Integrating Active Disturbance Rejection Control and Input Shaping for Enhanced Vibration Control of Warehouse Single Mast Stacker Crane

Thi Ly  Tong; Duy Canh  Nguyen; Minh Duc  Duong

doi:10.6180/jase.202511_28(11).0010

Integrating Active Disturbance Rejection Control and Input Shaping for Enhanced Vibration Control of Warehouse Single Mast Stacker Crane

Thi Ly Tong¹, Duy Canh Nguyen², and Minh Duc Duong²This email address is being protected from spambots. You need JavaScript enabled to view it.

¹Hanoi University of Industry, Hanoi, Vietnam

²Hanoi University of Science and Technology, Hanoi, Vietnam

Received: November 10, 2024
Accepted: February 17, 2025
Publication Date: March 16, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202511_28(11).0010

Warehouse single mast stacker cranes, which can reach heights of 80 meters, are becoming increasingly popular in the e-commerce sector as automated storage solutions due to their many benefits. Because stacker cranes are high and expected to move rapidly, the vibrations are inevitable. Therefore, it is essential to reduce unwanted vibrations to protect the structure and ensure precise positioning. To conduct this study, a system of partial differential equations has been developed to model the single mast stacker crane. The analysis of this model has led to a control solution that integrates Active Disturbance Rejecting Control (ADRC) with input shaping (IS) methods to provide precise positioning and vibration suppression. As demonstrated by simulation, the system is stable using the proposed control algorithm, the driving unit position is controlled precisely, and vibrations are nearly eliminated. In addition, an experimental prototype model has been developed to test the feasibility in practice, and the results indicate that the proposed controller can work effectively and be evaluated as a potential industrial solution.

Keywords: Single Mast Stacker Crane, Euler-Bernoulli beam, Active Disturbance Rejection Control, Input Shaping, Extended State Observer

[1] M. Takahashi, S. Kinoshita, H. Kato, Y. Kawasaki, and Z. Iwai, (2004) “Positioning control of a stacker crane using a robust simple adaptive control method" IFAC Proceedings Volumes 37(12): 161–166. DOI: 10.1016/S1474-6670(17)31461-1.
[2] F. He, Y. Chen, and S. Zhao. “Application of fuzzy control in the stacker crane of an AS/RS”. In: 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery. 3. IEEE. 2008, 508–512. DOI: 10.1109/FSKD.2008.177.
[3] S. Hajdu and P. Gáspár, (2014) “From modeling to ro bust control design of single-mast stacker cranes" Acta Polytechnica Hungarica 11(10): 135–149. DOI: 10.12700/APH.11.10.2014.10.8.
[4] S. Hajdu and P. Gáspár, (2017) “Robust Control of Single-Mast Stacker Cranes" Acta Polytechnica Hun garica 14: 105–119. DOI: 10.12700/APH.14.4.2017.4.6.
[5] X. M.G.Li andY. Li, (2024) “Robust Command Shaped Vibration Control for Stacker Crane Subject to Parameter Uncertainties and External Disturbances" IEEE Transac tions on Industrial Electronics 71(11): 14707–14752. DOI: 10.1109/TIE.2024.3366197.
[6] M. Bachmayer, H. Ulbrich, and J. Rudolph, (2011) “Flatness-based control of a horizontally moving erected beam with a point mass" Mathematical and Computer Modelling of Dynamical Systems 17(1): 49–69. DOI: 10.1080/13873954.2010.537517.
[7] M.S.Johannes Diwold Bernd Kolar, (2023) “Flatness Analysis for the Sampled-data Model of a Single Mast Stacker Crane" IFAC-PapersOnLine 56(1): 222–227. DOI: 10.1016/j.ifacol.2023.02.038.
[8] M. Staudecker, K. Schlacher, and R. Hansl, (2008) “Passivity based control and time optimal trajectory plan ning of a single mast stacker crane" IFAC Proceedings Volumes 41(2): 875–880. DOI: 10.3182/20080706-5 KR-1001.00150.
[9] H.RamsandM.Schöberl. “On structural invariants in the energy based control of port-Hamiltonian sys tems with second-order Hamiltonian”. In: 2017 Amer ican Control Conference (ACC). IEEE. 2017, 1139–1144. DOI: 10.23919/ACC.2017.7963106.
[10] H.Rams, M.Schöberl, and K. Schlacher, (2017) “Op timal motion planning and energy-based control of a sin gle mast stacker crane" IEEE Transactions on Control Systems Technology 26(4): 1449–1457. DOI: 10.1109/TCST.2017.2710953.
[11] J. Ismail and S. Liu. “Nonlinear model predictive control of a distributed parameter system with time varying soft constraints”. In: 2019 18th European Con trol Conference (ECC). IEEE. 2019, 2783–2788. DOI: 10.23919/ECC.2019.8795610.
[12] J. Ismail and S. Liu. “Tube-based Robust Model Pre dictive Control for a Distributed Parameter System Modeled as a Polytopic LPV”. In: 2020 American Con trol Conference (ACC). IEEE. 2020, 1998–2003. DOI: 10.23919/ACC45564.2020.9147478.
[13] J. Zhong, J. Zhang, X. Chen, D. Wang, and Y. Yuan, (2024) “RBF neural network disturbance observer based backstepping boundary vibration control for Euler Bernoulli beam model with input saturation" ISA trans actions 150: 67–76. DOI: 10.1016/j.isatra.2024.05.018.
[14] Y. Wang, W. Wu,X. Lou, and D. Görges, (2024) “Itera tive learning control of an Euler-Bernoulli beam with time varying boundary disturbance" Computers & Mathe matics with Applications 162: 145–154. DOI: 10.1016/j.camwa.2024.03.004.
[15] Y. Wang, W. Wu, X. Lou, and D. Görges, (2024) “Adaptive vibration control for stabilisation of the Euler Bernoulli beam with an unknownpayload" International Journal of Control: 1–12. DOI: 10.1080/00207179.2024.2410854.
[16] Z. Gao et al. “Scaling and bandwidth parameterization based controller tuning”. In: Acc. 4. 2003, 989–4. DOI: 10.1109/ACC.2003.1242516.
[17] J. Han, (2009) “From PID to active disturbance rejection control" IEEE transactions on Industrial Electronics 56(3): 900–906. DOI: 10.1109/TIE.2008.2011621.
[18] N. C. Singer and W. P. Seering, (1990) “Preshaping Command Inputs to Reduce System Vibration" Journal of Dynamic Systems, Measurement, and Control 112(1): 76–82. DOI: 10.1115/1.2894142.
[19] W.E.Singhose, (2009) “Command shaping for flexible systems: A review of the first 50 years" International Journal of Precision Engineering and Manufactur ing 10: 153–168. DOI: 10.1007/s12541-009-0084-2.
[20] D.-W. Lim, S.-W. Hong, S.-J. Ha, J.-H. Kim, and H.-T. Lee, (2023) “Input-shaping-based improvement in the ma chining precision of laser micromachining systems" The International Journal of Advanced Manufacturing Technology 125(9): 4415–4424. DOI: 10.1007/s00170-023-10869-5.
[21] K. Alghanim and F. Alobaid, (2024) “Comprehensive Analysis of Input Shaping Techniques for a Chain Sus pended From an Overhead Crane" Journal of Vibration and Acoustics 146(4): DOI: 10.1115/1.4066652.
[22] L. Meirovitch. Principles and techniques of vibrations. Pearson, 1996.
[23] G. Herbst, (2013) “A simulative study on active dis turbance rejection control (ADRC) as a control tool for practitioners" Electronics 2(3): 246–279. DOI: 10.3390/electronics2030246.
[24] C.-G. Kang, (2019) “Impulse vectors for input-shaping control: A mathematical tool to design and analyze input shapers" IEEE Control Systems Magazine 39(4): 40 55. DOI: 10.1109/MCS.2019.2913610.
[25] N.JiandJ.Liu.“Basic BoundaryControl of a Flexible Three-Dimensional Euler–Bernoulli Beam Based on Disturbance Observers”. In: Boundary Control of Flexi ble Three-Dimensional Euler–Bernoulli Beams. Springer, 2022, 37–64.