SpringerLink
Log in

Active torsional vibration suppression for integrated electric drive system considering nonlinear factors

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The problem of torque ripple of the motor and nonlinear excitation in the gear transmission system can exacerbate the torsional vibration of the integrated electric drive system, leading to a decrease for the electric drive system's reliability and the vehicle's comfort. This article establishes a nonlinear model for a permanent magnet synchronous motor and a gear transmission system, analyzes the effects of nonlinear factors such as time-varying mesh stiffness, gear backlash, and meshing error on the characteristics of the integrated electric drive system and proposes a torsional vibration suppression strategy based on a double-layer model predictive control. This strategy aims to suppress torsional vibration for the integrated electric drive system by controlling the motor's target torque and reducing current harmonics and torque ripple. The simulation and experimental results demonstrate that the control method proposed in this article effectively reduces motor torque ripple and current harmonics, diminishes torsional vibration for the integrated electric drive system, enhances the stability of the electric drive system, and improves vehicle comfort.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Data Availability

The datasets generated during and/or analysed during the current study are not publicly available due to [Data is confidential] but are available from the corresponding author on reasonable request.

References

  1. Islam, M.S., Mikail, R., Kabir, M.A., Husain, I.: Torque ripple and radial force minimization of fractional-slot permanent magnet machines through stator harmonic elimination. IEEE Trans. Transport. Electrific. 8, 1072–1084 (2022). https://doi.org/10.1109/TTE.2021.3104758

    Article  Google Scholar 

  2. Chen, S., Hu, M.: Active torsional vibration suppression of integrated electric drive system based on optimal harmonic current instruction analytic calculation method. Mech. Mach. Theory 180, 105136 (2023). https://doi.org/10.1016/j.mechmachtheory.2022.105136

    Article  Google Scholar 

  3. Vidal, V., Stano, P., Tavolo, G., Dhaens, M., Tavernini, D., Gruber, P., Sorniotti, A.: On pre-emptive in-wheel motor control for reducing the longitudinal acceleration oscillations caused by road irregularities. IEEE Trans. Veh. Technol. 71, 9322–9337 (2022). https://doi.org/10.1109/TVT.2022.3172172

    Article  Google Scholar 

  4. Liu, J., Zhou, F., Zhao, C., Wang, Z.: Mechanism analysis and suppression strategy research on permanent magnet synchronous generator wind turbine torsional vibration. ISA Trans. 92, 118–133 (2019). https://doi.org/10.1016/j.isatra.2019.02.006

    Article  Google Scholar 

  5. Chen, X., Wei, H., Deng, T., He, Z., Zhao, S.: Investigation of electromechanical coupling torsional vibration and stability in a high-speed permanent magnet synchronous motor driven system. Appl. Math. Model. 64, 235–248 (2018). https://doi.org/10.1016/j.apm.2018.07.030

    Article  MathSciNet  Google Scholar 

  6. Szolc, T., Konowrocki, R., Michajłow, M., Pręgowska, A.: An investigation of the dynamic electromechanical coupling effects in machine drive systems driven by asynchronous motors. Mech. Syst. Signal Process. 49, 118–134 (2014). https://doi.org/10.1016/j.ymssp.2014.04.004

    Article  Google Scholar 

  7. Chen, X., Chen, R., Deng, T.: An investigation on lateral and torsional coupled vibrations of high power density PMSM rotor caused by electromagnetic excitation. Nonlinear Dynam. 99, 1975–1988 (2020). https://doi.org/10.1007/s11071-019-05436-1

    Article  Google Scholar 

  8. Yamazaki, K., Utsunomiya, K., Tanaka, A., Nakada, T.: Rotor surface optimization of interior permanent magnet synchronous motors to reduce both rotor core loss and torque ripples. IEEE Trans. Ind. Appl. 58, 4488–4497 (2022). https://doi.org/10.1109/TIA.2022.3164418

    Article  Google Scholar 

  9. Sun, K., Tian, S.: Multiobjective optimization of IPMSM with FSCW applying rotor Notch design for torque performance improvement. IEEE Trans. Magn. 58, 1–9 (2022). https://doi.org/10.1109/TMAG.2022.3155269

    Article  Google Scholar 

  10. Chen, Q., Xu, Z., Hu, Y., Ding, J., **e, Y.: Research on torque ripple optimization of permanent magnet synchronous motor for electric vehicle based on modular poles. IEEJ Trans. Electr. Electron. Eng. 18, 613–622 (2023). https://doi.org/10.1002/tee.23759

    Article  Google Scholar 

  11. Hao, L., Li, W., Zhang, X.: Impact of gear modification on gear dynamic characteristics. J Fail. Anal. and Preven. 23, 853–864 (2023). https://doi.org/10.1007/s11668-023-01627-6

    Article  Google Scholar 

  12. Ilka, R., Alinejad-Beromi, Y., Yaghobi, H.: Cogging torque reduction of permanent magnet synchronous motor using multi-objective optimization. Math. Comput. Simulation. 153, 83–95 (2018). https://doi.org/10.1016/j.matcom.2018.05.018

    Article  MathSciNet  Google Scholar 

  13. Sun, X., Shi, Z., Lei, G., Guo, Y., Zhu, J.: Analysis and design optimization of a permanent magnet synchronous motor for a campus patrol electric vehicle. IEEE Trans. Veh. Technol. 68, 10535–10544 (2019). https://doi.org/10.1109/TVT.2019.2939794

    Article  Google Scholar 

  14. Chen, J., Qin, Y., Bozorgi, A.M., Farasat, M.: Low complexity dual-vector model predictive current control for surface-mounted permanent magnet synchronous motor drives. IEEE J. Emerg. Selected Topics Power Electron. 8, 2655–2663 (2020). https://doi.org/10.1109/JESTPE.2019.2917865

    Article  Google Scholar 

  15. Song, D., Wu, J., Yang, D., Chen, H., Zeng, X.: An active multiobjective real-time vibration control algorithm for parallel hybrid electric vehicle. Proc. Inst. Mech. Eng. D: J. Automob. Eng.. 237, 21–33 (2023). https://doi.org/10.1177/09544070221130122

    Article  Google Scholar 

  16. Xu, Y., Ren, J., Fan, L., Yin, Z.: Multidisturbance suppressed model predictive direct speed control with low pulsation for PMSM drives. IEEE J. Emerg. Selected Topics Power Electron. 10, 6135–6147 (2022). https://doi.org/10.1109/JESTPE.2022.3163424

    Article  Google Scholar 

  17. Li, Y., Zhang, Z., Li, K., Zhang, P., Gao, F.: Predictive current control for voltage source inverters considering dead-time effect. CES Trans. Electrical Mach. Syst. 4, 35–42 (2020). https://doi.org/10.30941/CESTEMS.2020.00006.

  18. Wang, Y., Wu, X., Dang, C., **e, W.: A desired voltage vector based MPTC strategy for PMSM with optimized switching pattern. IEEE Trans. Energy Convers. 37, 970–977 (2022). https://doi.org/10.1109/TEC.2021.3119902

    Article  Google Scholar 

  19. **, D., Zhang, H., Zhu, S., Wang, A., Jiang, J.: Two-vector predictive current control strategy based on maximum torque per ampere control for PMSMs. J. Power Electron. 22, 1313–1323 (2022). https://doi.org/10.1007/s43236-022-00442-w

    Article  Google Scholar 

  20. Chen, X., Peng, D., Hu, J., Li, C., Zheng, S., Zhang, W.: Adaptive torsional vibration active control for hybrid electric powertrains during start-up based on model prediction. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 236, 2219–2229 (2022). https://doi.org/10.1177/09544070211056176

    Article  Google Scholar 

  21. Navardi, M.-J., Milimonfared, J., Talebi, H.-A.: Flux and torque ripple minimisation for permanent magnet synchronous motor by finite-set hybrid direct torque control. IET Power Electronics. 13, 2547–2554 (2020). https://doi.org/10.1049/iet-pel.2019.0038

    Article  Google Scholar 

  22. Zhang, X., Hou, B., Mei, Y.: Deadbeat predictive current control of permanent-magnet synchronous motors with stator current and disturbance observer. IEEE Trans. Power Electron. 32, 3818–3834 (2017). https://doi.org/10.1109/TPEL.2016.2592534

    Article  Google Scholar 

  23. Yi, Y., Qin, D., Liu, C.: Investigation of electromechanical coupling vibration characteristics of an electric drive multistage gear system. Mech. Mach. Theory 121, 446–459 (2018). https://doi.org/10.1016/j.mechmachtheory.2017.11.011

    Article  Google Scholar 

  24. Li, X., Su, K., Li, T., Zhang, L.: Vibration characteristics analysis of face gear transmission system considering gyroscopic effect. J. Vibroeng. 24, 624–636 (2022). https://doi.org/10.21595/jve.2022.22289.

  25. Song, D., Yang, D., Zeng, X., Wang, Z.: Active dam** control strategy for a parallel hybrid electric vehicle based on model predictive control. Trans. Inst. Meas. Control. 45, 120–132 (2023). https://doi.org/10.1177/01423312221105936

    Article  Google Scholar 

  26. Zheng, X., Luo, W., Hu, Y., He, Z., Wang, S.: Analytical approach to mesh stiffness modeling of high-speed spur gears. Int. J. Mech. Sci. 224, 107318 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107318

    Article  Google Scholar 

  27. Lekshmi, S., Lal Priya, P. S.: Mathematical modeling of Electric vehicles—a survey. Control Eng. Pract. 92, 104138 (2019). https://doi.org/10.1016/j.conengprac.2019.104138.

  28. Hu, J., Guo, Q., Sun, Z., Yang, D.: Study on low-frequency torsional vibration suppression of integrated electric drive system considering nonlinear factors. Energy, 129251 (2023). https://doi.org/10.1016/j.energy.2023.129251.

  29. Hu, J., Yang, D., Sun, Z.: Torque fluctuation suppression strategy of integrated electric drive system based on the principle of minimization of instantaneous current tracking error. IEEE Access. 10, 124673–124684 (2022). https://doi.org/10.1109/ACCESS.2022.3225103

    Article  Google Scholar 

  30. Oshnoei, S., Aghamohammadi, M.R., Oshnoei, S., Sahoo, S., Fathollahi, A., Khooban, M.H.: A novel virtual inertia control strategy for frequency regulation of islanded microgrid using two-layer multiple model predictive control. Appl. Energy 343, 121233 (2023). https://doi.org/10.1016/j.apenergy.2023.121233

    Article  Google Scholar 

  31. Li, M., Cao, H., Li, G., Zhao, S., Song, X., Chen, Y., Cao, D.: A two-layer potential-field-driven model predictive shared control towards driver-automation cooperation. IEEE Trans. Intell. Transp. Syst. 23, 4415–4431 (2022). https://doi.org/10.1109/TITS.2020.3044666

    Article  Google Scholar 

  32. Serkies, P.J., Szabat, K.: Application of the MPC to the position control of the two-mass drive system. IEEE Trans. Ind. Electron. 60, 3679–3688 (2013). https://doi.org/10.1109/TIE.2012.2208435

    Article  Google Scholar 

  33. Yüceşan, A., Mugan, A.: Development of a model predictive controller for an active torsional vibration damper to suppress torsional vibrations in vehicle powertrains. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 236, 127–141 (2022). https://doi.org/10.1177/09544070211014791

    Article  Google Scholar 

  34. Li, Z., Liu, C., Song, X., Wang, C.: Vibration suppression of hub motor electric vehicle considering unbalanced magnetic pull. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 235, 3185–3198 (2021). https://doi.org/10.1177/09544070211004507

    Article  Google Scholar 

  35. Kouro, S., Cortes, P., Vargas, R., Ammann, U., Rodriguez, J.: Model predictive control—a simple and powerful method to control power converters. IEEE Trans. Industr. Electron. 56, 1826–1838 (2009). https://doi.org/10.1109/TIE.2008.2008349

    Article  Google Scholar 

  36. Wang, J., Yang, H., Liu, Y., Rodríguez, J.: Low-cost multistep FCS-MPCC for PMSM drives using a DC link single current senso. IEEE Trans. Power Electron. 37, 11034–11044 (2022). https://doi.org/10.1109/TPEL.2022.3167557

    Article  Google Scholar 

  37. Sun, Z., Ma, G., Xu, S., Zhang, H., Ren, G.: Reduced vector model predictive control of ANPC inverter for PMSM drives with optimized commutation. IEEE Trans. Transport. Electrific. 8, 3177–3191 (2022). https://doi.org/10.1109/TTE.2022.3166678

    Article  Google Scholar 

  38. Zhang, Y., Wei, X.: Torque ripple RMS minimization in model predictive torque control of PMSM drives. In: International Conference on Electrical Machines and Systems (ICEMS), 2013, 2183–2188 (2013). https://doi.org/10.1109/ICEMS.2013.6713197

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant No. 52172364] and Technology Innovation and Application Development Project of Chongqing [Grant No. CSTB2022TIADKPX0048].

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing, 400044, China

    Zhicheng Sun, Jianjun Hu, Yuntong **n, Qi Guo & Zutang Yao

  2. China Merchants Testing Vehicle Technology Research Institute Co., Ltd, Chongqing, 400044, China

    Ying Yang

Authors
  1. Zhicheng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianjun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuntong **n
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qi Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zutang Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ying Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Zhicheng Sun], [Jianjun Hu] and [Yuntong **n]. The first draft of the manuscript was written by [Zhicheng Sun] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Jianjun Hu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Z., Hu, J., **n, Y. et al. Active torsional vibration suppression for integrated electric drive system considering nonlinear factors. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09919-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11071-024-09919-8

Keywords

Search

Navigation