Nonlinear Optimal Control of Magnetically Geared Induction Motors

G. Rigatos; P. Siano; M. Abbaszadeh; G. Cuccurullo; K. Ouahada

doi:10.2478/pead-2025-0009

Abstract

The present article proposes a non-linear optimal control method for magnetically geared induction motors (MGIMs). It is proven that the dynamic model of the magnetically geared three-phase induction motor is differentially flat, which confirms the controllability of this system. Next, to apply the non-linear optimal control scheme, the dynamic model of the magnetically geared motor undergoes approximate linearisation with the use of a first-order Taylor-series expansion and through the computation of the associated Jacobian matrices. For the approximately linearised model of the MGIM, an H-infinity optimal feedback controller is designed. To compute the controller’s stabilizing feedback gains, an algebraic Riccati equation has to be solved repetitively at each time-step of the control algorithm. The global stability properties of the non-linear optimal control scheme are proven through Lyapunov analysis.

References

Basseville, M. and Nikiforov, I. (1993). Detection of Abrupt Changes: Theory and Applications. New Jersey, USA, Prentice-Hall.
Search in Google Scholar Back to article
Bidouche, B., Lubin, T. and Mezani, S. (2020). Transient Performance of A Magnetically Geared Induction Machine. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 39(5), pp. 1113–1130. doi: 10.1108/COMPEL-12-2019-0485
Open DOI Search in Google Scholar Back to article
Dobzhanskyi, O., Hossain, E., Amiri, E., Gouws, R., Grebenikov, V., Muzurenko, L., Pryinak, M. and Gamalijia, R. (2019). Axial-Flux PM Disk Generator with Magnetic Gear for Oceanic Wave Energy Harvesting. IEEE Access, 7, pp. 44813–44822. doi: 10.1109/ACCESS.2019.2908348
Open DOI Search in Google Scholar Back to article
Druant, J., de Belit, F., Sergeant, P. and Melkeboek, J. (2016). Field-Oriented Control for an Induction Machine based Electrical Variable Transmission. IEEE Transactions on Vehicular Technology, 65(6), pp. 4230–4240. doi: 10.1109/TVT.2015.2496625
Open DOI Search in Google Scholar Back to article
Gorecki, M. (2018). Optimization and Control of Dynamic Systems: Foundations, Main Developments, Examples and Challenges. Cham, Switzerland, Springer.
Search in Google Scholar Back to article
Grimble, M. J. and Majeski, P. (2020). Nonlinear Industrial Control Systems: Optimal Polynomial Systems and State-Space Approach. London, UK, Springer.
Search in Google Scholar Back to article
Habibi, H., Amimzhad, A. and Khosrowjerdi, M. J. (2024). Nonlinear Control of Coaxial Double Rotor Magnetic Gear Based on High-Gain Observer in Wind Turbines. IET Control Theory and Applications, 19, pp. 1314–1327. doi: 10.1049/cth2.12666
Open DOI Search in Google Scholar Back to article
Hazra, S., Kmt, P., Bhattacharya, S., Ouyaang, W. and Englebretson, S. (2020). Power Conversion with a Magnetically Geared Permanent Magnet Generator for Low-Speed Wave Energy Converter. IEEE Transactions on Industry Applications, 56(5), pp. 5308–5318. doi: 10.1109/TIA.2020.2997640
Open DOI Search in Google Scholar Back to article
Kumashira, A., Chen, L., Fujiti, Y., Chiba, A., Graber, W., Amrhen, W. and Jungmeyr, G. (2004). Novel Reluctance-Type Magnetic-Geared Motor Integrated with High-Speed Bearingless Motor. IEEE Transactions on Industry Applications, 60(3), pp. 3808–3819. doi: 10.1109/TIA.2024.3357049
Open DOI Search in Google Scholar Back to article
Liao, X., Bingham, C. and Smith, T. (2023). Robust Speed Control of Magnetic Drive-Trains with Low-Cost Drives. IEEE Transactions on Energy Conversion, 39(1), pp. 435–445. doi: 10.1109/TEC.2023.3329074
Open DOI Search in Google Scholar Back to article
Long, T. V., Sharkh, S. M., Anglada, J. R., Hendijamiczadeh, M. and Moshrefi-Torbati, M. (2023). Rotary-to-:Linear Magnetic Gear. IEEE Transactions on Industry Applications, 59(3), pp. 3310–3319. doi: 10.1109/TIA.2023.3252520
Open DOI Search in Google Scholar Back to article
McGilton, B., Crazier, D., McDonald, A. and Mueller, M. (2018). Review of Magnetic Gear Technologies and their Applications to Marine Energy. IET Renewable Power Generation, 12(2), pp. 174–181. doi: 10.1049/iet-rpg.2017.0210
Open DOI Search in Google Scholar Back to article
Molley, T. L., Charaja, J. L., Hohmann, S. and Perez, T. (2022). Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory: A Minimum Principle Approach. Springer.
Search in Google Scholar Back to article
Montegue, R., Bingham, C. and Atallah, K. (2012). Servo Control of Magnetic Gears. IEEE/ASME Transactions on Mechatronics, 17(2), pp. 269–278. doi: 10.1109/TMECH.2010.2096473
Open DOI Search in Google Scholar Back to article
Pop, C. V., Essaid, M., Idounchor, L. and Fodorean, D. (2018). Novel Differential Evolutionary Optimization Approach for an Integrated Motor-Magnetic Gear Used for Propulsion Systems. IEEE Access, 9, pp. 142114–142128. doi: 10.1109/ACCESS.2021.3119523
Open DOI Search in Google Scholar Back to article
Qu, R., Li D. and Wang, J. (2011). Relationship between magnetic gears and Vernier machines. In: IEEE 2011 International Conference on Electrical Machines and Systems, Beijing, China, August 2011.
Search in Google Scholar Back to article
Rigatos, G. (2015). Nonlinear Control and Filtering Using Differential Flatness Theory Approaches: Applications to Electromechanical Systems. Cham, Switzerland, Springer.
Search in Google Scholar Back to article
Rigatos, G. (2016). Intelligent Renewable Energy Systems: Modelling and Control. Springer.
Search in Google Scholar Back to article
Rigatos, G., Abbaszadeh, M., Hamida, M. A. and Siano, P. (2024a). Intelligent Control for Electric Power Systems and Electric Vehicles. CRC Publications.
Search in Google Scholar Back to article
Rigatos, G., Abbaszadeh, M. and Siano, P. (2022). Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and Applications. London, UK, IET Publications.
Search in Google Scholar Back to article
Rigatos, G., Abbaszadeh, M. and Siano, P. (2025). Nonlinear Optimal and Flatness-Based Control Methods and Applications for Complex Dynamical Systems. London, UK, IET Publications.
Search in Google Scholar Back to article
Rigatos, G., Abbaszadeh, M., Siano, P. and Wira, P. (2024b). Autonomous Electric Vehicles: Nonlinear Control, Traction and Propulsion. London, UK, Elsevier.
Search in Google Scholar Back to article
Rigatos, G., Siano, P., Al-Numay, M., Sari, B. and Abbaszadeh, M. (2024c). Nonlinear Optimal Control for the Five-Phase Induction Motor-Based Traction System of Electric Vehicles. COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 43(1), pp. 167–191. doi: 10.1108/COMPEL-05-2023-0186
Open DOI Search in Google Scholar Back to article
Rigatos, G. G. and Tzafestas, S. G. (2007). Extended Kalman Filtering for Fuzzy Modelling and Multi-Sensor Fusion. Mathematical and Computer Modelling of Dynamical Systems, 13, pp. 251–266. doi: 10.1080/01443610500212468
Open DOI Search in Google Scholar Back to article
Rigatos, G. and Zhang, Q. (2009). Fuzzy Model Validation Using the Local Statistical Approach. Fuzzy Sets and Systems, 60(7), pp. 882–904. doi: 10.1016/j.fss.2008.07.008
Open DOI Search in Google Scholar Back to article
Song, H., Lee, E., Seo, M. T. and Jeong, S. (2022). Magnetic Gear-Based Actuator: A Framework of Design, Optimization and Disturbance Observer-Based Torque Control. IEEE Robotics and Automation Letters, 8(11), pp. 7050–7060. doi: 10.1109/LRA.2023.3313011
Open DOI Search in Google Scholar Back to article
Sun, L., Cheng, M., Wen, H. and Song, L. (2017). Motion Control and Performance Evaluation of a Magnetic-geared Dual-Rotor Motor in Hybrid Powertrain. IEEE Transactions on Industrial Electronics, 64(3), pp. 1863–1872. doi: 10.1109/TIE.2016.2627018
Open DOI Search in Google Scholar Back to article
Tao, K. L., Li, B. and Rehbock, Y. (2021). Applied and Computational Optimal Control: A Control Parametrization Approach. Cham, Switzerland, Springer.
Search in Google Scholar Back to article
Tong, C., Long, J., Bai, J., Zhanga, P. and Ma, D. (2023). Deadbeat Direct-Torque and Flux Control of a Brushless Axial-Flux Magnetic-Geared Double-Rotor Machine for Power Splitting HEVs. IEEE Transactions on Industrial Electronics, 70(9), pp. 8734–8745. doi: 10.1109/TIE.2022.3213888
Open DOI Search in Google Scholar Back to article
Toussaint, G. J., Basar, T. and Bullo, F. (2000). H∞ optimal tracking control techniques for nonlinear underactuated systems. In: Proceedings of the IEEE CDC 2000, 39th IEEE Conference on Decision and Control, Sydney Australia, 2000.
Search in Google Scholar Back to article
Wang, R. J. and Gerber, S. (2014). Magnetically Geared Wind Generator Technologies. Applied Energy, 136, pp. 817–826. doi: 10.1016/j.apenergy.2014.07.079
Open DOI Search in Google Scholar Back to article
Xie, S., Zuo, Y., Song, Z., Cai, S., Chen, F., Goh, J. A., Mass, B. S. and Hoang, C. C. (2024). A Magnetic Gear Machine with Improved Magnetic Circuit Symmetry for Hybrid Electric Vehicle Applications. IEEE Transactions on Transportation Electrification, 10(1), pp. 2170–2182. doi: 10.1109/TTE.2023.3262301
Open DOI Search in Google Scholar Back to article
Xi, X., Guo, X., Gao, C., Wu, H., Liu, Y., Wang, R., Fu, W. and Lin, Q. (2023). Sliding-Mode Control of An Outer Rotor Magnetic-Gear Integrated Motor with a Halbach Array. Control Engineering Practice, 137, p. 105561. doi: 10.1016/j.conengprac.2023.105561
Open DOI Search in Google Scholar Back to article
Yang, Y., Wang, R., Zhu, X. and Du, J. (2024). Modelling, Analysis and Control of Nonlinear Kinetics of a Planetary Magnetic Gear Motor for A Steering System. Journal of Electrical Engineering and Technology, 19, pp. 2361–2368. doi: 10.1007/s42835-023-01756-w
Open DOI Search in Google Scholar Back to article
Zhu, Z. Q. (2018). Overview of Novel Magnetically Geared Machines with Partitioned States. IET Electric Power Applications, 12(5), pp. 595–604. doi: 10.1049/iet-epa.2017.0680
Open DOI Search in Google Scholar Back to article

Nonlinear Optimal Control of Magnetically Geared Induction Motors

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