Abstract
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.
Similar content being viewed by others
Notes
Due to the severe oscillation under this situation, the system has been shut done at about 40 s for the sake of safety. After then, no data have been collected.
References
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)
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)
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)
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)
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)
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)
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)
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)
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)
Evans, C., Rees, D.: Nonlinear distortions and multisine signals-part II: minimizing the distortion. IEEE Trans. Instrum. Meas. 49(3), 610–616 (2000)
Duarte, F.B., Machado, J.T.: Fractional describing function of systems with Coulomb friction. Nonlinear Dyn. 56(4), 381–387 (2009)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Aphale, S.S., Fleming, A.J., Moheimani, S.R.: Integral resonant control of collocated smart structures. Smart Mater. Struct. 16(2), 439 (2007)
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)
Yao, B.: Desired compensation adaptive robust control. ASME J. Dyn. Syst. Meas. Control 131(6), 1–7 (2009)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Li, C., Yao, B., Wang, Q.: Modeling and synchronization control of a dual drive industrial gantry stage. IEEE/ASME Transactions on Mechatronics, (2017)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
This work was supported by National Natural Science Foundation of China (Nos. 61603332, 51475412 and 51875508) and Science Fund for Creative Research Groups of National Natural Science Foundation of China (No. 51521064).
Rights and permissions
About this article
Cite this article
Li, C., Chen, Z. & Yao, B. Identification and adaptive robust precision motion control of systems with nonlinear friction. Nonlinear Dyn 95, 995–1007 (2019). https://doi.org/10.1007/s11071-018-4610-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-018-4610-6