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自抗扰控制框架下的摩擦力振动分析

朴敏楠, 王颖, 周亚靖, 孙明玮, 张新华, 陈增强

朴敏楠, 王颖, 周亚靖, 孙明玮, 张新华, 陈增强. 自抗扰控制框架下的摩擦力振动分析[J]. 力学学报, 2020, 52(5): 1485-1497. DOI: 10.6052/0459-1879-20-149
引用本文: 朴敏楠, 王颖, 周亚靖, 孙明玮, 张新华, 陈增强. 自抗扰控制框架下的摩擦力振动分析[J]. 力学学报, 2020, 52(5): 1485-1497. DOI: 10.6052/0459-1879-20-149
Piao Minnan, Wang Ying, Zhou Yajing, Sun Mingwei, Zhang Xinhua, Chen Zengqiang. ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1485-1497. DOI: 10.6052/0459-1879-20-149
Citation: Piao Minnan, Wang Ying, Zhou Yajing, Sun Mingwei, Zhang Xinhua, Chen Zengqiang. ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1485-1497. DOI: 10.6052/0459-1879-20-149
朴敏楠, 王颖, 周亚靖, 孙明玮, 张新华, 陈增强. 自抗扰控制框架下的摩擦力振动分析[J]. 力学学报, 2020, 52(5): 1485-1497. CSTR: 32045.14.0459-1879-20-149
引用本文: 朴敏楠, 王颖, 周亚靖, 孙明玮, 张新华, 陈增强. 自抗扰控制框架下的摩擦力振动分析[J]. 力学学报, 2020, 52(5): 1485-1497. CSTR: 32045.14.0459-1879-20-149
Piao Minnan, Wang Ying, Zhou Yajing, Sun Mingwei, Zhang Xinhua, Chen Zengqiang. ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1485-1497. CSTR: 32045.14.0459-1879-20-149
Citation: Piao Minnan, Wang Ying, Zhou Yajing, Sun Mingwei, Zhang Xinhua, Chen Zengqiang. ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1485-1497. CSTR: 32045.14.0459-1879-20-149

自抗扰控制框架下的摩擦力振动分析

基金项目: 1)国家自然科学基金资助项目(61573197);国家自然科学基金资助项目(61973175);国家自然科学基金资助项目(51777013)
详细信息
    通讯作者:

    孙明玮

  • 中图分类号: TP273,TH113.1

ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK

  • 摘要: 自抗扰控制(active disturbance rejection control, ADRC)是一种具有两自由度控制结构的工程化方法, 由于其能够直观有效地处理多种扰动, 近些年来在许多机电系统上得到了成功应用. 当采用ADRC对带有摩擦力的机电系统进行调节时, 可能会产生极限环振动. 目前, 还没有ADRC框架下摩擦力振动精确分析的相关工作. 因此, 本文采用非线性动力学系统的分析工具对这一问题进行研究. 首先, 考虑两种典型摩擦力模型, 静态切换模型和动态LuGre 模型, 对一类二阶运动系统设计不同阶次的ADRC, 得到控制器的等效形式, 并揭示出与比例积分微分(proportional-integral-derivative, PID)控制之间的联系. 然后, 采用打靶法结合拟弧长延拓方法求解系统中的极限环, 并根据Floquet理论判断极限环的稳定性、可能出现的分岔以及分岔类型. 此外, 通过雅克比矩阵和近似数值方法对系统平衡点集的局部稳定性进行了分析. 最后, 通过数值计算研究了摩擦力模型和参数、ADRC阶次和参数对极限环和平衡点集的影响. 计算结果表明, 决定摩擦力Stribeck效应负斜率的参数$\beta$作用较大. 当$\beta>1$时, 两种摩擦力模型下的闭环系统呈现出相同的特性, 极限环会出现环面折叠分岔(cyclic fold bifurcation, CFB)且平衡点集是局部稳定的. 然而当$\beta<1$时, 两种闭环系统呈现出完全不同的特性. 此外, 不同阶次的ADRC在极限环的存在性和稳定性、平衡点集的稳定性上面的结论是相同的, 而低阶次的ADRC能够更好地解决摩擦力补偿和稳定鲁棒性之间的矛盾问题. 这些结论对实际现象的理解、ADRC阶次的选择以及参数整定提供了一定指导.
    Abstract: Active disturbance rejection control(ADRC) is a practical control method with a two-degree-of-freedom structure. Due to its capability of handling multifarious disturbances in a straightforward and effective manner, ADRC has been successfully applied to many mechanical systems. However, the limit cycle vibration may be induced when employing the ADRC for mechanical systems with friction. At present, there is no precise analysis work about the friction induced vibration under the ADRC framework. Therefore, this paper investigates this problem by using the analysis tools of nonlinear dynamic systems. First, two representative friction models, static switch model and dynamic LuGre model, respectively, are considered, and active disturbance rejection controllers of different orders are designed for a class of second-order motion systems. Equivalent forms of the controllers are obtained and their relationships with the proportional-integral-derivative(PID) controller are revealed. Then, the limit cycle is calculated by using the shooting method combined with the pseudo arc-length continuation approach. Based on the Floquet theory, the stability, occurrence and type of bifurcation of the limit cycle can be determined. In addition, the local stability of the equilibrium points is analyzed based on the Jacobian matrix and approximate numerical method. Finally, the effects of the model and parameter of friction, the order and parameters of the ADRC on the limit cycle are investigated by numerical calculations. As shown by the calculation results, the parameter $\beta$, which determines the negative slope of the Stribeck effect, has a significant effect. When $\beta>1$, closed-loop systems with these two friction models have the same characteristics. Cyclic fold bifurcation(CFB) of the limit cycle occurs and the set of equilibrium points is locally stable. However, characteristics of these two closed-loop systems are totally different when $\beta<1$. As for the ADRC order, it is found that the order does not affect the conclusions in terms of the existence and stability of the limit cycle, and the stability of the set of equilibrium points. Moreover, low-order ADRC has superior performance in tackling the conflict between the friction compensation and stability robustness. These results can provide some guidelines on the understanding of practical phenomena, selection of the ADRC order, and parameter tuning.
  • [1] 郑鹏, 王琪, 吕敬 等. 摩擦与滚阻对被动行走器步态影响的研究. 力学学报, 2020,52(1):162-170
    [1] ( Zheng Peng, Wang Qi, Lü Jing, et al. Study on the influence of friction and rolling resistance on the gait of passive dynamic walker. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(1):162-170 (in Chinese))
    [2] 刘兴天, 陈树海, 王嘉登 等. 几何非线性摩擦阻尼隔振系统动力学行为研究. 力学学报, 2019,51(2):371-379
    [2] ( Liu Xingtian, Chen Shuhai, Wang Jiadeng, et al. Anlysis of the dynamic behavior and performance of a vibration isolation system with geometric nonlinear friction damping. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):371-379 (in Chinese))
    [3] 王晓军, 吕敬, 王琪. 含摩擦滑移铰平面多刚体系统动力学的数值算法. 力学学报, 2019,51(1):209-217
    [3] ( Wang Xiaojun, Lü Jing, Wang Qi. A numerical method for dynamics of planar multi-rigid-body system with frictional translational joints based on LuGre friction model. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):209-217 (in Chinese))
    [4] Han J. From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 2009,56(3):900-906
    [5] Tian G, Gao Z. Benchmark tests of active disturbance rejection control on an industrial motion control platform// Proceedings of the American Control Conference. New York: IEEE, 2009: 5552-5557
    [6] Goforth FJ. On motion control design and tuning techniques// Proceedings of the American Control Conference, New York: IEEE, 2004: 716-721
    [7] Xue W, Madonski R, Lakomy K, et al. Add-on module of active disturbance rejection for set-point tracking of motion control systems. IEEE Transactions on Industry Applications, 2017,53(4):4028-4040
    [8] Sun M, Wang Z, Wang Y, et al. On low-velocity compensation of brushless DC servo in the absence of friction model. IEEE Transactions on Industrial Electronics, 2013,60(9):3897-3905
    [9] Piao M, Wang Y, Sun M, et al. Friction compensation and limit cycle suppression at low velocities based on extended state observer// 21st IFAC World Congress in Berlin, Germany, July 12-17, 2020, Accepted
    [10] 陈增强, 王永帅, 孙明玮 等. 二阶非线性系统自抗扰控制的全局渐近稳定性. 控制理论与应用, 2018,35(11):1687-1696
    [10] ( Chen Zengqiang, Wang Yongshuai, Sun Mingwei, et al. Global and asymptotical stability of active disturbance rejection control for second-order nonlinear systems. Control Theory and Technology, 2018,35(11):1687-1696 (in Chinese))
    [11] Armstrong-Hélouvry B, Dupont P, Canudas de wit C. A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica, 1994,30(7):1083-1138
    [12] Kesarkar AA, Selvaganesan N, Priyadarshan H. A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers. Nonlinear Dynamics, 2014,78(4):2871-2882
    [13] Kim M, Chung S. Friction identification of ball-screw driven servomechanisms through the limit cycle analysis. Mechatronics, 2006,16(2):131-140
    [14] Armstrong-Hélouvry B, Amin B. PID control in the presence of static friction: A comparison of algebraic and describing function analysis. Automatica, 1996,32(5):679-692
    [15] Radcliffe CJ, Southward SC. A property of stick-slip friction models which promotes limit cycle generation// Proceedings of the American Control Conference, New York: IEEE, 1990: 1198-1203
    [16] Galvanetto U, Knudsen C. Events maps in a stick-slip system. Nonlinear Dynamics, 1997,13:99-115
    [17] Hensen RHA. Controlled mechanical systems with friction. Eindhoven: Eindhoven University of Technology, 2002
    [18] Hensen RHA, Molengraft MJGVD, Steinbuch M. Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model. Automatica, 2003,39(12):2131-2137
    [19] Jeon S. Integrator leakage for limit cycle suppression in servo mechanisms with stiction. Journal of Dynamic Systems, Measurement, and Control, 2012,134(3):034502
    [20] 朴敏楠, 王科磊, 孙明玮 等. 基于积分泄漏的机电伺服系统摩擦力补偿. 中南大学学报 (自然科学版), 2020,51(3):668-677
    [20] ( Piao Minnan, Wang Kelei, Sun Mingwei, et al. Friction compensation of electromechanical servo systems based on integrator leakage. Journal of Central South University (Science and Technology), 2020,51(3):668-677 (in Chinese))
    [21] Leine RI, Campen DHV, Kraker AD, et al. Stick-slip vibrations induced by alternate friction models. Nonlinear Dynamics, 1998,16(1):41-54
    [22] Putra D, Nijmeijer HH. Limit cycling in an observer-based controlled system with friction: Numerical analysis and experimental validation. International Journal of Bifurcation and Chaos, 2004,14(9):3083-3093
    [23] Leine RI, Campen DHV, Vrande BLVD. Bifurcations in nonlinear discontinuous systems. Nonlinear Dynamics, 2000,23(2):105-164
    [24] Vrande BLVD, Campen DHV, Kraker AD. An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure. Nonlinear Dynamics, 1999,19(2):159-171
    [25] Brindley J, Kaas-Petersen C, Spence A. Path-following methods in bifurcation problems. Physica D Nonlinear Phenomena, 1989,34(3):456-461
    [26] 易中贵, 戈新生. 自由下落猫姿态最优控制的混合优化策略. 力学学报, 2016,48(6):1390-1397
    [26] ( Yi Zhonggui, Ge Xinsheng. The attitude optimal control with a hybrid optimal strategy for a free-falling cat. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(6):1390-1397 (in Chinese))
    [27] Charroyer L, Chiello O, Sinou JJ. Self-excited vibrations of a non-smooth contact dynamical system with planar friction based on the shooting method. International Journal of Mechanical Sciences, 2018,144:90-101
    [28] Canudas de wit C, Olsson H, Astrom KJ, et al. A new model for control of systems with friction. IEEE Transactions on Automatic Control, 1995,40:419-425
    [29] 曲子芳, 张正娣, 彭淼 等. 双频激励下Filippov系统的非光滑簇发振荡机理. 力学学报, 2018,50(5):1145-1155
    [29] ( Qu Zifang, Zhang Zhengdi, Peng Miao, et al. Non-smooth bursting oscillation mechanisms in a Filippov-type system with multiple periodic excitations. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(5):1145-1155 (in Chinese))
    [30] 张毅, 韩修静, 毕勤胜. 串联式叉型滞后簇发振荡及其动力学机制. 力学学报, 2019,51(1):228-236
    [30] ( Zhang Yi, Han Xiujing, Bi Qinsheng. Series-mode pitchfork-hysteresis bursting oscillations and their dynamical mechanisms. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):228-236 (in Chinese))
    [31] 石建飞, 苟向锋, 朱凌云. 两空间耦合下齿轮传动系统多稳态特性研究. 力学学报, 2019,51(5):1489-1499
    [31] ( Shi Jianfei, Gou Xiangfeng, Zhu Lingyun. Research on multi-stability characteristics of gear transmission system with two-space coupling. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1489-1499 (in Chinese))
    [32] 郑健康, 张晓芳, 毕勤胜. 一类混沌系统中的簇发振荡及其延迟叉形分岔行为. 力学学报, 2019,51(2):540-549
    [32] ( Zheng Jiankang, Zhang Xiaofang, Bi Qinsheng. Bursting oscillations as well as the delayed pitchfork bifurcation behaviors in a class of chaos system. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):540-549 (in Chinese))
    [33] Karnopp D. Computer simulation of stick-slip friction in mechanical dynamic systems. Journal of Dynamic, Systems, Measurement, and Control, 1985,107(1):100-103
    [34] Marton L. On analysis of limit cycles in positioning systems near Striebeck velocities. Mechatronics, 2008,18(1):46-52
    [35] Wu Q, Sun M, Chen Z, et al. Tuning of active disturbance rejection attitude controller for statically unstable launch vehicle. Journal of Spacecraft and Rockets, 2017,54(6):1383-1389
    [36] Zhong S, Huang Y, Guo L. A Parameter formula connecting PID and ADRC. Science China Information Sciences, DOI: 10.1007/s11432-019-2712-7
    [37] Nayfeh AH, Balachandran B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. New Jersey: Wiley, 2004
    [38] Fey RHB. Steady State Behaviour of Reduced Dynamic Systems with Local Nonlinearities. Eindhoven: Eindhoven University of Technology, 1992
    [39] 贾宏杰, 余贻鑫, 李鹏. 电力系统环面分岔与混沌现象. 中国电机工程学报, 2002,22(8):7-11
    [39] ( Jia Hongjie, Yu Yixin, Li Peng. Torus bifurcation and chaos in power systems. Proceedings of the CSEE, 2002,22(8):7-11 (in Chinese))
    [40] 邱宇, 邱勇, 邱家俊. 机电耦联系统余维3动态分岔研究. 力学学报, 2006,38(3):421-428
    [40] ( Qiu Yu, Qiu Yong, Qiu Jiajun. Study of electro mechanical coupling system by codimension-3 dynamical bifurcation. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(3):421-428 (in Chinese))
    [41] Clarke FA, Ledyaev YS, Stem RJ, et al. Nonsmooth Analysis and Control Theory. New York: Graduate Texts in Mathematics, 1998
    [42] Leine RI, Wouw VD. Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact. Nonlinear Dynamics, 2008,51(4):551-583
    [43] Li Z, Cao Q, Leger A, et al. The equilibrium stability for a smooth and discontinuous oscillator with dry friction. Acta Mechanica Sinica, 2016,32(2):309-319
    [44] Foias C, Georgiou TT, Smith MC. Robust stability of feedback systems: a geometric approach using the gap metric. SIAM Journal on Control and Optimization, 1993,31(6):1518-1537
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出版历程
  • 收稿日期:  2020-05-05
  • 刊出日期:  2020-10-09

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