Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Advertisement

Scientific Reports
  • View all journals
  • Search
  • My Account Login
  • Content Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • RSS feed
  1. nature
  2. scientific reports
  3. articles
  4. article
Full-speed domain position sensorless control strategy for PMSM based on improved super-twisting sliding-mode observer and smooth transition optimization
Download PDF
Download PDF
  • Article
  • Open access
  • Published: 19 January 2026

Full-speed domain position sensorless control strategy for PMSM based on improved super-twisting sliding-mode observer and smooth transition optimization

  • Xia Zhang1,
  • Pengwei Li1,
  • Bo Wang1,
  • Minghao Lv1 &
  • …
  • Liangtong Shi1 

Scientific Reports , Article number:  (2026) Cite this article

  • 356 Accesses

  • Metrics details

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Physics

Abstract

In the sensorless control of permanent magnet synchronous motors (PMSMs), achieving smooth transitions from low to medium–high speeds remains a significant challenge. Aiming at the problem that PMSMs cannot be smoothly transitioned to medium–high speed range, this paper proposes a full-speed range control algorithm based on the fusion of pulsating high-frequency injection (HFI) with square waves and an improved super-twisting sliding-mode observer (STSMO). The proposed method enables smooth and stable operation over the full speed range, with notable improvements observed during transitional phases. In the low-speed range, high-frequency current signal is obtained by injecting a high-frequency (HF) square-wave signal, and the signal is processed to obtain rotor position and speed information. For medium–high speeds, a variable-gain linear STSMO (VGLSTSMO) combined with an adaptive back electromotive force (back-EMF) model is employed to improve robustness. Furthermore, this paper designs a Sine-weighted switching function to facilitate a smooth transition of motors from low to medium–high speeds domains. The effectiveness and superiority of the proposed methods are validated through simulations. The rotor position estimation errors of the improved STSMO method are approximately 0.2 rad, and Sine-weighted switching method enables motors to switch smoothly from the low-speed range to the medium- high-speed ranges.

Similar content being viewed by others

Sensorless control in full speed domain of interior permanent magnet synchronous motor based on hybrid observer

Article Open access 17 September 2024

Full-order adaptive sliding mode control with extended state observer for high-speed PMSM speed regulation

Article Open access 17 April 2023

PMSM sensorless control based on super-twisting algorithm sliding mode observer with the IAORLS parameter estimations

Article Open access 01 July 2025

Data availability

The data that supports the findings of this study are available within the article.

References

  1. Zhang, C. J., Wang, H. Z., Liu, W. F. & Fu, Z. R. Estimation of rotor position and speed of permanent magnet synchronous motor based on wideband synchronous fundamental frequency extraction filter. Electr. Eng. Technol. 37, 882–891 (2022).

    Google Scholar 

  2. Qureshi, I. & Sharma, V. Analysis of different control schemes of PMSM motor and also a comparison of FOPI and PI controller for sensorless MSVPWMM scheme. e-Prime-Adv. Electr. Eng. Electron. Energy 6, 100359 (2023).

    Google Scholar 

  3. Yao, G., Yang, Z., Han, S. & Wang, Z. Full-speed domain position sensorless control strategy for PMSM based on a novel phase-locked loop. Control Eng. Pract. 152, 106058. https://doi.org/10.1016/j.conengprac.2024.106058 (2024).

    Google Scholar 

  4. Bi, G. et al. High-frequency injection angle self-adjustment based online position error suppression method for sensorless PMSM drives. IEEE Trans. Power Electron. 38, 1412–1417 (2022).

    Google Scholar 

  5. Zhang, Y. P., Yin, Z. G., Su, M. & Liu, J. Unified full-speed-domain sensorless control for built-in permanent magnet synchronous motors based on resonance-expanded state observer. Electr. Eng. Technol. 38, 6070–6081 (2023).

    Google Scholar 

  6. Fu, K. Z., Liu, J. L., Mai, Z. Q., Mu, Y. L. & Li, K. F. Improved IF control combined with the effective flux linkage method for full-speed-domain sensorless control strategy of permanent magnet synchronous motor. Electr. Eng. Technol. 37, 5704–5716 (2022).

    Google Scholar 

  7. Jiang, Y. & Cheng, M. An improved initial rotor position estimation method using high-frequency pulsating voltage injection for PMSM. Def. Technol. 33, 19–29 (2024).

    Google Scholar 

  8. Bi, G. et al. High-frequency injection angle self-adjustment based online position error suppression method for sensorless PMSM drives. IEEE Trans. Power Electron. 38, 1412–1417 (2023).

    Google Scholar 

  9. Wen, D., Wang, W. & Zhang, Y. Sensorless control of permanent magnet synchronous motor in full speed range. Chinese J. Electr. Eng. 8, 97–107 (2022).

    Google Scholar 

  10. Wu, T. et al. Square-wave voltage injection based PMSM sensorless control considering time delay at low switching frequency. IEEE Trans. Ind. Electron. 69, 5525–5535 (2022).

    Google Scholar 

  11. Wang, C., Gou, L., Zhou, M., You, X. & Dong, S. Improved discrete-domain second-order sliding mode observer-based sensorless control of interior permanent magnet synchronous motor. Electr. Technol. 38, 387–397 (2023).

    Google Scholar 

  12. Jiang, F. et al. Robustness improvement of model-based sensorless SPMSM drivers based on an adaptive extended state observer and an enhanced quadrature PLL. IEEE Trans. Power Electron. 36, 4802–4814 (2021).

    Google Scholar 

  13. Gao, F., Yin, Z., Bai, C., Yuan, D. & Liu, J. A lag compensation-enhanced adaptive quasi-fading Kalman filter for sensorless control of synchronous reluctance motor. IEEE Trans. Power Electron. 37, 15322–15337 (2022).

    Google Scholar 

  14. Wang, S. et al. Flux observer based on enhanced second-order generalized integrator with limit cycle oscillator for sensorless PMSM drives. IEEE Trans. Power Electron. 38, 15982–15995 (2023).

    Google Scholar 

  15. Shahzad, K. et al. A hybrid approach for an efficient estimation and control of permanent magnet synchronous motor with fast dynamics and practically unavailable measurements. Appl. Sci. 12, 4958. https://doi.org/10.3390/app12104958 (2022).

    Google Scholar 

  16. Zuo, Y., Lai, C. & Iyer, K. L. V. A review of sliding mode observer-based sensorless control methods for PMSM drive. IEEE Trans. Power Electron. 38, 11352–11367 (2023).

    Google Scholar 

  17. Zhan, Y., Guan, J. & Zhao, Y. An adaptive second-order sliding-mode observer for permanent magnet synchronous motor with an improved phase-locked loop structure considering speed reverse. Trans. Inst. Meas. Control 42, 1008–1021 (2020).

    Google Scholar 

  18. Wang, F., Gao, M., Qin, J., Peng, Z. & Zheng, W. Adaptive super-twisting sliding mode observer based positionless direct torque control strategy for PMSM. Nondestruct. Test. Eval. 1, 1–24. https://doi.org/10.1080/10589759.2025.2451760 (2025).

    Google Scholar 

  19. Zhang, H., Liu, W., Chen, Z. & Jiao, N. An overall system delay compensation method for IPMSM sensorless drives in rail transit applications. IEEE Trans. Power Electron. 36, 1316–1329 (2021).

    Google Scholar 

  20. Huang, Y., Zhao, M., Wang, Y., Zhang, H. & Lu, M. An improved full-speed domain sensorless control scheme for permanent magnet synchronous motor based on hybrid position observer and disturbance rejection optimization. Electronics 12, 3759. https://doi.org/10.3390/electronics12183759 (2023).

    Google Scholar 

  21. Gao, Y. J. et al. Sensorless control in full speed domain of interior permanent magnet synchronous motor based on hybrid observer. Sci. Rep. 14, 21661. https://doi.org/10.1038/s41598-024-72574-x (2024).

    Google Scholar 

  22. Shi, L., Lv, M. & Li, P. Sensorless position control in high-speed domain of PMSM based on improved adaptive sliding mode observer. Processes 12, 2581. https://doi.org/10.3390/pr12112581 (2024).

    Google Scholar 

  23. Moreno, J. A. & Osorio, M. A Lyapunov approach to second-order sliding mode controllers and observers. In: Proc. 47th IEEE Conf. Decis. Control 2856–2861 (IEEE, 2008).

Download references

Funding

This work is supported by the Science and Technology Research Project of the Jilin Provincial Department of Education (JJKH20210046KJ).

Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Beihua University, Jilin, 132021, China

    Xia Zhang, Pengwei Li, Bo Wang, Minghao Lv & Liangtong Shi

Authors
  1. Xia Zhang
    View author publications

    Search author on:PubMed Google Scholar

  2. Pengwei Li
    View author publications

    Search author on:PubMed Google Scholar

  3. Bo Wang
    View author publications

    Search author on:PubMed Google Scholar

  4. Minghao Lv
    View author publications

    Search author on:PubMed Google Scholar

  5. Liangtong Shi
    View author publications

    Search author on:PubMed Google Scholar

Contributions

X.Z. proposed the design concept and drafted the manuscript. P.L. oversaw the research, provided key revisions, and ensured the technical integrity of the paper. X.Z. and B.W. conducted the simulation experiments. X.Z., M.L., and L.S. analyzed the simulation results, edited the manuscript, created the figures and tables, and performed the final proofreading. All authors reviewed the manuscript.

Corresponding author

Correspondence to Pengwei Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

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

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Li, P., Wang, B. et al. Full-speed domain position sensorless control strategy for PMSM based on improved super-twisting sliding-mode observer and smooth transition optimization. Sci Rep (2026). https://doi.org/10.1038/s41598-026-35994-5

Download citation

  • Received: 10 November 2025

  • Accepted: 09 January 2026

  • Published: 19 January 2026

  • DOI: https://doi.org/10.1038/s41598-026-35994-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • PMSMs
  • Full speed range position sensorless control
  • Variable-gain linear super-twisting sliding-mode observer (VGLSTSMO)
  • High-frequency injection (HFI)
  • Sine-weighted switching function
Download PDF

Advertisement

Explore content

  • Research articles
  • News & Comment
  • Collections
  • Subjects
  • Follow us on Facebook
  • Follow us on Twitter
  • Sign up for alerts
  • RSS feed

About the journal

  • About Scientific Reports
  • Contact
  • Journal policies
  • Guide to referees
  • Calls for Papers
  • Editor's Choice
  • Journal highlights
  • Open Access Fees and Funding

Publish with us

  • For authors
  • Language editing services
  • Open access funding
  • Submit manuscript

Search

Advanced search

Quick links

  • Explore articles by subject
  • Find a job
  • Guide to authors
  • Editorial policies

Scientific Reports (Sci Rep)

ISSN 2045-2322 (online)

nature.com sitemap

About Nature Portfolio

  • About us
  • Press releases
  • Press office
  • Contact us

Discover content

  • Journals A-Z
  • Articles by subject
  • protocols.io
  • Nature Index

Publishing policies

  • Nature portfolio policies
  • Open access

Author & Researcher services

  • Reprints & permissions
  • Research data
  • Language editing
  • Scientific editing
  • Nature Masterclasses
  • Research Solutions

Libraries & institutions

  • Librarian service & tools
  • Librarian portal
  • Open research
  • Recommend to library

Advertising & partnerships

  • Advertising
  • Partnerships & Services
  • Media kits
  • Branded content

Professional development

  • Nature Awards
  • Nature Careers
  • Nature Conferences

Regional websites

  • Nature Africa
  • Nature China
  • Nature India
  • Nature Japan
  • Nature Middle East
  • Privacy Policy
  • Use of cookies
  • Legal notice
  • Accessibility statement
  • Terms & Conditions
  • Your US state privacy rights
Springer Nature

© 2026 Springer Nature Limited

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing