Journal of Central South University

, Volume 25, Issue 12, pp 3004–3020 | Cite as

Dynamic friction modelling and parameter identification for electromagnetic valve actuator

  • Da Shao (邵达)
  • Si-chuan Xu (许思传)
  • Ai-min Du (杜爱民)Email author


A new modified LuGre friction model is presented for electromagnetic valve actuator system. The modification to the traditional LuGre friction model is made by adding an acceleration-dependent part and a nonlinear continuous switch function. The proposed new friction model solves the implementation problems with the traditional LuGre model at high speeds. An improved artificial fish swarm algorithm (IAFSA) method which combines the chaotic search and Gauss mutation operator into traditional artificial fish swarm algorithm is used to identify the parameters in the proposed modified LuGre friction model. The steady state response experiments and dynamic friction experiments are implemented to validate the effectiveness of IAFSA algorithm. The comparisons between the measured dynamic friction forces and the ones simulated with the established mathematic friction model at different frequencies and magnitudes demonstrate that the proposed modified LuGre friction model can give accurate simulation about the dynamic friction characteristics existing in the electromagnetic valve actuator system. The presented modelling and parameter identification methods are applicable for many other high-speed mechanical systems with friction.

Key words

LuGre friction model artificial fish swarm algorithm Gauss mutation chaotic search parameter identification electromagnetic valve actuator 



提出了一种应用于发动机电磁气门系统的改进LuGre 摩擦模型,对传统的LuGre 摩擦模型进行 了修正,增加了加速度分部和非线性连续开关函数。改进的摩擦模型解决了传统LuGre 模型应用在高 速离散场合下容易发散的固有缺陷,同时不仅保留了传统LuGre 摩擦模型对于预滑动区域滞环效应的 描述能力,又增加了对于滑动区域滞环效应的预测能力。将混沌搜索和高斯变异算子融入传统人工鱼 群算法中形成优化的人工鱼群算法(IAFSA),用来对改进的LuGre 摩擦模型中的参数进行辨识。通过 静态特性试验和动态摩擦试验验证了IAFSA 算法的有效性。利用所建立的精确摩擦力数学模型预测 了在不同频率和不同位移下的摩擦力,并与实测的摩擦力进行了对比,结果表明,改进的LuGre 摩擦 模型能够准确地模拟电磁气门系统的动态摩擦特性。所提出的建模和参数辨识方法也适用于其他具有 摩擦的高速机械系统。


LuGre 摩擦模型 人工鱼群算法 高斯变异 混沌搜索 参数辨识 电磁气门 


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  1. [1]
    KAMIL M, RAHMAN M M, BAKAR R A. An integrated model for predicting engine friction losses in internal combustion engines [J]. Journal of Clinical Immunology, 2014, 4(1): 18–22.Google Scholar
  2. [2]
    YONG Jia, GAO Feng, DING Neng, HE Yu. Pressure-tracking control of a novel electro-hydraulic braking system considering friction compensation [J]. Journal of Central South University, 2017, 24(8): 1909–1921.CrossRefGoogle Scholar
  3. [3]
    LI Zhi, ZHOU Qing, ZHANG Zhi, ZHANG Lian, FAN Da. Prestiction friction compensation in direct-drive mechatronics systems [J]. Journal of Central South University, 2013, 20(11): 3031–3041.CrossRefGoogle Scholar
  4. [4]
    de WIT C C, OLSSON H, ASTROM K J, LISCHINSKY P. A new model for control of systems with friction [J]. IEEE Transactions on Automatic Control, 1995, 40(3): 419–425.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    LI Zhi. LuGre-model-based friction compensation in direct-drive inertially stabilization platforms [C]//Mechatronic Systems. Hangzhou: IFAC Proceedings Volumes, 2013: 636–642.Google Scholar
  6. [6]
    YANG Hui, ZHAO Yan, LI Min, ZHOU Yong. Study on the friction torque test and identification algorithm for gimbal axis of an inertial stabilized platform [J]. Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2015, 303(C): 66–79.Google Scholar
  7. [7]
    ZHOU Xiang, ZHAO Bei, LIU Wei, YUE Hai, YU Rui, ZHAO Yu. A compound scheme on parameters identification and adaptive compensation of nonlinear friction disturbance for the aerial inertially stabilized platform [J]. ISA Transactions, 2017, 67: 293–305.Google Scholar
  8. [8]
    FREIDOVICH L, ROBERTSSON A, SHIRIAEV A, JOHANSSON R. LuGre-model-based friction compensation [J]. IEEE Transactions on Control Systems Technology, 2010, 18(1): 194–200.CrossRefGoogle Scholar
  9. [9]
    LU Lu, YAO Bin, WANG Qing, CHEN Zheng. Adaptive robust control of linear motors with dynamic friction compensation using modified LuGre model [J]. Automatica, 2009, 45(12): 2890–2896.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    GUO Ke, ZHANG Xing, LI Hong, MENG Guang. Non-reversible friction modeling and identification [J]. Archive of Applied Mechanics, 2008, 78(10): 795–809.CrossRefzbMATHGoogle Scholar
  11. [11]
    SAHA A, WAHI P, WIERCIGROCH M, STEFAŃSKI A. A modified LuGre friction model for an accurate prediction of friction force in the pure sliding regime [J]. International Journal of Non-Linear Mechanics, 2016, 80: 122–131.CrossRefGoogle Scholar
  12. [12]
    STEFAŃSKI A, WOJEWODA J, WIERCIGROCH M, KAPITANIAK T. Chaos caused by non-reversible dry friction [J]. Chaos, Solitons & Fractals, 2003, 16(5): 661–664.CrossRefzbMATHGoogle Scholar
  13. [13]
    TRAN X B, HAFIZAH N, YANADA H. Modeling of dynamic friction behaviors of hydraulic cylinders [J]. Mechatronics, 2012, 22(1): 65–75.CrossRefGoogle Scholar
  14. [14]
    TRAN X B, DAO H T, TRAN K D. A new mathematical model of friction for pneumatic cylinders [J]. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2016, 230(14): 2399–2412.Google Scholar
  15. [15]
    LI Yi, PAN Qing, HUANG Ming. Model-based parameter identification of comprehensive friction behaviors for giant forging press [J]. Journal of Central South University, 2013, 20(9): 2359–2365.CrossRefGoogle Scholar
  16. [16]
    TAKROURI M H. Nonlinear friction identification of a linear voice coil DC motor [D]. Sharjah: American University of Sharjah, 2015.Google Scholar
  17. [17]
    LIN C J, YAU H T, TIAN Y C. Identification and compensation of nonlinear friction characteristics and precision control for a linear motor regime [J]. IEEE/ASME Transactions on Mechatronics, 2013, 18(4): 1385–1396.CrossRefGoogle Scholar
  18. [18]
    WU Guo, RU Lai, LIU Xiang. Parameters identification of valve dynamic damping system based on LuGre model and adaptive chaotic particle swarm algorithm [J]. Procedia Engineering, 2012, 29: 3732–3736.CrossRefGoogle Scholar
  19. [19]
    LU Yong, YAN Dan, LEVY D. Friction coefficient estimation in servo systems using neural dynamic programming inspired particle swarm search [J]. Applied Intelligence, 2015, 43(1): 1–14.MathSciNetCrossRefGoogle Scholar
  20. [20]
    YU Yang, LI Yan, LI Jian. Parameter identification and sensitivity analysis of an improved LuGre friction model for magnetorheological elastomer base isolator [J]. Meccanica, 2015, 50(11): 2691–2707.CrossRefGoogle Scholar
  21. [21]
    WANG Xing, WANG Shao. New approach of friction identification for electro-hydraulic servo system based on evolutionary algorithm and statistical logics with experiments [J]. Journal of Mechanical Science and Technology, 2016, 30(5): 2311–2317.CrossRefGoogle Scholar
  22. [22]
    CHENG Xiao, JIANG Ming. An improved artificial bee colony algorithm based on Gaussian mutation and chaos disturbance [C]//International Conference on Advances in Swarm Intelligence. Shenzhen: Springer-Verlag, 2012: 326–333.Google Scholar
  23. [23]
    NESHAT M, SEPIDNAM G, SARGOLZAEI M, TOOSI A N. Artificial fish swarm algorithm: a survey of the state-ofthe-art, hybridization, combinatorial and indicative applications [J]. Artificial Intelligence Review, 2014, 42(4): 965–997.CrossRefGoogle Scholar
  24. [24]
    OLSSON H. Control systems with friction [D]. Lund: Lund Institute of Technology, 1996.Google Scholar
  25. [25]
    de WIT C C, ÅSTRÖM K J, SORIN M. Slides of the workshop on control of systems with friction [C]//IEEE Conference on Decision and Control. Florida, USA, 1997.Google Scholar
  26. [26]
    LI Xiao. A new intelligent optimization-artificial fish swarm algorithm [D]. Hangzhou: Zhejiang University of Zhejiang, 2003. (in Chinese)Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Automotive StudiesTongji UniversityShanghaiChina
  2. 2.Clean Energy Automotive Engineering CenterTongji UniversityShanghaiChina

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