Wavelet Neural Network-Based Controller Design for Magnetic Levitation System

Authors

  • Abdulla Ibrahim Abdulla Ninevah University
  • Mohammed Qasim University of Ninevah
  • Mohammed Almaged Ninevah University

DOI:

https://doi.org/10.18196/jrc.v6i3.26237

Keywords:

Wavelet Neural Network, Magnetic Levitation System, Fick's Law Algorithm, External Disturbances, Parameter Uncertainties

Abstract

The magnetic levitation system (MLS) poses a substantial control challenge owing to its intrinsic instability and pronounced nonlinear dynamics. The implementation of robust control methodologies is imperative to guarantee stable operational performance, particularly in environments characterized by external disturbances and parametric uncertainties. This study investigates the development of a PID-like control strategy for a magnetic levitation system (MLS), employing WNN architecture. The parameters of the proposed controller are optimized by employing Fick's Law Algorithm (FLA). The optimization process utilizes a cost function that comprises a weighted sum of the Integral Time-weighted Square Error (ITSE), Integral Time-weighted Absolute Error (ITAE), maximum overshoot (MO), and minimum undershoot (MU). This multi-objective cost function enables a comprehensive evaluation of the controller's performance across various criteria. A square wave reference signal is employed to conduct the optimization process, presenting a challenging test case for control system performance due to its abrupt transitions. The efficacy of the proposed controller is evaluated through a comparative analysis with a conventional PID controller. Comparative simulations are conducted employing three distinct reference trajectories: step, sinusoidal, and square waves. These diverse trajectories provide a comprehensive evaluation of the controller's performance. To assess the robustness of the proposed controller, simulations are conducted within the MATLAB/Simulink environment, subjecting the MLS model to both external disturbances and parametric uncertainties. The developed controller exhibits superior performance and robustness characteristics in comparison to the conventional PID controller. It effectively attenuates the detrimental impact of both parametric uncertainties and external disturbances, while concurrently maintaining a high degree of performance accuracy in terms of overshoot, steady-state error, and energy consumption.

References

M. Jastrzębski and J. Kabziński, “Adaptive control of magnetic levitation system based on fuzzy inversion,” Scientific Reports, vol. 14, no. 1, Oct. 2024, doi: 10.1038/s41598-024-76067-9.

Z. Deng, L. Wang, H. Li, J. Li, H. Wang, and J. Yu, “Dynamic Studies of the HTS Maglev Transit System,” IEEE Transactions on Applied Superconductivity, vol. 31, no. 5, pp. 1–5, Aug. 2021, doi: 10.1109/tasc.2021.3052452.

I. Iswanto and A. Ma’arif, “Robust Integral State Feedback Using Coefficient Diagram in Magnetic Levitation System,” IEEE Access, vol. 8, pp. 57003–57011, 2020, doi: 10.1109/access.2020.2981840.

S. R. Dabbagh, M. M. Alseed, M. Saadat, M. Sitti, and S. Tasoglu, “Biomedical Applications of Magnetic Levitation,” Advanced NanoBiomed Research, vol. 2, no. 3, Dec. 2021, doi: 10.1002/anbr.202100103.

J. Xie, P. Zhao, C. Zhang, J. Fu, and L.-S. Turng, “Current state of magnetic levitation and its applications in polymers: A review,” Sensors and Actuators B: Chemical, vol. 333, p. 129533, Apr. 2021, doi: 10.1016/j.snb.2021.129533.

L. Zhou and J. Wu, “Magnetic Levitation Technology for Precision Motion Systems: A Review and Future Perspectives,” International Journal of Automation Technology, vol. 16, no. 4, pp. 386–402, Jul. 2022, doi: 10.20965/ijat.2022.p0386.

S. Ge et al., “Magnetic Levitation in Chemistry, Materials Science, and Biochemistry,” Angewandte Chemie International Edition, vol. 59, no. 41, pp. 17810–17855, Aug. 2020, doi: 10.1002/anie.201903391.

P. Carneiro et al., “Electromagnetic energy harvesting using magnetic levitation architectures: A review,” Applied Energy, vol. 260, p. 114191, Feb. 2020, doi: 10.1016/j.apenergy.2019.114191.

B. Karakuzu et al., “Magnetic levitation-based miniaturized technologies for advanced diagnostics,” Emergent Materials, Jul. 2024, doi: 10.1007/s42247-024-00762-6.

T. Halawa, “Numerical and Experimental Investigation of the Performance of a Vertical Axis Wind Turbine Based on the Magnetic Levitation Concept,” Journal of Energy Resources Technology, vol. 144, no. 9, Feb. 2022, doi: 10.1115/1.4053577.

M. Fekry and S. Yoshida, “Aeroelastic numerical simulation of a magnetically levitated horizontal axis wind turbine,” Sustainable Energy Technologies and Assessments, vol. 43, p. 100899, Feb. 2021, doi: 10.1016/j.seta.2020.100899.

Y. Liu, K. Fan, and Q. Ouyang, “Intelligent Traction Control Method Based on Model Predictive Fuzzy PID Control and Online Optimization for Permanent Magnetic Maglev Trains,” IEEE Access, vol. 9, pp. 29032–29046, 2021, doi: 10.1109/access.2021.3059443.

Y. Xu, K. Fan, Q. Hu, and X. Zhang, “Positioning of Suspended Permanent Magnet Maglev Trains Using Satellite–Ground Multisensor Fusion,” IEEE Sensors Journal, vol. 24, no. 10, pp. 16816–16825, May 2024, doi: 10.1109/jsen.2024.3384699.

Y. Jiang, Y. Deng, P. Zhu, M. Yang, and F. Zhou, “Optimization on Size of Halbach Array Permanent Magnets for Magnetic Levitation System for Permanent Magnet Maglev Train,” IEEE Access, vol. 9, pp. 44989–45000, 2021, doi: 10.1109/access.2021.3058124.

M. M. Alseed, S. Rahmani Dabbagh, P. Zhao, O. Ozcan, and S. Tasoglu, “Portable magnetic levitation technologies,” Advanced Optical Technologies, vol. 10, no. 2, pp. 109–121, Apr. 2021, doi: 10.1515/aot-2021-0010.

D. K. Supreeth, S. I. Bekinal, S. R. Chandranna, and M. Doddamani, “A Review of Superconducting Magnetic Bearings and Their Application,” IEEE Transactions on Applied Superconductivity, vol. 32, no. 3, pp. 1–15, Apr. 2022, doi: 10.1109/tasc.2022.3156813.

S. Zheng and C. Wang, “Rotor Balancing for Magnetically Levitated TMPs Integrated With Vibration Self-Sensing of Magnetic Bearings,” IEEE/ASME Transactions on Mechatronics, vol. 26, no. 6, pp. 3031–3039, Dec. 2021, doi: 10.1109/tmech.2021.3051372.

R. Bonetti, D. Bortis, L. Beglinger, and J. W. Kolar, “Exploring the Physical Limits of Axial Magnetic Bearings Featuring Extremely Large Vertical Levitation Distances,” IEEE Transactions on Industry Applications, vol. 57, no. 6, pp. 6931–6943, Nov. 2021, doi: 10.1109/tia.2021.3096170.

S. Dey, S. Banerjee, and J. Dey, “Practical Application of Fractional-Order PID Controller based on Evolutionary Optimization Approach for a Magnetic Levitation System,” IETE Journal of Research, vol. 69, no. 11, pp. 8168–8192, Mar. 2022, doi: 10.1080/03772063.2022.2052983.

C. Lyu, C. Zhang, D. Tang, and P. Zhao, “Magnetic Levitation in Medicine and Bioengineering,” Magnetic Levitation, pp. 163–179, 2024, doi: 10.1007/978-981-99-8314-8_9.

Q. Chen, Y. Tan, J. Li, and I. Mareels, “Decentralized PID Control Design for Magnetic Levitation Systems Using Extremum Seeking,” IEEE Access, vol. 6, pp. 3059–3067, 2018, doi: 10.1109/access.2017.2787052.

A. Ghosh, T. Rakesh Krishnan, P. Tejaswy, A. Mandal, J. K. Pradhan, and S. Ranasingh, “Design and implementation of a 2-DOF PID compensation for magnetic levitation systems,” ISA Transactions, vol. 53, no. 4, pp. 1216–1222, Jul. 2014, doi: 10.1016/j.isatra.2014.05.015.

A. Mughees and S. A. Mohsin, “Design and Control of Magnetic Levitation System by Optimizing Fractional Order PID Controller Using Ant Colony Optimization Algorithm,” IEEE Access, vol. 8, pp. 116704–116723, 2020, doi: 10.1109/access.2020.3004025.

M. Qasim, A. I. Abdulla, and A. B. Ayoub, " Design of a Robust Component-wise Sliding Mode Controller for a Two-Link Manipulator," Journal of Robotics and Control (JRC), vol. 6, no. 2, pp. 527–534, doi: 10.18196/jrc.v6i2.25632.

B. Oppeneiger et al., “Model predictive control of a magnetic levitation system with prescribed output tracking performance,” Control Engineering Practice, vol. 151, p. 106018, Oct. 2024, doi: 10.1016/j.conengprac.2024.106018.

M. Qasim, A. B. Ayoub, and A. I. Abdulla, “NMPC Based-Trajectory Tracking and Obstacle Avoidance for Mobile Robots,” International Journal of Robotics and Control Systems, vol. 4, no. 4, pp. 2026–2040, Nov. 2024, doi: 10.31763/ijrcs.v4i4.1605.

W. Hu, Y. Zhou, Z. Zhang, and H. Fujita, “Model Predictive Control for Hybrid Levitation Systems of Maglev Trains With State Constraints,” IEEE Transactions on Vehicular Technology, vol. 70, no. 10, pp. 9972–9985, Oct. 2021, doi: 10.1109/tvt.2021.3110133.

W. Hu, Y. Zhou, Z. Zhang, and H. Fujita, “Model Predictive Control for Hybrid Levitation Systems of Maglev Trains With State Constraints,” IEEE Transactions on Vehicular Technology, vol. 70, no. 10, pp. 9972–9985, Oct. 2021, doi: 10.1109/tvt.2021.3110133.

O. Y. Ismael, M. Almaged, and A. I. Abdulla, “Nonlinear Model Predictive Control-based Collision Avoidance for Mobile Robot,” Journal of Robotics and Control (JRC), vol. 5, no. 1, pp. 142–151, Jan. 2024, doi: 10.18196/jrc.v5i1.20615

M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Comparison of Controller Performance for UGV-Landing Platform Self-Leveling,” 2020 28th Mediterranean Conference on Control and Automation (MED), Sep. 2020, doi: 10.1109/med48518.2020.9182837.

M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Passivity-Based Adaptive Controller for Dynamic Self-Leveling of a Custom-Built Landing Platform on Top of a UGV,” 2020 28th Mediterranean Conference on Control and Automation (MED), Sep. 2020, doi: 10.1109/med48518.2020.9182807.

M. Qasim and O. Y. Ismael, “Shared Control of a Robot Arm Using BCI and Computer Vision,” Journal Européen des Systèmes Automatisés, vol. 55, no. 1, pp. 139–146, Feb. 2022, doi: 10.18280/jesa.550115.

M. N. Noaman, M. Qasim, and O. Y. Ismael, "Landmarks exploration algorithm for mobile robot indoor localization using VISION sensor," Journal of Engineering Science & Technology, vol. 16, no. 4, pp. 3165-3184, 2021.

J. Zhang, X. Wang, and X. Shao, “Design and Real-Time Implementation of Takagi–Sugeno Fuzzy Controller for Magnetic Levitation Ball System,” IEEE Access, vol. 8, pp. 38221–38228, 2020, doi: 10.1109/access.2020.2971631.

D. Zhang, Y. Sun, N. Jia, J. Xu, and W. Sun, “Adaptive Fuzzy Super-twisting Sliding Mode Control for the Multi-electromagnets Levitation System of Maglev Vehicles: Design and Experiments,” IEEE Transactions on Intelligent Vehicles, pp. 1–11, 2024, doi: 10.1109/tiv.2024.3463632.

M. Abdollahzadeh and M. Pourgholi, “Adaptive fuzzy sliding mode control of magnetic levitation system based on Interval Type-2 Fuzzy Neural Network Identification with an Extended Kalman–Bucy filter,” Engineering Applications of Artificial Intelligence, vol. 130, p. 107645, Apr. 2024, doi: 10.1016/j.engappai.2023.107645.

J. de J. Rubio et al., “Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process,” Information Sciences, vol. 569, pp. 669–686, Aug. 2021, doi: 10.1016/j.ins.2021.05.018.

H. Chi, F. Meng, H. Chen, and Y. Zhang, “H-infinity Optimal Performance Design of Maglev Control System based on Bode Integral Constraint,” 2022 IEEE 6th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), pp. 1423–1430, Oct. 2022, doi: 10.1109/iaeac54830.2022.9930067.

J. Jose and S. J. Mija, “Design of H∞ Controller for Magnetic Levitation Systems,” 2020 First IEEE International Conference on Measurement, Instrumentation, Control and Automation (ICMICA), pp. 1–6, Jun. 2020, doi: 10.1109/icmica48462.2020.9242769.

O. Y. Ismael, M. Qasim, and M. N. Noaman, “Equilibrium Optimizer-Based Robust Sliding Mode Control of Magnetic Levitation System,” Journal Européen des Systèmes Automatisés, vol. 54, no. 1, pp. 131–138, Feb. 2021, doi: 10.18280/jesa.540115.

J. Wang, L. Zhao, and L. Yu, “Adaptive Terminal Sliding Mode Control for Magnetic Levitation Systems With Enhanced Disturbance Compensation,” IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 756–766, Jan. 2021, doi: 10.1109/tie.2020.2975487.

W. Wang, G. Yang, J. Yan, H. Ge, and P. Zhi, “Magnetic levitation planar motor and its adaptive contraction backstepping control for logistics system,” Advances in Mechanical Engineering, vol. 13, no. 3, Mar. 2021, doi: 10.1177/16878140211004782.

M. Wang, Z. Hao, Y. He, S. Zeng, Z. Qi, and P. Liu, “Active Disturbance Rejection Backstepping Cross-Coupling Controller Design for a Magnetic Levitation Vehicle Suspension Frame,” IEEE Transactions on Transportation Electrification, pp. 1–1, 2024, doi: 10.1109/tte.2024.3467711.

D. Wang, F. Meng, and S. Meng, “Linearization Method of Nonlinear Magnetic Levitation System,” Mathematical Problems in Engineering, vol. 2020, pp. 1–5, Jun. 2020, doi: 10.1155/2020/9873651.

B. Mansi, S. Nachiket, A. Sheikh, K. Sunny, and F. Kazi, “Parameter Estimator based Feedback Linearization Control strategy of Magnetic Levitation System,” 2021 31st Australasian Universities Power Engineering Conference (AUPEC), pp. 1–6, Sep. 2021, doi: 10.1109/aupec52110.2021.9597715.

O. Y. Ismael, M. Qasim, M. N. Noaman, and A. Kurniawan, “Salp Swarm Algorithm-Based Nonlinear Robust Control of Magnetic Levitation System Using Feedback Linearization Approach,” Proceedings of the 3rd International Conference on Electronics, Communications and Control Engineering, Apr. 2020, doi: 10.1145/3396730.3396734.

A. Fatemimoghadam, H. Toshani, and M. Manthouri, “Control of magnetic levitation system using recurrent neural network-based adaptive optimal backstepping strategy,” Transactions of the Institute of Measurement and Control, vol. 42, no. 13, pp. 2382–2395, Apr. 2020, doi: 10.1177/0142331220911821.

Y. Zheng and H.-J. Ahn, “Improvement of the Transient Levitation Response of a Magnetic Levitation System Using Hybrid Fuzzy and Artificial Neural Network Control,” International Journal of Precision Engineering and Manufacturing, Nov. 2024, doi: 10.1007/s12541-024-01173-7.

T. N. Truong, A. T. Vo, and H.-J. Kang, “Implementation of an Adaptive Neural Terminal Sliding Mode for Tracking Control of Magnetic Levitation Systems,” IEEE Access, vol. 8, pp. 206931–206941, 2020, doi: 10.1109/access.2020.3036010.

W. Yang, F. Meng, S. Meng, S. Man, and A. Pang, “Tracking Control of Magnetic Levitation System Using Model-Free RBF Neural Network Design,” IEEE Access, vol. 8, pp. 204563–204572, 2020, doi: 10.1109/access.2020.3037352.

T. Peng, H. Peng, and T. Kang, “RBF-ARX model-based trust region nonlinear model predictive control and its application on magnetic levitation ball system,” Nonlinear Dynamics, vol. 113, no. 3, pp. 2521–2543, Sep. 2024, doi: 10.1007/s11071-024-10342-2.

Y. Qin, H. Peng, F. Zhou, X. Zeng, and J. Wu, “Nonlinear modeling and control approach to magnetic levitation ball system using functional weight RBF network-based state-dependent ARX model,” Journal of the Franklin Institute, vol. 352, no. 10, pp. 4309–4338, Oct. 2015, doi: 10.1016/j.jfranklin.2015.06.014.

Y. Sun, J. Xu, H. Qiang, C. Chen, and G. Lin, “Adaptive sliding mode control of maglev system based on RBF neural network minimum parameter learning method,” Measurement, vol. 141, pp. 217–226, Jul. 2019, doi: 10.1016/j.measurement.2019.03.006.

B. Kumar, S. K. Swain, S. K. Mishra, Y. K. Singh, and S. Ghosh, “Radial Basis Function-based Adaptive Gain Super-Twisting Controller for Magnetic Levitation System with Time-Varying External Disturbance,” IEEE Transactions on Transportation Electrification, vol. 10, no. 4, pp. 9121-9132, 2024, doi: 10.1109/tte.2024.3354795.

Y. Sun, J. Xu, G. Lin, and N. Sun, “Adaptive neural network control for maglev vehicle systems with time-varying mass and external disturbance,” Neural Computing and Applications, vol. 35, no. 17, pp. 12361–12372, Mar. 2021, doi: 10.1007/s00521-021-05874-2.

Y. Xiao, X. Wang, Y. Zhao, and W. Liu, “Research on Dynamic Control Method of Loom Spindle Braking System Based on Fuzzy Neural Network,” IEEE Access, vol. 10, pp. 116723–116734, 2022, doi: 10.1109/access.2022.3219211.

Z. Ma, Z. Zhang, and X. Cai, “Robust adaptive control of voltage-type MLS based on wavelet neural network,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 9213–9218, 2020, doi: 10.1016/j.ifacol.2020.12.2194.

S.-Y. Chen, Y.-C. Hung, Y.-H. Hung, and C.-H. Wu, “Application of a recurrent wavelet fuzzy-neural network in the positioning control of a magnetic-bearing mechanism,” Computers & Electrical Engineering, vol. 54, pp. 147–158, Aug. 2016, doi: 10.1016/j.compeleceng.2015.11.022.

F. A. Hashim, R. R. Mostafa, A. G. Hussien, S. Mirjalili, and K. M. Sallam, “Fick’s Law Algorithm: A physical law-based algorithm for numerical optimization,” Knowledge-Based Systems, vol. 260, p. 110146, Jan. 2023, doi: 10.1016/j.knosys.2022.110146.

O. Y. Ismael, M. N. Noaman, and I. K. Abdullah, "Fick’s Law Algorithm Based-Nonlinear Model Predictive Control of Twin Rotor MIMO System," Journal of Robotics and Control (JRC), vol. 5, no. 3, pp. 694–705, 2024, doi: 10.18196/jrc.v5i3.21725.

K. H. Khalil and J. W. Grizzle, Nonlinear Systems. Upper Saddle River, NJ, USA: Prentice Hall, 2002.

Downloads

Published

2025-05-17

Issue

Vol. 6 No. 3 (2025)

Section

Articles

License

Copyright (c) 2025 Abdulla Ibrahim Abdulla, Mohammed Qasim, Mohammed Almaged

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Authors who publish with this journal agree to the following terms: 

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

 

This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:

  1. Share – copy and redistribute the material in any medium or format.
  2. Adapt – remix, transform, and build upon the material for any purpose, even comercially.

The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:

  1. Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  2. ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  3. No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

 

• Creative Commons Attribution-ShareAlike (CC BY-SA)

Creative Commons License
JRC is licensed under an International License