多尺度法在时滞弹性关节机械臂非线性振动问题中的应用
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摘要
针对非线性弹性关节机械臂,研究传动过程中的时滞效应对机械臂系统周期振动的影响.本文改进了具有弹性关节的非线性机械臂动力学模型,引入时滞参数,应用多尺度法,得到系统的近似解析解,考察了时滞对机械臂系统周期运动的影响规律.数值软件计算结果表明解析解与数值解具有较好的吻合度.从而验证了本文多尺度方法的有效性和正确性.
For the nonlinear elastic joint manipulator, the effect of time-delay in the transmission process on the periodic vibration of the manipulator system is studied. In this paper, the dynamic model of a nonlinear manipulator with elastic joints is improved. Specifically, time-delay parameters are introduced, multi-scale method is applied, the approximate analytical solution of the system is obtained and the influence of time delay on the periodic motion of the manipulator system is investigated. Numerical software results show that the analytical solution is in good agreement with the numerical solution. This verifies the effectiveness and correctness of the multiscale methods proposed in this paper.
For the nonlinear elastic joint manipulator, the effect of time-delay in the transmission process on the periodic vibration of the manipulator system is studied. In this paper, the dynamic model of a nonlinear manipulator with elastic joints is improved. Specifically, time-delay parameters are introduced, multi-scale method is applied, the approximate analytical solution of the system is obtained and the influence of time delay on the periodic motion of the manipulator system is investigated. Numerical software results show that the analytical solution is in good agreement with the numerical solution. This verifies the effectiveness and correctness of the multiscale methods proposed in this paper.
引文
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[6]荣吉利,项阳,辛鹏飞,等.考虑关节柔性的双连杆机械臂振动控制及实验研究[J].宇航学报,2017,38(10):1024-1031.
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[9]洪昭斌,陈力,李文望.柔性空间机械臂协调运动的鲁棒神经网络控制及柔性振动PD反馈控制[J].力学季刊,2014,35(1):98-104.
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[11]陈志勇,陈力.柔性空间机械臂振动抑制的模糊终端滑模控制[J].振动、测试与诊断,2010,30(5):481-486.
[12]王在华,胡海岩.时滞动力系统的稳定性与分岔:从理论走向应用[J].力学季刊,2013,43(1):3-20.
[13]徐鉴,裴利军.时滞系统动力学近期研究进展与展望[J].力学进展,2006,36(1):17-30.
[14]赵艳影,徐鉴.时滞非线性动力吸振器的减振机理[J].力学学报,2008,1:98-106.
[15]陈明金,李树荣,曹乾磊.时滞柔性关节机械臂自适应位置/力控制[J].控制理论与应用,2015,32(2):217-223.
[16]张栋,徐鉴.时滞对柔性悬臂梁饱和控制的影响[J].力学季刊,2009,30(3):385-392.
[17]李树荣,尹怀强.具有时滞的柔性关节多机械臂协同自适应位置/力控制[J].控制理论与应用,2017,34(9):1208-1214.
[18]JIANG S Y,XU J,YAN Y.Stability and oscillations in a slow-fast flexible joint system with transformation delay[J].Acta Mechanica Sinica,2014,30(5):727-738.
[19]NAYFEH A H.Order reduction of retarded nonlinear systems-the method of multiple scales versus center-manifold reduction[J].Nonlinear Dynamics,2008,51(4):483-500.
[2]MATSUMARU T.Design and control of the modular robot system:TOMMS[C]//Proceedings of IEEEInternational Conference on Robotics and Automation,Piscataway:IEEE,1995,2125-2131.
[3]赵杰亮,谷勇霞,阎绍泽,等.谐波传动对柔性机械臂动力学特性的影响[J].清华大学学报:自然科学版,2013,53(4):482-486.
[4]SPONG M W.Modeling and control of elastic joint robots[J].Journal of Dynamic Systems,Measurement,and Control,1987,109(1):310-319.
[5]BRIDGES M M,DAWSON D M.Redesign of robust controllers for RLFJ robotic manipulators actuated with harmonic drives[C]//American Control Conference,IEEE,1993,2507-2510.
[6]荣吉利,项阳,辛鹏飞,等.考虑关节柔性的双连杆机械臂振动控制及实验研究[J].宇航学报,2017,38(10):1024-1031.
[7]JIA X X,WEN J C.Direct tip regulation of a single-link flexible manipulator by adaptive variable structure control[J].International Journal of Systems Science,2001,32(1):121-135.
[8]郭益深,陈力.空间机械臂关节轨迹跟踪的自适应反演滑模控制[J].力学季刊,2009,30(3):445-450.
[9]洪昭斌,陈力,李文望.柔性空间机械臂协调运动的鲁棒神经网络控制及柔性振动PD反馈控制[J].力学季刊,2014,35(1):98-104.
[10]王晓军,王宇嘉.基于混合控制的机械臂定位和振动控制研究[J].轻工机械,2017,35(3):45-48.
[11]陈志勇,陈力.柔性空间机械臂振动抑制的模糊终端滑模控制[J].振动、测试与诊断,2010,30(5):481-486.
[12]王在华,胡海岩.时滞动力系统的稳定性与分岔:从理论走向应用[J].力学季刊,2013,43(1):3-20.
[13]徐鉴,裴利军.时滞系统动力学近期研究进展与展望[J].力学进展,2006,36(1):17-30.
[14]赵艳影,徐鉴.时滞非线性动力吸振器的减振机理[J].力学学报,2008,1:98-106.
[15]陈明金,李树荣,曹乾磊.时滞柔性关节机械臂自适应位置/力控制[J].控制理论与应用,2015,32(2):217-223.
[16]张栋,徐鉴.时滞对柔性悬臂梁饱和控制的影响[J].力学季刊,2009,30(3):385-392.
[17]李树荣,尹怀强.具有时滞的柔性关节多机械臂协同自适应位置/力控制[J].控制理论与应用,2017,34(9):1208-1214.
[18]JIANG S Y,XU J,YAN Y.Stability and oscillations in a slow-fast flexible joint system with transformation delay[J].Acta Mechanica Sinica,2014,30(5):727-738.
[19]NAYFEH A H.Order reduction of retarded nonlinear systems-the method of multiple scales versus center-manifold reduction[J].Nonlinear Dynamics,2008,51(4):483-500.