Friction compensation based on dynamic models in a synchronous electric drive of a mechatronic robotic module

Friction compensation based on dynamic models in a synchronous electric drive of a mechatronic robotic module

Yuriy A. Zhukov
Senior Lecturer, Baltic State Technical University «VOENMEH», 1, ul. 1-ya Krasnoarmeyskaya, Saint Petersburg, 190005, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it., ORCID: 0000-0001-7552-2899

Aleksey A. Kiselev
Head of Sector, Russian State Scientific Center for Robotics and Technical Cybernetics (RTC), 21, Tikhoretsky pr., Saint Petersburg, 194064, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Mikhail I. Nadezhin
Head of Sector, Russian State Scientific Center for Robotics and Technical Cybernetics (RTC), 21, Tikhoretsky pr., Saint Petersburg, 194064, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Nataliya N. Safronova
Candidate of Economic Sciences, Deputy General Director, Association of Organizations of the Nuclear Industry Construction Complex, 30/1-1, ul. Obrucheva, Moscow, 117485, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

UDC identifier: 681.5

EDN: XLFYBH

Abstract. The paper presents a review of dynamic friction models used to solve the problem of compensating friction forces when controlling the drive of a mechatronic robotic module based on a three-phase synchronous motor with permanent magnets. Frictions are described on the basis of nonlinear differential equations with one state variable in the form of the LuGre model and the elasto-plastic friction model, as well as with several state space variables in the form of the generalized Maxwell-slip model. A model of a mechatronic actuator with an elastic transmission based on a synchronous motor taking into account the first two harmonics of phase and mutual inductances of windings are defined. The parameters of the actuator and friction models are presented. A field-oriented proportional-integral-differential algorithm for actuator control with compensation of friction torque is described. A simulation model of the actuator control system created in the Matlab mathematical modeling environment using the Matlab-function and S-function blocks are defined, in which the equations of state space of the analog part and discrete algorithms of current and position regulators are implemented, respectively. The results of modeling the digital actuator control system in the harmonic mode of movement with small amplitudes are demonstrated. Based on the presented dynamic models, the quality of friction compensation is estimated by the values of amplitude, average and relative errors. It is noted that friction compensation allows an order of magnitude reduction in control errors in motion modes with near-zero speeds, ensuring an increase in the quality of precision actuator control systems. The best results are demonstrated based on compensation using the generalized Maxwell-Slip model and the elasto-plastic friction model.

Key words: friction compensation, LuGre friction model, elastoplastic friction model, generalized Maxwell-Slip, mechatronic module, drive, precision control, simulation

For citation: Zhukov, Yu.A., Kiselev, A.A., Nadezhin, M.I. and Safronova, N.N. (2025), "Friction compensation based on dynamic models in a synchronous electric drive of a mechatronic robotic module", Robotics and Technical Cybernetics, vol. 13, no. 4, pp. 309-320, EDN: XLFYBH. (in Russian).

Acknowledgements
The work was carried out within the framework of the project «Creation of a technology for the design and manufacture of bilateral electromechanical manipulation systems for operation in high fields of ionizing radiation» (FNRG-2025-0014) 1024061000015-8-2.2.2 within the framework of state assignment No. 075-00553-25-02 dated 03/28/2025.

References

  1. Siciliano, B. and Khatib, O. (ed.) (2016), Springer Handbook of Robotics, DOI: 10.1007/978-3-319-32552-1
  2. Rafaq, M.S., Midgley, W. and Steffen, T. (2024), “A Review of the State of the Art of Torque Ripple Minimization Techniques for Permanent Magnet Synchronous Motors”, IEEE Transactions on Industrial Informatics, vol. 20, no. 1, pp. 1019-1031, DOI: 10.1109/TII.2023.3272689
  3. Chen, R., Tong, T. (2023), “Induction Motors and Permanent Magnet Motors in Electric Vehicles: Characteristics and Development Trends”, 2023 International Conference on Internet of Things, Robotics and Distributed Computing (ICIRDC), 221-224, DOI: 10.1109/ICIRDC62824.2023.00046
  4. Lewis, F.L., Dawson, D.M. and Abdallah, C.T. (2004), Robot Manipulator Control: Theory and Practice, 2nd ed., CRC Press, DOI: 10.1201/9780203026953
  5. Huang, S., Liang, W.and Tan, K.K. (2019), “Intelligent Friction Compensation: A Review”, IEEE/ASME Transactions on Mechatronics, v 24, no. 4, pp. 1763–1774, DOI: 10.1109/TMECH.2019.2916665
  6. Serebrennyj, V.V., Boshlyakov, A.A. and Ogorodnik A.I. (2019). “Drive unit mathematical model of robot gripping devices”, Vestnik BSTU named after V.G. Shukhov, 6, pp.1 23–135, DOI: 10.34031/article_5d079791aeaae3.67485144 (in Russian).
  7. Hess, D.P. and Soom, A. (1990), “Friction at a lubricated line contact operating at oscillating sliding velocities”, Transactions ASME J. Tribology, vol. 112, no. 1, pp. 147–152.
  8. Dahl, P. (1968), A solid friction model. Technical Report TOR-0158H3107 18I-1, E1 Segundo, Aerospace Corporation.
  9. Astrom, K. and Canudas-de-Wit C. (2008), “Revisiting the LuGre friction model: Stick-slip motion and rate dependence”, IEEE Control Systems Magazine, 28, pp. 101–114, DOI: 10.1109/MCS.2008.929425
  10. Hayward, V., Armstrong, B., Dupont, P. and Altpeter, F. (2002), “Single State Elasto-Plastic Friction Models”, IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 787–792, DOI:10.1109/TAC.2002.1000274
  11. Al-Bender, F., Lampaert, V. and Swevers, J. (2005), “The generalized Maxwell-slip model: A novel model for friction simulation and compensation”, IEEE Trans. Autom. Control, vol. 50, no. 11, pp. 1883–1887, DOI: 10.1109/TAC.2005.858676
  12. Xia, Y., Qi, M., Lyu, L., Jin, Z. et al. (2024), “B. Advanced Motion Control of Hydraulic Manipulator With Precise Compensation of Dynamic Friction”, IEEE Transactions on Industrial Informatics, vol. 20, no. 7, pp. 9375-9384, DOI: 10.1109/TII.2024.3384600
  13. Wang, C., Peng, J. and Pan J. (2023), “A Novel Friction Compensation Method Based on Stribeck Model With Fuzzy Filter for PMSM Servo Systems”, IEEE Transactions on Industrial Electronics, vol. 70, no. 12, pp. 12124-12133, DOI: 10.1109/TIE.2022.3232667
  14. Zhukov, Yu.A. and Nadezhin, M.I. S(2018), “Simulation friction in a linear drive of a space hexapod control system”, In Proceedings of the International Scientific and Technical Internet Conference of Young Scientists "Automation, Mechatronics, Information Technologies", 134–142, Omsk, Russia. (in Russian).
  15. Büchner, S., Zschaeck, S., Amthor, A., Ament, C. and Eichhorn, M. (2012), “Dynamic friction modeling and identification for high precision mechatronic systems”, IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, pp. 2263–2268, DOI: 10.1109/IECON.2012.6388884
  16. Keck, A., Zimmermann, J. and Sawodny, O. (2017), “Friction parameter identification and compensation using the ElastoPlastic friction model”, Mechatronics, vol. 47, pp. 168–182, DOI: 10.1016/j.mechatronics.2017.02.009
  17. Boegli, M., De Laet, T., De Schutter, J. and Swevers, J. (2014), “A Smoothed GMS Friction Model Suited for Gradient-Based Friction State and Parameter Estimation”, IEEE/ASME Transactions on mechatronics, vol. 19, no. 5, DOI: 10.1109/TMECH.2013.2288944
  18. Xia, Y., Wang, C., Song, Y., Cai, J. and Cheng, G. (2023), “Adaptive Neural Backstepping Control for Harmonic Drive System Based on Modified LuGre Friction Model”, IEEE Access, vol. 11, pp. 96093-96102, DOI: 10.1109/ACCESS.2023.3311714
  19. Tang, С, Fan, Y., Yang, C., Cheng, M. and Lee, C.H.T. (2024), “Friction Identification and Compensation for SPMSM Using Robust Adaptive Observer”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 12, no. 5, pp. 4754-4766, DOI: 10.1109/JESTPE.2024.3435474
  20. Zhang, X. and Chen, L. (2022), “Neural Network Based Friction Compensation of Motion Control on A 6-DoF Robot Manipulator”, 5th International Conference on Mechatronics, Robotics and Automation (ICMRA), pp. 14–18, Wuhan, China, DOI: 10.1109/ICMRA56206.2022.10145700
  21. Gu, C., Liu, S., Bao, W., Meng, D and Yang, S. (2025), “End-Effector Trajectory Tracking Control of Stacking Robot Based on LuGre Model”, IEEE/ASME Transactions on Mechatronics, pp. 1–12, DOI: 10.1109/TMECH.2024.3524590
  22. Tjahjowidodo, T., Al-Bender, F. and Van Brussel, H. (2005), “FRICTION IDENTIFICATION AND COMPENSATION IN A DC MOTOR”, IFAC Proceedings Volumes, vol. 38, is. 1, pp. 554–559, DOI: 10.3182/20050703-6-cz-1902.00093
  23. Bida, V.M., Samokhvalov, D.V. and Al-Mahturi, F.S. (2018), “PMSM vector control techniques – A survey”, IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), pp. 577–581, DOI: 10.1109/EIConRus.2018.8317164
  24. Kalachyov, Yu.N. (2012), SimInTech: modelirovanie v elektroprivode [SimInTech: simulation in electric drive], DMK Press, Moscow, Russia. (in Russian).
  25. Astrom, K.J. and Hagglund, T. (2006), Advanced PID Control, ISA, Research Triangle Park, North Carolina.

Received 01.06.2025
Revised 18.06.2025
Accepted 15.10.2025