IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i19p4040-d1246191.html
   My bibliography  Save this article

Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System

Author

Listed:
  • Moayed Almobaied

    (Electrical Engineering Department, Islamic University of Gaza, Gaza 108, Palestine)

  • Hassan S. Al-Nahhal

    (Electrical Engineering Department, Islamic University of Gaza, Gaza 108, Palestine)

  • Orlando Arrieta

    (Instituto de Investigaciones en Ingeniería, Facultad de Ingeniería, Universidad de Costa Rica, San Jose 11501-2060, Costa Rica
    Departament de Telecomunicació i d’Enginyeria de Sistemes, Escola d’Enginyeria, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain)

  • Ramon Vilanova

    (Departament de Telecomunicació i d’Enginyeria de Sistemes, Escola d’Enginyeria, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain)

Abstract

This study focuses on the design of a robust PD gain-scheduling controller (PD-GS-C) for an unstable SISO (single-input, single-output) magnetic levitation system with two electromagnets (MLS2EM). Magnetic levitation systems offer various advantages, including friction-free, reliable, fast, and cost-effective operations. However, due to their unstable and highly nonlinear nature, these systems require sophisticated feedback control techniques to ensure optimal performance and functionality. To address these challenges, in this study, we derive the nonlinear state-space mathematical model of the MLS2EM and linearize it around five different operating points. The PD-GS-C controller aims to stabilize the system and improve steady-state control error. The strategy for obtaining the PD controller gains involves a parameter space technique, which specifies performance requirements. This technique results in ranges of proportional ( K P ) and derivative ( K D ) gains that are used by the PD-GS-C structure. To optimize the controller’s performance further, we utilize the big bang–big crunch optimization technique (BB-BC) to determine the optimal PD gains within the specified ranges. The optimization process focuses on achieving optimal performance in terms of a specific performance index function. This function quantifies the system’s time-domain step response criteria, which include minimizing overshoot percentage, settling time, and rising time. The index function is inversely proportional to the desired performance criteria, meaning that the goal is to maximize the index function to optimize the system’s performance. To validate the effectiveness and viability of the proposed strategy, we conducts MATLAB simulations and real-time experiments. The simulations and experimental findings serve to demonstrate the controller’s performance and verify its capabilities in stabilizing the MLS2EM magnetic levitation system.

Suggested Citation

  • Moayed Almobaied & Hassan S. Al-Nahhal & Orlando Arrieta & Ramon Vilanova, 2023. "Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4040-:d:1246191
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/19/4040/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/19/4040/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. N. F. Al-Muthairi & M. Zribi, 2004. "Sliding mode control of a magnetic levitation system," Mathematical Problems in Engineering, Hindawi, vol. 2004, pages 1-15, January.
    2. Bianchi, F.D. & Sánchez-Peña, R.S. & Guadayol, M., 2012. "Gain scheduled control based on high fidelity local wind turbine models," Renewable Energy, Elsevier, vol. 37(1), pages 233-240.
    3. Dounis, Anastasios I. & Kofinas, Panagiotis & Alafodimos, Constantine & Tseles, Dimitrios, 2013. "Adaptive fuzzy gain scheduling PID controller for maximum power point tracking of photovoltaic system," Renewable Energy, Elsevier, vol. 60(C), pages 202-214.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sales-Setién, Ester & Peñarrocha-Alós, Ignacio, 2020. "Robust estimation and diagnosis of wind turbine pitch misalignments at a wind farm level," Renewable Energy, Elsevier, vol. 146(C), pages 1746-1765.
    2. Moradi, Hamed & Vossoughi, Gholamreza, 2015. "Robust control of the variable speed wind turbines in the presence of uncertainties: A comparison between H∞ and PID controllers," Energy, Elsevier, vol. 90(P2), pages 1508-1521.
    3. Guerrero-Rodríguez, N.F. & Rey-Boué, Alexis B. & Herrero-de Lucas, Luis C. & Martinez-Rodrigo, Fernando, 2015. "Control and synchronization algorithms for a grid-connected photovoltaic system under harmonic distortions, frequency variations and unbalances," Renewable Energy, Elsevier, vol. 80(C), pages 380-395.
    4. Chettibi, N. & Mellit, A., 2018. "Intelligent control strategy for a grid connected PV/SOFC/BESS energy generation system," Energy, Elsevier, vol. 147(C), pages 239-262.
    5. Kostas Bavarinos & Anastasios Dounis & Panagiotis Kofinas, 2021. "Maximum Power Point Tracking Based on Reinforcement Learning Using Evolutionary Optimization Algorithms," Energies, MDPI, vol. 14(2), pages 1-23, January.
    6. Kofinas, P. & Doltsinis, S. & Dounis, A.I. & Vouros, G.A., 2017. "A reinforcement learning approach for MPPT control method of photovoltaic sources," Renewable Energy, Elsevier, vol. 108(C), pages 461-473.
    7. Saud Alotaibi & Ahmed Darwish, 2021. "Modular Multilevel Converters for Large-Scale Grid-Connected Photovoltaic Systems: A Review," Energies, MDPI, vol. 14(19), pages 1-30, September.
    8. Wu, Zhenlong & Li, Donghai & Xue, Yali & Chen, YangQuan, 2019. "Gain scheduling design based on active disturbance rejection control for thermal power plant under full operating conditions," Energy, Elsevier, vol. 185(C), pages 744-762.
    9. Chun-Liang Liu & Jing-Hsiao Chen & Yi-Hua Liu & Zong-Zhen Yang, 2014. "An Asymmetrical Fuzzy-Logic-Control-Based MPPT Algorithm for Photovoltaic Systems," Energies, MDPI, vol. 7(4), pages 1-17, April.
    10. Tabanjat, Abdulkader & Becherif, Mohamed & Hissel, Daniel, 2015. "Reconfiguration solution for shaded PV panels using switching control," Renewable Energy, Elsevier, vol. 82(C), pages 4-13.
    11. Hiyam Farhat & Coriolano Salvini, 2022. "Novel Gas Turbine Challenges to Support the Clean Energy Transition," Energies, MDPI, vol. 15(15), pages 1-17, July.
    12. Inthamoussou, Fernando A. & De Battista, Hernán & Mantz, Ricardo J., 2016. "LPV-based active power control of wind turbines covering the complete wind speed range," Renewable Energy, Elsevier, vol. 99(C), pages 996-1007.
    13. Rajesh, R. & Carolin Mabel, M., 2015. "A comprehensive review of photovoltaic systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 231-248.
    14. Khaoula Ghefiri & Aitor J. Garrido & Eugen Rusu & Soufiene Bouallègue & Joseph Haggège & Izaskun Garrido, 2018. "Fuzzy Supervision Based-Pitch Angle Control of a Tidal Stream Generator for a Disturbed Tidal Input," Energies, MDPI, vol. 11(11), pages 1-21, November.
    15. Ali Bughneda & Mohamed Salem & Anna Richelli & Dahaman Ishak & Salah Alatai, 2021. "Review of Multilevel Inverters for PV Energy System Applications," Energies, MDPI, vol. 14(6), pages 1-23, March.
    16. Boukenoui, R. & Ghanes, M. & Barbot, J.-P. & Bradai, R. & Mellit, A. & Salhi, H., 2017. "Experimental assessment of Maximum Power Point Tracking methods for photovoltaic systems," Energy, Elsevier, vol. 132(C), pages 324-340.
    17. Ying Yang & Bin Wang & Yuqiang Tian & Peng Chen, 2020. "Fractional-Order Finite-Time, Fault-Tolerant Control of Nonlinear Hydraulic-Turbine-Governing Systems with an Actuator Fault," Energies, MDPI, vol. 13(15), pages 1-20, July.
    18. Yang, Libing & Entchev, Evgueniy & Ghorab, Mohamed & Lee, Euy-Joon & Kang, Eun-Chul & Kim, Yu-Jin & Nam, Yujin & Bae, Sangmu & Kim, Kwonye, 2022. "Advanced smart trigeneration energy system design for commercial building applications – Energy and cost performance analyses," Energy, Elsevier, vol. 259(C).
    19. Kermadi, Mostefa & Berkouk, El Madjid, 2017. "Artificial intelligence-based maximum power point tracking controllers for Photovoltaic systems: Comparative study," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 369-386.
    20. Khaoula Ghefiri & Izaskun Garrido & Soufiene Bouallègue & Joseph Haggège & Aitor J. Garrido, 2018. "Hybrid Neural Fuzzy Design-Based Rotational Speed Control of a Tidal Stream Generator Plant," Sustainability, MDPI, vol. 10(10), pages 1-26, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4040-:d:1246191. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.