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Volume 11
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10.3390/electronics11213543
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Article

A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper

by
Tianlei Wang
1,†,
Jing Zhou
1,†,
Zhiqin Wu
2,
Renju Liu
1,
Jingling Zhang
1,* and
Yanyang Liang
1
1
Faculty of Intelligent Manufacturing, Wuyi University, Jiangmen 529020, China
2
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Electronics 2022, 11(21), 3543; https://doi.org/10.3390/electronics11213543
Submission received: 1 October 2022 / Revised: 19 October 2022 / Accepted: 27 October 2022 / Published: 30 October 2022
(This article belongs to the Section Systems & Control Engineering)
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Abstract

For the multi-rope structure of the container crane system and its large mass payload anti-swing positioning problem, an equivalent double-swing model based on radial spring-dampers is established and a time-varying PD sliding mode controller (TVPD-SMC) with improved transient performance is proposed. In particular, the dynamics of the container crane system are first analyzed using the Lagrange method, and an equivalent double pendulum dynamics model of the crane is established. Compared with the traditional double pendulum model, this model ensures the accuracy of modeling without measuring the second pendulum angle. On this basis, an enhanced coupled time-varying sliding mode control method is designed to eliminate the sliding mode control method’s reaching phase and improves the robustness of the controller. Finally, the convergence and stability of the closed-loop system are proved using the Lyapunov technique and the Lasalle invariance theorem, and the simulation results demonstrate the effectiveness of the method.
Keywords: container crane; anti-swing control of crane; sliding mode control; dynamics modeling; radial spring-damper container crane; anti-swing control of crane; sliding mode control; dynamics modeling; radial spring-damper

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MDPI and ACS Style

Wang, T.; Zhou, J.; Wu, Z.; Liu, R.; Zhang, J.; Liang, Y. A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper. Electronics 2022, 11, 3543. https://doi.org/10.3390/electronics11213543

AMA Style

Wang T, Zhou J, Wu Z, Liu R, Zhang J, Liang Y. A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper. Electronics. 2022; 11(21):3543. https://doi.org/10.3390/electronics11213543

Chicago/Turabian Style

Wang, Tianlei, Jing Zhou, Zhiqin Wu, Renju Liu, Jingling Zhang, and Yanyang Liang. 2022. "A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper" Electronics 11, no. 21: 3543. https://doi.org/10.3390/electronics11213543

APA Style

Wang, T., Zhou, J., Wu, Z., Liu, R., Zhang, J., & Liang, Y. (2022). A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper. Electronics, 11(21), 3543. https://doi.org/10.3390/electronics11213543

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