Performance Enhancement in Double-Pendulum Overhead Crane Control: A Fixed-Time Extended State Observer-Based Approach

Hue Luu Thi

doi:10.48084/etasr.14777

Authors

Hue Luu Thi Faculty of Electrical Engineering, Electric Power University, Vietnam

Volume: 15 | Issue: 6 | Pages: 30452-30461 | December 2025 | https://doi.org/10.48084/etasr.14777

Received: 14 September | Revised: 14 October 2025, 20 October 2025, and 21 October 2025 | Accepted: 22 October 2025 | Online: 8 November 2025

Corresponding author: Hue Luu Thi

Abstract

This study presents an effective control solution for a two-Dimensional Double-pendulum Overhead Crane (2DDOC) system, which combines a fixed-time adaptive hierarchical sliding mode controller with a Fixed-Time Extended State Observer (FxT-ESO). First, the 2DDOC model is introduced. Next, the FxT-ESO is analyzed and designed for the 2DDOC system to estimate several state variables, which are difficult to measure directly with sensors, such as the swing velocities of the hook and payload. Based on the system's dynamic model, the fixed-time adaptive hierarchical sliding mode controller was designed under external disturbance conditions, utilizing the state signals provided by the FxT-ESO. The stability of the closed-loop system was analyzed and proven to be stable in fixed-time through Lyapunov stability theory. Finally, simulation scenarios are presented to demonstrate the performance and effectiveness of the proposed observer and controller.

Keywords:

double-pendulum crane, fixed-time adaptive hierarchical sliding mode controller, fixed-time extended state observer

Downloads

Download data is not yet available.

References

M. D. Duong, Q. T. Dao, and T. H. Do, "Settling Time Optimization of a Critically Damped System with Input Shaping for Vibration Suppression Control," Engineering, Technology & Applied Science Research, vol. 12, no. 5, pp. 9388–9394, Oct. 2022. DOI: https://doi.org/10.48084/etasr.5242

H. B. T. Khanh, M. H. Thi, L. T. Hue, T. L. Nguyen, and D. H. Nguyen, "Flatness-based Motion Planning and Model Predictive Control of Industrial Cranes," Engineering, Technology & Applied Science Research, vol. 14, no. 4, pp. 15141–15148, Aug. 2024. DOI: https://doi.org/10.48084/etasr.7662

H. Ouyang, X. Xu, and G. Zhang, "Energy-shaping-based nonlinear controller design for rotary cranes with double-pendulum effect considering actuator saturation," Automation in Construction, vol. 111, Mar. 2020, Art. no. 103054. DOI: https://doi.org/10.1016/j.autcon.2019.103054

M. Giacomelli, F. Padula, L. Simoni, and A. Visioli, "Simplified input-output inversion control of a double pendulum overhead crane for residual oscillations reduction," Mechatronics, vol. 56, pp. 37–47, Dec. 2018. DOI: https://doi.org/10.1016/j.mechatronics.2018.10.002

H. I. Jaafar, Z. Mohamed, M. A. Shamsudin, N. A. Mohd Subha, L. Ramli, and A. M. Abdullahi, "Model reference command shaping for vibration control of multimode flexible systems with application to a double-pendulum overhead crane," Mechanical Systems and Signal Processing, vol. 115, pp. 677–695, Jan. 2019. DOI: https://doi.org/10.1016/j.ymssp.2018.06.005

H. I. Jaafar, Z. Mohamed, M. A. Ahmad, N. A. Wahab, L. Ramli, and M. H. Shaheed, "Control of an underactuated double-pendulum overhead crane using improved model reference command shaping: Design, simulation and experiment," Mechanical Systems and Signal Processing, vol. 151, Apr. 2021, Art. no. 107358. DOI: https://doi.org/10.1016/j.ymssp.2020.107358

Y. Zhao, X. Wu, F. Li, and Y. Zhang, "Positioning and Swing Elimination Control of the Overhead Crane System with Double-Pendulum Dynamics," Journal of Vibration Engineering & Technologies, vol. 12, pp. 971–978, Jan. 2024. DOI: https://doi.org/10.1007/s42417-023-00887-8

M. Idrees, "Control of a Double-Pendulum Overhead Crane System Based on Hierarchical Sliding Mode Control Techniques," Biophysical Reviews and Letters, vol. 19, no. 4, pp. 375–390, Dec. 2024. DOI: https://doi.org/10.1142/S1793048023410023

Q. Wu, X. Wang, L. Hua, and M. Xia, "Modeling and nonlinear sliding mode controls of double pendulum cranes considering distributed mass beams, varying roped length and external disturbances," Mechanical Systems and Signal Processing, vol. 158, Sept. 2021, Art. no. 107756. DOI: https://doi.org/10.1016/j.ymssp.2021.107756

T. Wang, J. Qiu, W. Luo, and J. Zhang, "Based on the two-dimensional air resistance bridge crane anti-swing control research," Procedia Computer Science, vol. 183, pp. 175–181, Jan. 2021. DOI: https://doi.org/10.1016/j.procs.2021.02.047

B. Lu, Y. Fang, and N. Sun, "Enhanced-coupling adaptive control for double-pendulum overhead cranes with payload hoisting and lowering," Automatica, vol. 101, pp. 241–251, Mar. 2019. DOI: https://doi.org/10.1016/j.automatica.2018.12.009

X. Yao, H. Chen, Y. Liu, and Y. Dong, "Tracking approach of double pendulum cranes with variable rope lengths using sliding mode technique," ISA Transactions, vol. 136, pp. 152–161, May 2023. DOI: https://doi.org/10.1016/j.isatra.2022.11.019

M. Lei, X. Wu, Y. Zhao, and F. Li, "Output feedback control for overhead cranes subject to double-pendulum swing effects and uncertain disturbances," Transactions of the Institute of Measurement and Control, vol. 46, no. 7, pp. 1350–1361, Apr. 2024. DOI: https://doi.org/10.1177/01423312231196945

Y. Zhao, X. Wu, Y. Zhang, and L. Ke, "Lyapunov approach for the control of overhead crane systems with double-pendulum dynamics and uncertain disturbances," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 238, no. 6, pp. 1002–1012, July 2024. DOI: https://doi.org/10.1177/09596518241228331

Y. Zhang, C. Dai, and X. Wu, "Finite-time plant-parameter-free trajectory tracking control for overhead cranes with double-pendulum dynamics and uncertain disturbances," Transactions of the Institute of Measurement and Control, Dec. 2024, https://doi.org/10.1177/01423312241295579. DOI: https://doi.org/10.1177/01423312241295579

Y. Xiao, C. Zhu, W. Li, and J. Xie, "Sliding mode control for double-pendulum overhead cranes with playload swing state observation," Journal of Central South University(Science and Technology), vol. 52, no. 4, pp. 1129–1137, 2021.

M. Basin, P. Yu, and Y. Shtessel, "Finite- and fixed-time differentiators utilising HOSM techniques," IET Control Theory & Applications, vol. 11, no. 8, pp. 1144–1152, 2017. DOI: https://doi.org/10.1049/iet-cta.2016.1256

J. Ni, L. Liu, M. Chen, and C. Liu, "Fixed-Time Disturbance Observer Design for Brunovsky Systems," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 65, no. 3, pp. 341–345, Mar. 2018. DOI: https://doi.org/10.1109/TCSII.2017.2710418

B. Tian, Z. Zuo, X. Yan, and H. Wang, "A fixed-time output feedback control scheme for double integrator systems," Automatica, vol. 80, pp. 17–24, June 2017. DOI: https://doi.org/10.1016/j.automatica.2017.01.007

Y. Huang and Y. Jia, "Fixed-time consensus tracking control for second-order multi-agent systems with bounded input uncertainties via NFFTSM," IET Control Theory & Applications, vol. 11, no. 16, pp. 2900–2909, 2017. DOI: https://doi.org/10.1049/iet-cta.2017.0304

Z. Anjum, Z. Sun, and B. Chen, "Disturbance-observer-based fault-tolerant control of robotic manipulator: A fixed-time adaptive approach," IET Control Theory & Applications, vol. 18, no. 11, pp. 1398–1413, 2024. DOI: https://doi.org/10.1049/cth2.12672

W. Wang, J. Yi, D. Zhao, and D. Liu, "Design of a stable sliding-mode controller for a class of second-order underactuated systems," IEE Proceedings - Control Theory and Applications, vol. 151, no. 6, pp. 683–690, Nov. 2004. DOI: https://doi.org/10.1049/ip-cta:20040902