Nonlinear Dynamics

, Volume 95, Issue 2, pp 995–1007 | Cite as

Identification and adaptive robust precision motion control of systems with nonlinear friction

  • Chao Li
  • Zheng ChenEmail author
  • Bin Yao
Original Paper


Both accurate system identification and high-performance controller design are necessary for precision motion systems. This paper first considers the unavoidable issue of nonlinear friction effect on traditional frequency identification widely used by practicing engineers and simultaneously presented an improved identification method with nonlinear friction compensation, which has two freedoms to guarantee an accurate estimation of the frequency response of the underlying linear dynamics in practice. The effectiveness of the proposed identification method is verified through different experimental platforms, which also shows the applicability of the proposed method to different kinds of dynamics subjected to nonlinear friction. An adaptive robust controller (ARC) is then synthesized to obtain a guaranteed robust performance in the presence of various uncertainties. Furthermore, with the obtained identification results, certain gain tuning rules are given in the paper to help engineers choose proper ARC controller gains quickly to maximize the achievable control performance in practice. Comparative experimental results obtained show the excellent tracking performance of the proposed ARC algorithm, which also validates the practical significance of the proposed frequency identification method.


Nonlinear friction effect Frequency identification Adaptive robust control Gain tuning rules 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Hu, C., Hu, Z., Zhu, Y., Wang, Z.: Advanced GTCF based LARC contouring motion control on an industrial x-y linear-motor-driven stage with experimental investigation. IEEE Trans. Ind. Electron. 64(4), 3308–3318 (2017)CrossRefGoogle Scholar
  2. 2.
    Teo, T.J., Zhu, H., Chen, S.L., Yang, G., Pang, C.K.: Principle and modeling of a novel moving coil linear-rotary electromagnetic actuator. IEEE Trans. Ind. Electron. 63(11), 6930–6940 (2016)CrossRefGoogle Scholar
  3. 3.
    Hu, C., Wang, Z., Zhu, Y., Zhang, M., Liu, H.: Performance oriented precision LARC tracking motion control of a magnetically levitated planar motor with comparative experiments. IEEE Trans. Ind. Electron. 63(9), 5763–5773 (2016)CrossRefGoogle Scholar
  4. 4.
    Al-Bender, F., Symens, W., Swevers, J., Van Brussel, H.: Theoretical analysis of the dynamic behavior of hysteresis elements in mechanical systems. Int. J. Non-Linear Mech. 39(10), 1721–1735 (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Maeda, Y., Iwasaki, M.: Initial friction compensation using rheology-based rolling friction model in fast and precise positioning. IEEE Trans. Ind. Electron. 60(9), 3865–3876 (2013)CrossRefGoogle Scholar
  6. 6.
    Maeda, Y., Iwasaki, M.: Rolling friction model-based analyses and compensation for slow settling response in precise positioning. IEEE Trans. Ind. Electron. 60(12), 5841–5853 (2013)CrossRefGoogle Scholar
  7. 7.
    Takemura T., Fujimoto, H.: Simultaneous identification of linear parameters and nonlinear rolling friction for ball screw driven stage. In: Proceedings of IEEE Annual Industrial Electronics Society Conference, pp. 3424–3429 (2011)Google Scholar
  8. 8.
    Chen, S.L., Li, X., Teo, C.S., Tan, K.K.: Composite jerk feedforward and disturbance observer for robust tracking of flexible systems. Automatica 80, 253–260 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Evans, E., Rees, D., Jones, L.: Nonlinear disturbance errors in system identification using multisine test signals. IEEE Trans. Instrum. Meas. 43(2), 238–244 (1994)CrossRefGoogle Scholar
  10. 10.
    Evans, C., Rees, D.: Nonlinear distortions and multisine signals-part II: minimizing the distortion. IEEE Trans. Instrum. Meas. 49(3), 610–616 (2000)CrossRefGoogle Scholar
  11. 11.
    Duarte, F.B., Machado, J.T.: Fractional describing function of systems with Coulomb friction. Nonlinear Dyn. 56(4), 381–387 (2009)CrossRefzbMATHGoogle Scholar
  12. 12.
    Li, Z., Ouyang, H., Guan, Z.: Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment. Nonlinear Dyn. 87(2), 1045–1067 (2017)CrossRefGoogle Scholar
  13. 13.
    Makarenkov, O.: A new test for stick-slip limit cycles in dry-friction oscillators with a small nonlinearity in the friction characteristic. Meccanica 52(11–12), 2631–2640 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lin, C.J., Yau, H.T., Tian, Y.C.: Identification and compensation of nonlinear friction characteristics and precision control for a linear motor stage. IEEE/ASME Trans. Mechatron. 18(4), 1385–1396 (2013)CrossRefGoogle Scholar
  15. 15.
    Chen, Y.Y., Huang, P.Y., Yen, J.Y.: Frequency-domain identification algorithms for servo systems with friction. IEEE Trans. Control Syst. Technol. 10(5), 654–665 (2002)CrossRefGoogle Scholar
  16. 16.
    Keikha, E., Al Mamun, A., Lee, T.H., Bhatia, C.S.: Multi-frequency technique for frequency response measurement and its application to servo system with friction. IFAC Proc. Vol. 44(1), 5273–5278 (2011)CrossRefGoogle Scholar
  17. 17.
    Yao, J., Jiao, Z., Ma, D.: A practical nonlinear adaptive control of hydraulic servomechanisms with periodic-like disturbances. IEEE/ASME Trans. Mechatron. 20(6), 2752–2760 (2015)CrossRefGoogle Scholar
  18. 18.
    Barambones, O., Alkorta, P.: Position control of the induction motor using an adaptive sliding-mode controller and observers. IEEE Trans. Ind. Electron. 61(12), 6556–6565 (2014)CrossRefGoogle Scholar
  19. 19.
    Sun, Z., Zhang, G., Yang, J., Zhang, W.: Research on the sliding mode control for underactuated surface vessels via parameter estimation. Nonlinear Dyn. 91(2), 1163C1175 (2017)Google Scholar
  20. 20.
    Jafari, P., Teshnehlab, M., Tavakoli-Kakhki, M.: Synchronization and stabilization of fractional order nonlinear systems with adaptive fuzzy controller and compensation signal. Nonlinear Dyn. 90(2), 1037–1052 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Sun, W., Tang, S., Gao, H., Zhao, J.: Two time-scale tracking control of nonholonomic wheeled mobile robots. IEEE Trans. Control Sys. Technol. 24(6), 2059–2069 (2016)CrossRefGoogle Scholar
  22. 22.
    Sun, W., Zhang, Y., Huang, Y., Gao, H., Kaynak, O.: Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems. IEEE Trans. Ind. Electron. 63(10), 6510–6518 (2016)CrossRefGoogle Scholar
  23. 23.
    Mahapatra, S., Subudhi, B.: Design of a steering control law for an autonomous underwater vehicle using nonlinear \(H_{\infty }\) state feedback technique. Nonlinear Dyn. 90(2), 837–854 (2017)CrossRefzbMATHGoogle Scholar
  24. 24.
    Aphale, S.S., Fleming, A.J., Moheimani, S.R.: Integral resonant control of collocated smart structures. Smart Mater. Struct. 16(2), 439 (2007)CrossRefGoogle Scholar
  25. 25.
    Namavar, M., Fleming, A.J., Aleyaasin, M., Nakkeeran, K., Aphale, S.S.: An analytical approach to integral resonant control of second-order systems. IEEE/ASME Trans. Mechatron. 19(2), 651–659 (2014)CrossRefGoogle Scholar
  26. 26.
    Yao, B.: Desired compensation adaptive robust control. ASME J. Dyn. Syst. Meas. Control 131(6), 1–7 (2009)CrossRefGoogle Scholar
  27. 27.
    Yao, B.: Advanced motion control: from classical PID to nonlinear adaptive robust control. In: 11th IEEE International Workshop Advanced Motion Control, pp. 815-829 (2010)Google Scholar
  28. 28.
    Roy, S., Kar, I.N., Lee, J., Jin, M.: Adaptive-robust time-delay control for a class of uncertain Euler-Lagrange systems. IEEE Trans. Ind. Electron. 64(9), 7109–7119 (2017)CrossRefGoogle Scholar
  29. 29.
    Roy, S., Kar, I.N.: Adaptive sliding mode control of a class of nonlinear systems with artificial delay. J. Frankl. Inst. 354(18), 8156–8179 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Roy, S., Roy, S.B., Kar, I.N.: Adaptive-robust control of Euler-Lagrange systems with linearly parametrizable uncertainty bound. IEEE Trans. Control Sys. Technol. 26(5), 1842–1850 (2017)CrossRefGoogle Scholar
  31. 31.
    Chen, Z., Yao, B., Wang, Q.: Accurate motion control of linear motors with adaptive robust compensation of nonlinear electromagnetic field effect. IEEE/ASME Trans. Mechatron. 18(3), 1122–1129 (2013)CrossRefGoogle Scholar
  32. 32.
    Chen, Z., Yao, B., Wang, Q.: \(\mu \)-synthesis-based adaptive robust control of linear motor driven stages with high-frequency dynamics: a case study. IEEE/ASME Trans. Mechatron. 20(3), 1482–1490 (2015)CrossRefGoogle Scholar
  33. 33.
    Chen, Z., Pan, Y.J., Gu, J.: Integrated adaptive robust control for multilateral teleoperation systems under arbitrary time delays. Int. J. Robust Nonlinear Control 26(12), 2708–2728 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Yuan, M., Chen, Z., Yao, B., Zhu, X.: Time optimal contouring control of industrial biaxial gantry: a high-efficient analytical solution of trajectory planning. IEEE/ASME Trans. Mechatron. 22(1), 247–257 (2017)CrossRefGoogle Scholar
  35. 35.
    Li, C., Chen, Z., Yao, B., Zhu, X., Liu, H.: Modeling, identification, and adaptive robust motion control of voice-voil motor driven stages. ASME Dynamic Systems and Control Conference, pp. V001T14A002 (2013)Google Scholar
  36. 36.
    Li, C., Li, C., Chen, Z., Yao, B.: Advanced synchronization control of a dual-linear-motor-driven gantry with rotational dynamics. IEEE Trans. Ind. Electron. 65(9), 7526–7535 (2018)CrossRefGoogle Scholar
  37. 37.
    Li, C., Yao, B., Wang, Q.: Modeling and synchronization control of a dual drive industrial gantry stage. IEEE/ASME Transactions on Mechatronics, (2017)Google Scholar
  38. 38.
    Yao, J., Deng, W., Jiao, Z.: Adaptive control of hydraulic actuators with LuGre model based friction compensation. IEEE Trans. Ind. Electron. 62(10), 6469–6477 (2015)CrossRefGoogle Scholar
  39. 39.
    Li, C., Yao, B., Zhu, X.: Analysis and compensation of nonlinear friction effect on frequency identification. In: Proceedings of IEEE Annual Industrial Electronics Society Conference, pp. 4453–4458 (2015)Google Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhouChina
  2. 2.Ocean CollegeZhejiang UniversityHangzhouChina
  3. 3.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

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