含变质量构件的轴向运动梁的横向振动主动控制
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摘要
轴向运动结构是一类广泛使用的工程传送元件,而在传送过程中常常包含质量运动或者质量变化,质量的运动或改变和轴向运动间相互耦合作用,使结构的振动更加突出。为满足轴向运动机构高精度准定位的需求,围绕含变质量构件的机械臂结构,开展变质量-轴向运动耦合作用结构的振动主动控制研究。首先基于Galerkin法和模态叠加法建立了变质量-轴向运动压电梁的控制方程,然后针对系统的时变特性,设计LQG控制器对系统进行振动主动控制,并分析了多种工况下结构的振动抑制问题,最后采用Choi-Williams分布将信号在时频域上分解,分析了控制前后系统的时频特性。数值分析表明,施加LQG控制后,系统的横向振动在相关频率内都得到了有效的抑制,使用Choi-Williams分布可以准确反映系统振动频率与振动能量随时间的变化规律。通过研究含时变参数的轴向运动结构的运动特性和振动主动控制,对于智能机械臂结构设计具有一定指导意义。
Axially moving structures are widely used as basic components in kinds of delivery systems.It is very common that mass changing or mass moving occurs in the process of delivery,which causes the increase or decrease of the total mass.The coupling of variation of the mass and the axially moving makes more significant vibration of the structures.This paper studies the active vibration control of the axially moving structures with time varying mass by taking an axially moving manipulator attached with a time varying concentrated mass as a specific subject.The governing equations of the time varying system are derived using Galerkin method and mode superposition method.Then LQG controller is designed for controlling the vibration of the system with different conditions taken into account,including the increasing mass system and the decreasing mass system.Finally,the response signals are decomposed by the method of Choi Williams distribution,and the time frequency features are obtained.Numerical simulations demonstrate that the vibration of the system is effectively controlled under the LQG controller in the limited range of frequencies,and the variation of the frequency and vibration energy can be given by Choi Williams distribution,showing that it is a much more powerful tool than FFT.The study on the dynamic characteristics and active control of the axially moving structures with time varying mass can offer guides to innovative design of smart manipulators.
Axially moving structures are widely used as basic components in kinds of delivery systems.It is very common that mass changing or mass moving occurs in the process of delivery,which causes the increase or decrease of the total mass.The coupling of variation of the mass and the axially moving makes more significant vibration of the structures.This paper studies the active vibration control of the axially moving structures with time varying mass by taking an axially moving manipulator attached with a time varying concentrated mass as a specific subject.The governing equations of the time varying system are derived using Galerkin method and mode superposition method.Then LQG controller is designed for controlling the vibration of the system with different conditions taken into account,including the increasing mass system and the decreasing mass system.Finally,the response signals are decomposed by the method of Choi Williams distribution,and the time frequency features are obtained.Numerical simulations demonstrate that the vibration of the system is effectively controlled under the LQG controller in the limited range of frequencies,and the variation of the frequency and vibration energy can be given by Choi Williams distribution,showing that it is a much more powerful tool than FFT.The study on the dynamic characteristics and active control of the axially moving structures with time varying mass can offer guides to innovative design of smart manipulators.
引文
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[6]刘金建,蔡改改,谢锋,等.轴向运动功能梯度黏弹性梁横向振动的稳定性分析[J].动力学与控制学报,2016,14(06):533-541.Liu Jinjian,Cai Gaigai,Xie Feng,et al.Stability anslysis on transverse vibration of axially moving functionally graded viscoelastic beams[J].Journal of Dynamics and Control,2016,14(06):533-541.
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[10]刘定强,王忠民.轴向运动矩形薄膜的横向振动控制[J].西安理工大学学报,2007,23(01):62-65.Liu Dingqiang,Wang Zhongmin.The transverse vibration control of an axially moving rectangular membrane[J].Journal of Xi′an University of Technology,2007,23(01):62-65.
[11]王亮,陈怀海,贺旭东,等.轴向运动变长度悬臂梁的振动控制[J].振动工程学报,2009,22(06):565-570.Wang Liang,Chen Huaihai,He Xudong,et al.Vibration control of an axially moving cantilever beam with varying length[J].Journal of Vibration Engineering,2009,22(06):565-570.
[12]王亮,陈怀海,贺旭东,等.轴向运动悬臂梁横向振动的磁力控制[J].南京航空航天大学学报,2010,42(05):568-573.Wang Liang,Chen Huaihai,He Xudong,et al.Active vibration control of axially moving cantilever beam by magnetic force[J].Journal of Nanjing University of Aeronautics&Astronautics,2010,42(05):568-573.
[13]Zhao L,Hu Z D.Active vibration control of an axially translating robot arm with rotating prismatic joint using self-sensing actuator[J].Shock and Vibration,2015,2015:964139.
[14]He W,Nie S,Meng T,et al.Modeling and vibration control for a moving beam with application in a drilling riser[J].IEEE Transactions on Control Systems Technology,2017,25(3):1036-1043.
[15]Meirovitch L.Dynamics and Control of Structures[M].New York:Wiley,1990.
[16]Gawronski W K.Advanced Structural Dynamics and Active Control of Structures[M].New York:Springer,2004
[17]Cohen L. Time frequency distributions-review[J].Proceedings of the IEEE,1989,77(7):941-981.
[18]姜鸣,陈进,汪慰军.几种Cohen类时频分布的比较及应用[J].机械工程学报,2003,29(3):129-134.Jiang Ming,Chen Jin,Wang Weijun.Comparison and application of some time-frequency distribution of belonging to Cohen class[J].Chinese Journal of Mechanical Engineering,2003,29(3):129-134.
[2] Ghayesh M H,Amabili M.Steady-state transverse response of an axially moving beam with time-dependent axial speed[J].International Journal of Non-Linear Mechanics,2013,49:40-49.
[3] Yang X D,Zhang W.Nonlinear dynamics of axially moving beam with coupled longitudinal transversal vibrations[J].Nonlinear Dynamics,2014,78(4):2547-2556.
[4]吕海炜,李映辉,李亮,等.轴向运动软夹层梁横向振动分析[J].振动与冲击,2014,33(02):41-46.Lv Haiwei,Li Yinghui,Li Liang et al.Analysis of transverse vibration of axially moving soft sandwich beam[J].Journal of Vibration and Shock,2014,33(02):41-46.
[5]陈红永,李上明.轴向运动梁在轴向载荷作用下的动力学特性研究[J].振动与冲击,2016,35(19):75-80.Chen Hongyong,Li Shangming.Dynamic characteristics of an axially moving Timoshenko beam under axial loads[J].Journal of Vibration and Shock,2016,35(19):75-80.
[6]刘金建,蔡改改,谢锋,等.轴向运动功能梯度黏弹性梁横向振动的稳定性分析[J].动力学与控制学报,2016,14(06):533-541.Liu Jinjian,Cai Gaigai,Xie Feng,et al.Stability anslysis on transverse vibration of axially moving functionally graded viscoelastic beams[J].Journal of Dynamics and Control,2016,14(06):533-541.
[7]张伟,陈立群.轴向运动弦线横向振动控制的自适应方法[J].机械工程学报,2006,42(04):96-100.Zhang Wei,Chen Liqun.Transverse vibration control of an axially moving string system by adaptive method[J].Chinese Journal of Mechanical Engineering,2006,42(04):96-100.
[8]张伟,陈立群.轴向运动弦线横向振动控制的Lyapunov方法[J].控制理论与应用,2006,23(04):531-535.Zhang Wei,Chen Liqun.Transverse vibration control of an axially moving string system by Lyapunov method[J].Control Theory&Applications,2006,23(04):531-535.
[9] He W,Ge S S,Huang D.Modeling and vibration control for a nonlinear moving string with output constraint[J].IEEE/ASME Transactions on Mechatronics,2015,20(4):1886-1897.
[10]刘定强,王忠民.轴向运动矩形薄膜的横向振动控制[J].西安理工大学学报,2007,23(01):62-65.Liu Dingqiang,Wang Zhongmin.The transverse vibration control of an axially moving rectangular membrane[J].Journal of Xi′an University of Technology,2007,23(01):62-65.
[11]王亮,陈怀海,贺旭东,等.轴向运动变长度悬臂梁的振动控制[J].振动工程学报,2009,22(06):565-570.Wang Liang,Chen Huaihai,He Xudong,et al.Vibration control of an axially moving cantilever beam with varying length[J].Journal of Vibration Engineering,2009,22(06):565-570.
[12]王亮,陈怀海,贺旭东,等.轴向运动悬臂梁横向振动的磁力控制[J].南京航空航天大学学报,2010,42(05):568-573.Wang Liang,Chen Huaihai,He Xudong,et al.Active vibration control of axially moving cantilever beam by magnetic force[J].Journal of Nanjing University of Aeronautics&Astronautics,2010,42(05):568-573.
[13]Zhao L,Hu Z D.Active vibration control of an axially translating robot arm with rotating prismatic joint using self-sensing actuator[J].Shock and Vibration,2015,2015:964139.
[14]He W,Nie S,Meng T,et al.Modeling and vibration control for a moving beam with application in a drilling riser[J].IEEE Transactions on Control Systems Technology,2017,25(3):1036-1043.
[15]Meirovitch L.Dynamics and Control of Structures[M].New York:Wiley,1990.
[16]Gawronski W K.Advanced Structural Dynamics and Active Control of Structures[M].New York:Springer,2004
[17]Cohen L. Time frequency distributions-review[J].Proceedings of the IEEE,1989,77(7):941-981.
[18]姜鸣,陈进,汪慰军.几种Cohen类时频分布的比较及应用[J].机械工程学报,2003,29(3):129-134.Jiang Ming,Chen Jin,Wang Weijun.Comparison and application of some time-frequency distribution of belonging to Cohen class[J].Chinese Journal of Mechanical Engineering,2003,29(3):129-134.