)
Tong, S., Shi, H., Zhou, P., Xu, W., Ma, J.: Research on accurate motion control of cable crane based on variable structure sliding mode. J. Braz. Soc. Mech. Sci. Eng. 45(6), 316 (2023)
Zhang, Q., Fan, B., Wang, L., Liao, Z.: Fuzzy sliding mode control on positioning and anti-swing for overhead crane. Int. J. Precis. Eng. Manuf. 24, 1381–1390 (2023)
Tuan, L.A., Cuong, H.M., Van Trieu, P., Nho, L.C., Thuan, V.D., Anh, L.V.: Adaptive neural network sliding mode control of shipboard container cranes considering actuator backlash. Mech. Syst. Signal Process. 112, 233–250 (2018)
Ma, Z., Sun, G.: Dual terminal sliding mode control design for rigid robotic manipulator. J. Franklin Inst. 355(18), 9127–9149 (2018)
Wu, Q., Wang, X., Hua, L., **a, M.: Modeling and nonlinear sliding mode controls of double pendulum cranes considering distributed mass beams, varying roped length and external disturbances. Mech. Syst. Signal Process. 158, 107756 (2021)
Ngo, Q.H., Hong, K.S.: Sliding-mode antisway control of an offshore container crane. IEEE/ASME Trans. Mechatron. 17(2), 201–209 (2012)
Ouyang, H., Wang, J., Zhang, G., Mei, L., Deng, X.: Novel adaptive hierarchical sliding mode control for trajectory tracking and load sway rejection in double-pendulum overhead cranes. IEEE Access 7, 10353–10361 (2019)
Kim, G.H., Hong, K.S.: Adaptive sliding-mode control of an offshore container crane with unknown disturbances. IEEE/ASME Trans. Mechatron. 24(6), 2850–2861 (2019)
Saghafi Zanjani, M., Mobayen, S.: Anti-sway control of offshore crane on surface vessel using global sliding mode control. Int. J. Control 95(8), 2267–2278 (2022)
Wu, X., Xu, K., Lei, M., He, X.: Disturbance-compensation-based continuous sliding mode control for overhead cranes with disturbances. IEEE Trans. Autom. Sci. Eng. 17(4), 2182–2189 (2020)
Ngo, Q.H., Nguyen, N.P., Truong, Q.B., Kim, G.H.: Application of fuzzy moving sliding surface approach for container cranes. Int. J. Control Autom. Syst. 19, 1133–1138 (2021)
Piao, M., Shah, M.U.H., Huang, G., Hong, K.S.: Super-twisting sliding mode control of container cranes with triangle-trapezoid rope reeving system. Int. J. Control Autom. Syst. 22(1), 16–26 (2024)
Quanser Inc.: Instructor Workbook - Linear Pendulum Gantry Experiment for MATLAB®/Simulink® Users (2011)
Chen, H., Fang, Y., Sun, N.: A swing constraint guaranteed MPC algorithm for underactuated overhead cranes. IEEE/ASME Trans. Mechatron. 21(5), 2543–2555 (2016)
Zhang, S., He, X., Zhu, H., Chen, Q., Feng, Y.: Partially saturated coupled-dissipation control for underactuated overhead cranes. Mech. Syst. Signal Process. 136, 106449 (2020)
Vazquez, C., Collado, J., Fridman, L.: Super twisting control of a parametrically excited overhead crane. J. Franklin Inst. 351(4), 2283–2298 (2014)
Moreno, J.A., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control 57(4), 1035–1040 (2012)
Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, Berlin (2014)
Chen, Y., Dong, H., Lü, J., Sun, X., Guo, L.: A super-twisting-like algorithm and its application to train operation control with optimal utilization of adhesion force. IEEE Trans. Intell. Transp. Syst. 17(11), 3035–3044 (2016)
Nguyen, N.P., Oh, H., Moon, J.: Continuous nonsingular terminal sliding-mode control with integral-type sliding surface for disturbed systems: Application to attitude control for quadrotor uavs under external disturbances. IEEE Trans. Aerosp. Electron. Syst. 58(6), 5635–5660 (2022)
Mei, K., Ding, S., Yu, X.: A generalized supertwisting algorithm. IEEE Trans. Cybern. 53(6), 3951–3960 (2023)
Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)
Hu, Q., Jiang, B.: Continuous finite-time attitude control for rigid spacecraft based on angular velocity observer. IEEE Trans. Aerosp. Electron. Syst. 54(3), 1082–1092 (2018)
Datta, B.: Numerical Methods for Linear Control Systems. Academic Press, Cambridge (2004)
Hangos, K.M., Bokor, J., Szederkényi, G.: Analysis and Control of Nonlinear Process Systems. Springer Science & Business Media, Berlin (2006)
Ang, K.H., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 13(4), 559–576 (2005)
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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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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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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DOI: https://doi.org/10.1007/s11071-024-09891-3