基于压电致动器的空间柔性机械臂系统的轨迹跟踪与振动抑制一体化控制研究
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摘要
空间柔性机械系统的轨迹跟踪和振动抑制问题是当前柔性结构和航天科技领域中及其重要又富有挑战性的课题。本学位论文在国家自然科学基金的资助下,以空间柔性机械臂系统的运动控制和振动抑制技术为研究背景,以一类由压电致动器/传感器、伺服电机减速器驱动结构和柔性臂等构成的典型智能空间柔性机械臂系统为研究对象,研究了伺服电机和压电致动器联合作用下柔性臂系统的动力学特性,并建立系统的动力学模型和驱动模型；解决了系统中致动器/传感器的优化配置问题；深入研究了空间柔性机械臂系统的抑振轨迹规划机理和优化算法；确定了柔性臂系统的运动控制策略和振动抑制策略,最终实现了在伺服电机驱动和压电致动器主动控制下空间柔性机械臂系统的轨迹跟踪和振动抑制一体化控制。提高了系统的运动控制精度和工作效率。
以一类包含伺服电机、减速器、柔性臂、末端操作对象以及压电致动器/传感器在内的空间柔性机械臂系统为研究对象,基于假设模态法和Hamilton原理建立了系统的动力学方程。并对伺服电机的驱动机理进行研究,提出了考虑摩擦力矩、减速器及柔性臂弹性振动的耦合反力矩的伺服电机机电耦合模型。
基于线性二次最优控制理论,提出了致动器/传感器的复合优化配置准则,该准则包含两个控制指标：①综合柔性臂弹性振动能量、压电致动器控制能量,系统刚体转动能量、以及伺服电机驱动能量的LQR综合能量指标；②致动器引入对系统特性影响的系统结构固有频率变化率指标。然后采用改进的多岛遗传算法得到了不同频率变化率指标下,一组、两组压电致动器/传感器的尺寸、位置和控制增益的最优配置结果。
从系统动力学方程出发,揭示了伺服电机驱动、压电致动器主动控制下空间柔性机械臂系统的抑振轨迹规划机理,提出了包含系统柔性部分激振力矩和刚性部分驱动力矩的综合指标。并选择激起柔性臂振动较小的五次多项式样条函数作为轨迹优化的基础曲线和插值曲线,利用改进的多岛遗传算法对空间柔性机械臂系统的运动轨迹进行优化,得到了综合指标最小的最优抑振轨迹。
引入奇异摄动因子对系统动力学方程进行分解,分别推导得到系统基于奇异摄动模型的快、慢子系统动力学方程。针对快、慢子系统在各自时标下的动力学特性,对具有强耦合性及强非线性的慢变子系统提出模糊滑模控制策略；而对由于模态截断带来模型不确定性以及多模态特性的快变子系统采用分级自适应模糊PID控制策略,从而实现了空间柔性机械臂系统在伺服驱动电机和压电致动器联合控制下的轨迹跟踪和振动抑制一体化控制,提高了系统的运动精度和操作效率。
Trajcectory tracking of space flexible manipulators together with suppressing their vibrations during their operation has been the main concern of many recent stuies in aeronautics and robotics. This thesis is mainly concerned with trajcectory tracking and vibration suppression control of a typical space flexible manipulator system using piezoelectric actuators. Funded by National Natural Science Foundation, dynamic modeling of the flexible manipulator system, optimal placing of the actuators/sensors, optimal trajectory planning for vibration suppression of the manipulator and the integrated control strategies for trajcectory tracking and vibration suppression of the system are studied deeply in this dissertation. The main contents of this dissertation are as follows:
In chapter1. scientific backgrounds and siganificances of this thesis are presented. Then, state-of-art for several key technologies concerning this field are elaborated. The structure and main contents of this dissertation are depicted.
In chapter2. a dynamic model of the space flexible manipulator system is drived using extended Hamilton's principle with discretization by the assumed mode method. In addition, introduced the friction torque and the coupling torque between the motor and the flexible manipulator, dynamics of the driving set-up(sevo-motor and harmonic gear)is described. In the end. a further verification of the dynamic characterics of the system is made through numerical simulation.
The objective of chapter3is to determine the optimal locations of multiple distributed actuators/sensors. The dynamic model in chapter2is converted to state space form for control design. To find the optimal location of piezoelectric sensor/actuator pairs, a hybrid optimization strategy combined with minimization of the input energy, maximization of the transferring energy and minimization of natural frequencies changes is proposed. The performance criterion is composed of two parts:(1)a LQR performance criterion including flexible vibration energy, rigid motion energy and driving energy of the motor.(2) The change ratio of the natural frequencies. To solve this complex multi-objective optimization problem, a modified Multi-Island Genetic Algorithm (MIGA) is developed for identifying optimal sizing and location of piezoelectric patches as well as the optimal feedback control gains. Also, a series of comparable research is implemented in different conditions.
In chapter4. an optimal trajectory planning technique for suppressing vibrations of the system is proposed. At first, vibrations responses of the manipulator between polynomial and cycloidal motions are compared. Then, the principle of optimal trajectory planning technique for suppressing vibrations of the flexible manipulator system, which is controlled by the sevo-motor and piezoelectric actuators, are elucidated, and a performance criterion considering the exciting torque for the flexible part and the driving torque for the rigid part is presented. In order to get the displacement, the five order polynomial functions, which arouses less vibrations, is used to constructe and interpolate the discrete displacements. And the optimal trajectory is found using Multi-Island Genetic Algorithm (MIGA), again. It is confirmed from the simulation results that the proposed trajectory planning technique is effective in suppressing vibrations of the flexible manipulator.
In Chapter5, it deals with the integrated control strategies of trajectory tracking and vibration suppression for the space flexible manipulator system with PZT actuators. Using the singular perturbation theory, the flexible-rigid-coupled dymanics of the system, is separated into flexible and rigid subsystems, by considering the fact that it takes place in two time scales. And then, a composite control strategy consisting of a fuzzy sliding controller for slow subsystem and a hierarchical fuzzy PID controller for fast subsystem is developed. According to the numerical simulation results, it can be concluded that the proposed integrated control strategies have a suitable and efficient performance for trajectory tracking and suppressing vibrations of the flexible manipulator in different intial contiditons and trajectories. Both motion precision and operation efficiency are improved.
In chapter six. experimental system of the space flexible manipulator is set up, and the corresponding software and hardware are summarized. Experimental studies on system dynamics, optimal locations of multiple distributed piezoelectric actuators/sensors, optimal trajectory planning for suppressing vibrations and the integrated control strategies of trajectory tracking and vibration suppression are elaborated respectively.
Conclusions and prospects are briefly depicted at the end of this thesis.
以一类包含伺服电机、减速器、柔性臂、末端操作对象以及压电致动器/传感器在内的空间柔性机械臂系统为研究对象,基于假设模态法和Hamilton原理建立了系统的动力学方程。并对伺服电机的驱动机理进行研究,提出了考虑摩擦力矩、减速器及柔性臂弹性振动的耦合反力矩的伺服电机机电耦合模型。
基于线性二次最优控制理论,提出了致动器/传感器的复合优化配置准则,该准则包含两个控制指标：①综合柔性臂弹性振动能量、压电致动器控制能量,系统刚体转动能量、以及伺服电机驱动能量的LQR综合能量指标；②致动器引入对系统特性影响的系统结构固有频率变化率指标。然后采用改进的多岛遗传算法得到了不同频率变化率指标下,一组、两组压电致动器/传感器的尺寸、位置和控制增益的最优配置结果。
从系统动力学方程出发,揭示了伺服电机驱动、压电致动器主动控制下空间柔性机械臂系统的抑振轨迹规划机理,提出了包含系统柔性部分激振力矩和刚性部分驱动力矩的综合指标。并选择激起柔性臂振动较小的五次多项式样条函数作为轨迹优化的基础曲线和插值曲线,利用改进的多岛遗传算法对空间柔性机械臂系统的运动轨迹进行优化,得到了综合指标最小的最优抑振轨迹。
引入奇异摄动因子对系统动力学方程进行分解,分别推导得到系统基于奇异摄动模型的快、慢子系统动力学方程。针对快、慢子系统在各自时标下的动力学特性,对具有强耦合性及强非线性的慢变子系统提出模糊滑模控制策略；而对由于模态截断带来模型不确定性以及多模态特性的快变子系统采用分级自适应模糊PID控制策略,从而实现了空间柔性机械臂系统在伺服驱动电机和压电致动器联合控制下的轨迹跟踪和振动抑制一体化控制,提高了系统的运动精度和操作效率。
Trajcectory tracking of space flexible manipulators together with suppressing their vibrations during their operation has been the main concern of many recent stuies in aeronautics and robotics. This thesis is mainly concerned with trajcectory tracking and vibration suppression control of a typical space flexible manipulator system using piezoelectric actuators. Funded by National Natural Science Foundation, dynamic modeling of the flexible manipulator system, optimal placing of the actuators/sensors, optimal trajectory planning for vibration suppression of the manipulator and the integrated control strategies for trajcectory tracking and vibration suppression of the system are studied deeply in this dissertation. The main contents of this dissertation are as follows:
In chapter1. scientific backgrounds and siganificances of this thesis are presented. Then, state-of-art for several key technologies concerning this field are elaborated. The structure and main contents of this dissertation are depicted.
In chapter2. a dynamic model of the space flexible manipulator system is drived using extended Hamilton's principle with discretization by the assumed mode method. In addition, introduced the friction torque and the coupling torque between the motor and the flexible manipulator, dynamics of the driving set-up(sevo-motor and harmonic gear)is described. In the end. a further verification of the dynamic characterics of the system is made through numerical simulation.
The objective of chapter3is to determine the optimal locations of multiple distributed actuators/sensors. The dynamic model in chapter2is converted to state space form for control design. To find the optimal location of piezoelectric sensor/actuator pairs, a hybrid optimization strategy combined with minimization of the input energy, maximization of the transferring energy and minimization of natural frequencies changes is proposed. The performance criterion is composed of two parts:(1)a LQR performance criterion including flexible vibration energy, rigid motion energy and driving energy of the motor.(2) The change ratio of the natural frequencies. To solve this complex multi-objective optimization problem, a modified Multi-Island Genetic Algorithm (MIGA) is developed for identifying optimal sizing and location of piezoelectric patches as well as the optimal feedback control gains. Also, a series of comparable research is implemented in different conditions.
In chapter4. an optimal trajectory planning technique for suppressing vibrations of the system is proposed. At first, vibrations responses of the manipulator between polynomial and cycloidal motions are compared. Then, the principle of optimal trajectory planning technique for suppressing vibrations of the flexible manipulator system, which is controlled by the sevo-motor and piezoelectric actuators, are elucidated, and a performance criterion considering the exciting torque for the flexible part and the driving torque for the rigid part is presented. In order to get the displacement, the five order polynomial functions, which arouses less vibrations, is used to constructe and interpolate the discrete displacements. And the optimal trajectory is found using Multi-Island Genetic Algorithm (MIGA), again. It is confirmed from the simulation results that the proposed trajectory planning technique is effective in suppressing vibrations of the flexible manipulator.
In Chapter5, it deals with the integrated control strategies of trajectory tracking and vibration suppression for the space flexible manipulator system with PZT actuators. Using the singular perturbation theory, the flexible-rigid-coupled dymanics of the system, is separated into flexible and rigid subsystems, by considering the fact that it takes place in two time scales. And then, a composite control strategy consisting of a fuzzy sliding controller for slow subsystem and a hierarchical fuzzy PID controller for fast subsystem is developed. According to the numerical simulation results, it can be concluded that the proposed integrated control strategies have a suitable and efficient performance for trajectory tracking and suppressing vibrations of the flexible manipulator in different intial contiditons and trajectories. Both motion precision and operation efficiency are improved.
In chapter six. experimental system of the space flexible manipulator is set up, and the corresponding software and hardware are summarized. Experimental studies on system dynamics, optimal locations of multiple distributed piezoelectric actuators/sensors, optimal trajectory planning for suppressing vibrations and the integrated control strategies of trajectory tracking and vibration suppression are elaborated respectively.
Conclusions and prospects are briefly depicted at the end of this thesis.
引文
[1]Sabatini M, Gasbarri P, Monti R, et al. Vibration control of a flexible space manipulator during on orbit operations[J]. Acta Astronautica.2012,73:109-121.
[2]黄登峰,陈力.柔性空间机械臂的模糊控制及抑振最优控制[J].系统仿真学报.2012(12)：2530-2534.
[3]Malekzadeh M, Naghash A, Talebi H A. A Robust Nonlinear Control Approach for Tip Position Tracking of Flexible Spacecraft[J]. IEEE Transactions on Aerospace and Electronic Systems.2011,47(4):2423-2434.
[4]Ramos F, Feliu V, Payo I. Design of trajectories with physical constraints for very lightweight single link flexible arms[J]. Journal of Vibration and Control.2008,14(8): 1091-1110.
[5]张祥通.基于视觉的智能柔性结构的振动测量及控制研究[D].华南理工大学,2012.
[6]http://www.nasa.gov/multimedia/imagegallery/iss032e016906.html[Z].
[7]洪嘉振,刘铸永.刚柔耦合动力学的建模方法[J].上海交通大学学报.2008(11)：1922-1926.
[8]Krishnamurthy K, Chao M C. Active Vibration Control during Deployment of Space Structures[J]. Journal of Sound and Vibration.1992,152(2):205-218.
[9]褚明.空间柔性机械臂的动力学特性与主动控制研究[D].北京邮电大学,2010.
[10]黄文虎,王心清,张景绘,et al.航天柔性结构振动控制的若干新进展[J].力学进展.1997(01)：6-19.
[11]杨大智.智能材料与智能系统[M].天津：天津大学出版社,2000.
[12]Gurses K, Buckham B J, Park E J. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators[J]. Mechatronics.2009,19(2): 167-177.
[13]陆佑方,冯冠民,齐朝晖.柔性机械臂动力学与控制建模的若干基本问题[J].机器人.1993(05)：52-59.
[14]Dwivedy S K, Eberhard P. Dynamic analysis of flexible manipulators, a literature review[J]. Mechanism and Machine Theory.2006,41(7):749-777.
[15]洪嘉振,尤超蓝.刚柔耦合系统动力学研究进展[J].动力学与控制学报.2004(02)：3-8.
[16]Sakawa Y, Matsuno F, Fukushima S. Modeling and Feedback-Control of A Flexible arm [J].Journal of Robotic Systems.1985,2(4):453-472.
[17]Lee H H. New dynamic modeling of flexible-link robots[J]. Journal of Dynamic Systems Measurement and Control.2005,127(2):307-309.
[18]Chanron V, Singh T, Lewis K. Equilibrium stability in decentralized design systems[J]. International Journal of Systems Science.2005,36(10):651-662.
[19]邱志成,韩建达,王越超.基于复合喷气压电驱动器的柔性机械臂振动控制[J].机械工程学报.2009(05)：184-192.
[20]陈炜,余跃庆,张绪平,et al.欠驱动柔性机器人的动力学建模与耦合特性[J].机械工程学报.2006(06)：16-23.
[21]Martins J M, Mohamed Z, Tokhi M O, et al. Approaches for dynamic modelling of flexible manipulator systems[J]. IEEE Proceedings Control Theory and Applications.2003, 150(4):401-411.
[22]Ge S S, Lee T H, Zhu G. A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model [J].Journal of Robotic Systems.1997,14(3): 165-178.
[23]Meghdari A, Fahimi F. On the first-order decoupling of dynamical equations of motion for elastic multibody systems as applied to a two-link flexible manipulator[J]. Multibody System Dynamics.2001,5(1):1-20.
[24]Yue S G, Tso S K, Xu W L. Maximum-dynamic-payload trajectory for flexible robot manipulators with kinematic redundancy [J]. Mechanism and Machine theory.2001,36(6SI): 785-800.
[25]崔玲丽,张建宇,高立新,et al.柔性机械臂系统动力学建模的研究[J].系统仿真学报.2007(06)：1205-1208.
[26]Hong Z, Yun C, Chen L. Modeling and Trajectory Tracking Control of a Free-Floating Space Robot with Flexible Manipulators [J]. Robot.2007,29:92-96.
[27]褚明,贾庆轩,叶平,et al.关节驱动柔性臂非最小相位系统的全局终端滑模控制[J].机械工程学报.2012(03)：41-49.
[28]Sun D, Mills J K, Shan J J, et al. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement[J]. Mechatronics.2004, 14(4):381-401.
[29]Gurses K, Buckham B J, Park E J. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators[J]. Mechatronics.2009,19(2): 167-177.
[30]Spong M W. Modeling and Control of Elastic Joint Robots[J] Journal of Dynamic Systems Measurement and Control.1987,109(4):310-319.
[31]Seyfferth W, Maghzal A J, Angeles J. Nonlinear modeling and parameter identification of harmonic drive robotic transmissions:IEEE International Conference on Robotics and Automation[Z]. Nagoya:1995,3027-3032.
[32]邱志成.基于特征模型的柔性关节机械臂的控制[J].系统仿真学报.2002(08)：971-974.
[33]孙汉旭,褚明,贾庆轩.柔性关节摩擦和不确定补偿的小波神经——鲁棒复合控制[J].机械工程学报.2010(13)：68-75.
[34]Pereira E, Aphale S S, Feliu V, et al. Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator[J]. IEEE-ASME Transactions on Mechatronics.2011,16(2):232-240.
[35]Diaz I M, Pereira E, Feliu V, et al. Concurrent Design of Multimode Input Shapers and Link Dynamics for Flexible Manipulators[J]. IEEE-ASME Transactions on Mechatronics.2010, 15(4):646-651.
[36]Becedas J, Trapero J R, Sira-Ramirez H, et al. Fast identification method to control a flexible manipulator with parameter uncertainties[M].2007,3445-3450.
[37]Becedas J, Feliu V, Sira-Ramirez H. Control of flexible manipulators affected by non-linear friction torque based on the generalized proportional integral concept[J].2007 IEEE International Symposium on Industrial Electronics, Proceedings, VOLS 1-8.2007:12-17.
[38]Baroudi M, Saad M, Ghie W. State-Feedback and Linear Quadratic Regulator Applied to a Single-Link Flexible Manipulator[J].2009 IEEE International Conference on Robotics and Biomimetics (ROBIO2009), VOLS 1-4.2009:1381-1386.
[39]Payo I, Feliu V, Daniel Cortazar O. Force control of a very lightweight single-link flexible arm based on coupling torque feedback[J]. Mechatronics.2009,19(3):334-347.
[40]Bossi L, Rottenbacher C, Mimmi G, et al. Multivariable predictive control for vibrating structures:An application[J]. Control Engineering Practice.2011,19(10):1087-1098.
[41]褚明.空间柔性机械臂的动力学特性与主动控制研究[D].北京邮电大学,2010.
[42]李传兵,廖昌荣,张玉磷,et al.压电智能结构的研究进展[J].压电与声光.2002(01)：42-46.
[43]叶春德.智能柔性结构建模及控制研究[D].华南理工大学,2010.
[44]Robert C H, Schmitz E. Initial experiments on end-point control of a flexible one-link robot[J]. International Journal of Robotics Research.1984(3):62-75.
[45]刘福强,张令弥.作动器/传感器优化配置的研究进展[J].力学进展.2000(04)：506-516.
[46]顾仲权,马扣根,陈卫东.振动主动控制[M].北京：国防工业出版社,1997.
[47]Choe K, Baruh H. Actuator Placement in Structural Control[J], Journal of Guidance Control and Dynamics.1992,15(1):40-48.
[48]Ning H H, Optimal number and placements of piezoelectric patch actuators in structural active vibration control[J]. Engineering Computations.2004,21(5-6):651-665.
[49]詹训慧.分布式压电智能结构的建模与振动控制[D].中国科学技术大学,2007.
[50]方水良.现代控制理论及其MATLAB实践[M].杭州：浙江大学出版社,2006.
[51]潘继.结构作动器/传感器的优化配置及其主动控制研究[D].上海交通大学,2008.
[52]Qiu Z, Zhang X, Wu H, et al. Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate[J]. Journal of Sound and Vibration.2007,301(3-5): 521-543.
[53]Gawronski W, Lim K B. Balanced actuator and sensor placement for flexible structures[J]. International Journal of Control.1996,65(1):131-145.
[54]Leleu S, Abou-Kandil H, Bonnassieux Y. Piezoelectric actuators and sensors location for active control of flexible structures [J]. IEEE Transactions on Instrumentation and Measurement. 2001,50(6):1577-1582.
[55]陈光.密集模态挠性结构的多变量实验辨识及自适应逆控制[D].中国科学技术大学,2006.
[56]吴印泽.挠性体振动控制中传感器/致动器位置的优化配置[D].南京理工大学,2004.
[57]刘福强,张令弥.作动器/传感器优化配置的研究进展[J].力学进展.2000(04)：506-516.
[58]Yang Y W, Jin Z L, Soh C K. Integrated optimal design of vibration control system for smart beams using genetic algorithms [J]. Journal of Sound and Vibration.2005,282(3-5): 1293-1307.
[59]程耀东,顾荣荣,童忠钫.挠性结构主动减振中传感器和激振器的优化布置[J].振动与冲击.1995(03)：12-18.
[60]Lee A C, Chen S T. Collocated Sensor Actuator Positioning and Feedback Design in the Control of Flexible Structure-System[J]. Journal of Cibration and Acoustics-Transactions of the ASME.1994,116(2):146-154.
[61]Kumar K R, Narayanan S. The optimal location of piezoelectric actuators and sensors for vibration control of plates[J]. Smart Materials & Structures.2007,16(6):2680-2691.
[62]朱灯林,吕蕊,俞洁.压电智能悬臂梁的压电片位置、尺寸及控制融合优化设计[J].机械工程学报.2009(02)：262-267.
[63]黄全振.压电智能结构自适应滤波振动主动控制研究[D].上海大学,2012.
[64]Rang Y K, Park H C, Hwang W B, et al. Optimum placement of piezoelectric sensor/actuator for vibration control of laminated beams[J]. AIAA Journal.1996,34(9): 1921-1926.
[65]周星德,汪凤泉.基于可靠性的框架结构作动器/传感器最优配置[J].东南大学学报(自然科学版).2003(06)：746-749.
[66]Ryou J K, Park K Y, Kim S J. Electrode pattern design of piezoelectric sensors and actuators using genetic algorithms[J]. AIAA Journal.1998,36(2):227-233.
[67]Spier C, Jr Bruch J C, Sloss J M, et al. Study of optimal locations of piezo-patch actuators and sensors on a cantilever beam for maximum frequency gaps[M].2006:6166.
[68]吕永桂,魏燕定,吕存养,et al.悬臂板振动控制传感器/致动器优化配置[J].兵工学报.2006(01)：88-92.
[69]Lindberg R E, Longman R W. On the Number and Placement of Actuators for Independent Modal Space Control[J]. Journal of Guidance Control and Dynamics.1984,7(2): 215-221.
[70]Hakim S, Fuchs M B. Quasistatic optimal actuator placement with minimum worst case distortion criterion[J]. AIAA Journal.1996,34(7):1505-1511.
[71]Chen S T, Fan Y H, Lee A C. Effective Active Damping Design for Suppression of Vibration in Flexible Systems Via Dislocated Sensor Actuator Positioning[J]. JSME International Journal Series dynamics Control Robotics Design and Manufacturing.1994,37(2): 252-259.
[72]陈龙祥.结构振动的时滞反馈控制及其实验研究[D].上海交通大学,2009.
[73]田莉,陈换过,祝俊,et al.基于自适应模拟退火遗传算法的传感器优化配置研究[J].振动工程学报.2012(03)：238-243.
[74]吴立成,孙富春,孙增圻.空间机器人建模、规划与控制研究现状分析[C].中国青岛：2005.
[75]吴立成,孙富春,孙增圻,et al.柔性空间机器人振动抑制轨迹规划算法[J].机器人2003(03)：250-254.
[76]Park K, Park Y. Fourier-Based Optimal-Design of a Flexible Manipulator Path to Reduce Residual Vibration of the End-Point[J]. ROBOTICA.1993,11(3):263-272.
[77]Sarkar P K, Yamamoto M, Mohri A. Significance of spline curve in path planning of flexible manipulator:IEEE International Conference on Robotics and Automation [Z]. New Mexico:19972535-2540.
[78]Mohri A, Sarkar P K, Yamamoto M. An efficient motion planning of flexible manipulator along specified path[M].1998,1104-1109.
[79]Yue S G, Yu Y G, Bai S X. Flexible rotor beam element for the manipulators with joint and link flexibility[J]. Mechanism and Machine theory.1997,32(2):209-219.
[80]Kojima H, Kibe T. Optimal trajectory planning of a two-link flexible robot arm based on genetic algorithm for residual vibration reduction[J]. IROS 2001:Proceedings of the 2001 IEEE/ International Conference on Intelligent Robots and Systems,2001:2276-2281.
[81]Korayem M H, Davarzani E, Bamdad M. Optimal Trajectory Planning with the Dynamic Load Carrying Capacity of a Flexible Cable-Suspended Manipulator[J]. Scientia Iranica Transaction B-Mechanical Engineering.2010,17(4):315-326.
[82]吴立成,孙富春,孙增圻,et al.柔性空间机器人振动抑制轨迹规划算法[J].机器人.2003(03)：250-254.
[83]邵君奕,张传清,刘召,et al.考虑振动抑制的多冗余度特种操作机器人轨迹优化方法[J].机械工程学报.2012(01)：13-18.
[84]黎田.柔性关节机械臂及其运动学标定和振动抑制的研究[D].哈尔滨工业大学,2012.
[85]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[86]Reis J C P, Da Costa J S. Motion planning and actuator specialization in the control of active-flexible link robots[J]. Journal of Sound and Vibration.2012,331(14):3255-3270.
[87]张晓东.空间柔性机械臂控制策略研究[D].北京邮电大学,2009.
[88]Alberts T E, Dickerson S L, Book W J. On the transfer function modeling of flexible structures with distributed damping:ASME[Z].1986.
[89]孔宪仁,杨正贤,叶东,et al.基于输入成形的柔性航天器振动闭环抑制方法研究[J].振动与冲击.2010(03)：72-76.
[90]柳硕.输入整形技术对柔性臂结构振动抑制的研究[D].哈尔滨工业大学,2010.
[91]W S. Command gcneration for flexible systems[D]. Cambridge:MIT,1997.
[92]Chatlatanagulchai W, Beazel V M, Meckl P H. Command shaping applied to a flexible robot with configuration-dependent resonance[M].2006:1-12,1766-1771.
[93]Hyde J M, Seering W P. Inhibiting Multiple Mode Vibration in Controlled Flexible Systems:American Control Conference[Z]. Boston:19912449-2454.
[94]Pai M. Closed-loop input shaping control of vibration in flexible structures via adaptive sliding mode control[J]. SHOCK AND VIBRATION.2012,19(2):221-233.
[95]Yan A Z, Wang G Q, Xu H, et al. Reduction of residual vibration in a rotating flexible beam[J]. ACTA MECHANICA.2004,171(3-4):137-149.
[96]董明晓,梅雪松.时滞滤波理论及其工程应用[M].北京：科学出版社,2008.
[97]滕悠优.柔性机械臂的主动控制与实验研究[D].上海交通大学,2007.
[98]Wang D, Vidyasagar M. Modeling a Class of Multilink Manipulators with the last Link Flexible[J]. IEEE Transactions on Robotics and Automation.1992,8(1):33-41.
[99]Chapnik B V, Heppler G R, Aplevich J D. Controlling the Impact Response of a One-link Flexible Robotic arm[J]. IEEE Transactions on Robotics and Automation.1993,9(3):346-351.
[100]毕士华,费从宇,黄文虎,et al.柔性机械臂的两种逆动力学方法[J].应用力学学报.1996(03)：22-29.
[101]Morris A S, Madani A. Quadratic optimal control of a two-flexible-link robot manipulator[J]. Robotica.1998,16(1):97-108.
[102]戈新生,崔玮,赵秋玲.刚柔性耦合机械臂轨迹跟踪与振动抑制[J].工程力学.2005(06)：188-191.
[103]Yang J H, Lian F L, Fu L C. Nonlinear adaptive control for flexible-link manipulators[J]. IEEE Transactions on Robotics and Automation.1997,13(1):140-148.
[104]Shawky A, Ordys A, Grimble M J. End-point control of a flexible-link manipulator using H(infinity) nonlinear control via a state-dependent Riccati equation[J]. proceedings of the 2002 IEEE Tnternational Conference on Control Applications, VOLS 1 & 2.2002:501-506.
[105]吴立成,陆震,于守谦,et al.一种柔性机器人的神经网络控制方法[J].北京航空航天大学学报.2002(03)：316-318.
[106]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[107]K T, I Y. The study control based on neural network in flexible structure and its application in single-link flexible arm[J]. ASME Transactions on Measurement and control .1994,16(4):792-795.
[108]Yesildirek A, Vandegrift M W, Lewis F L. A neural network controller for flexible-link robots[J]. Journal of Intelligent & Robotic Systems.1996,17(4):327-349.
[109]黄登峰,陈力.具有外部扰动的参数未知漂浮基柔性空间机械臂的对角递归神经网络控制[J].机械工程学报.2012(01)：91-97.
[110]谢立敏,陈力.控制力矩受限情况下漂浮基柔性空间机械臂鲁棒自适应控制[J].机械工程学报.2012(21)：41-46.
[111]洪昭斌,陈力.漂浮基柔性空间机械臂基于奇异摄动法的模糊控制和柔性振动主动控制[J].机械工程学报.2010(07)：35-41.
[112]Baz A, Poh S. Performance of an Active Control-System with Piezoelectric Actuators[J]. Journal of Sound and Vibration.1988,126(2):327-343.
[113]Sun D, Mills J K, Shan J J, et al. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement[J]. Mechatronics.2004, 14(4):381-401.
[114]陈岩.利用压电陶瓷对柔性悬臂梁进行主动控制试验研究[J].甘肃联合大学学报(自然科学版).2008(06)：43-45.
[115]魏燕定,吕永桂,吕存养,et a1.机器人柔性臂的扭转振动主动控制研究[J].浙江大学学报(工学版).2005(11)：1761-1764.
[116]吕永桂,魏燕定,陈子辰.空间两连杆柔性构件弯扭耦合振动主动控制[J].浙江大学学报(工学版).2007(05)：715-719.
[117]Kermani M R, Moallem M, Patel R V. Study of system parameters and control design for a flexible manipulator using piezoelectric transducers [J]. Smart materials & Structures.2005, 14(4):843-849.
[118]邱志成.刚柔耦合系统的振动主动控制[J].机械工程学报.2006(11)：26-33.
[119]Hu Q, Ma G. Manoeuvring and vibration reduction of a flexible spacecraft integrating optimal sliding mode controller and distributed piezoelectric sensors/actuators[J]. International Journal of Adaptive Control and Signal Processing.2007,21(6):452-476.
[120]杜欣.双连杆柔性机械臂的主动控制研究[D].上海交通大学,2009.
[121]刘延柱,陈立群.振动力学[M].北京：高等教育出版社,2011.
[122]历虹,杨黎明,艾红.伺服技术[M].北京：国防工业出版社,2008.
[123]Becedas J, Payo I, Feliu V. Generalised proportional integral torque control for single-link flexible manipulators[J]. let Control Theory and Applications.2010,4(5):773-783.
[124]Mamani G, Becedas J, Feliu V. Sliding mode tracking control of a very lightweight single-link flexible robot robust to pay load changes and motor friction [J]. Journal of Vibration and Control.2012,18(8):1141-1155.
[125]胡庆雷.挠性航天器姿态机动的主动振动控制[D].哈尔滨工业大学,2006.
[126]张春良,梅德庆,陈子辰.振动主动控制及应用[M].哈尔滨：哈尔滨工业大学出版社,2011.
[127]Dhuri K D, Seshu P. Piezo actuator placement and sizing for good control effectiveness and minimal change in original system dynamics[J]. Smart materials & Structures.2006,15(6): 1661-1672.
[128]陆锋,吕刚,张景绘.结构振动控制中主、被动构件的优化配置[J].强度与环境.1998(03)：13-20.
[129]Crawley E F, Deluis J. Use of Piezoelectric Actuators as Elements of Intelligent Structures[J]. AIAA Journal.1987,25(10):1373-1385.
[130]李磊.压电柔性梁的振动主动控制研究[D].浙江大学,2008.
[131]刘其超.柔性臂系统主动控制研究[D].南京理工大学,2008.
[132]朱灯林,吕蕊,俞洁.压电智能悬臂梁的压电片位置、尺寸及控制融合优化设计[J].机械工程学报.2009(02)：262-267.
[133]王小平.遗传算法：理论应用与软件实现[M].西安：西安交通大学出版社,2002.
[134]王四春.遗传程序设计技术及应用研究[M].长沙：中南大学出版社,2006.
[135]石秀华,孟祥众,杜向党,et a1.基于多岛遗传算法的振动控制传感器优化配置[J].振动、测试与诊断.2008(01)：62-65.
[136]魏承.空间柔性机器人在轨抓取与转移目标动力学与控制[D].哈尔滨工业大学,2010.
[137]黎田.柔性关节机械臂及其运动学标定和振动抑制的研究[D].哈尔滨工业大学,2012.
[138]Ghariblu H, Korayem M H. Trajectory optimization of flexible mobile manipulators[J]. Robotica.2006,24(3):333-335.
[139]Korayem M H, Nohooji H R. Trajectory Optimization of Flexible Mobile Manipulators Using Open-Loop Optimal Control Method[M].2008:5314,54-63.
[140]丰保民.自由漂浮空间机器人轨迹规划与轨迹跟踪问题研究[D].哈尔滨工业大学,2007.
[141]吴立成,杨国胜,郐新凯,et al.柔性臂机器人：建模、分析与控制[M].北京：高等教育出版社,2012.
[142]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[143]Ge S S, Tee K P, Vahhi I E, et al. Tracking and vibration control of flexible robots using shape memory alloys[J]. IEEE-ASME Transactions on Mechatronics.2006,11(6):690-698.
[144]Vakil M, Fotouhi R, Nikiforuk P N. Maneuver control of the multilink flexible manipulators[J]. International Journal of Non-Linear Mechanics.2009,44(8):831-844.
[145]Siciliano B, Book W J. A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators[J]. International Journal of Robotics Research.1988,7(4):79-90.
[146]钱伟长.奇异摄动理论及其在力学中的应用[M].北京：科学出版社,1981.
[147]Mirzaee E, Eghtesad M, Fazelzadeh S A. Maneuver control and active vibration suppression of a two-link flexible arm using a hybrid variable structure/Lyapunov control design[J]. Acta Astronautica.2010,67(9-10):1218-1232.
[148]奥马利RE,江福汝,尚汉冀,et al. Introduction to singular perturbations[M].北京：科学出版社,1983.
[149]许可康.控制系统中的奇异摄动[M].北京：科学出版社,1986.
[150]唐志国.机械臂操作柔性负载系统分布参数建模与控制方法研究[D].吉林大学,2011.
[151]Subudhi B, Morris A S. Singular perturbation based neuro-H-infinity control scheme for a manipulator with flexible links and joints[J]. Robotica.2006,24(2):151-161.
[152]Subudhi B, Morris A S. On the singular perturbation approach to trajectory control of a multilink manipulator with flexible links and joints[J]. Proceedings of the Institution of Mechanical Engineers part i-Journal of Systems and Control Engineering.2001,215(16): 587-598.
[153]张昌凡,何静.滑模变结构的智能控制理论与应用研究[M].北京：科学出版社,2005.
[154]张晓东.空间柔性机械臂控制策略研究[D].北京邮电大学,2009.
[155]罗战武.自由浮动空间柔性双臂机器人系统的动力学控制研究[D].南京航空航天大学,2008.
[156]Bazzi B A, Chalhoub N G. Fuzzy sliding mode controller for a flexible single-link robotic manipulator[J]. Journal of Vibration and Control.2005,11(2):295-314.
[157]Kwok N M, Lee C K. Control of a flexible manipulator using a sliding mode controller with a fuzzy-like weighting factor[J]. ISIE 2001:IEEE International Symposium onIndustrial
Electronics Proceedings, VOLS Ⅰ-Ⅲ.2001:52-57.[158]王艳敏.柔性机械手非奇异终端滑模控制方法的研究[D].哈尔滨工业大学,2009.
[159]Kovacic Z, Bogdan S,胡玉玲.模糊控制器设计理论与应用：Fuzzy controller design theory and applications[Z].北京：机械工业出版社,2010.
[160]白志刚.自动调节系统解析与PID整定[M].北京：化学工业出版社,2012.
[161]刘金琨.先进PID控制及其MATLAB仿真[M].北京：电子工业出版社,2011.
[162]梁捷,陈力.柔性空间机械臂系统的双环积分滑模控制[J].中国机械工程.2011(16)：1906-1912.
[2]黄登峰,陈力.柔性空间机械臂的模糊控制及抑振最优控制[J].系统仿真学报.2012(12)：2530-2534.
[3]Malekzadeh M, Naghash A, Talebi H A. A Robust Nonlinear Control Approach for Tip Position Tracking of Flexible Spacecraft[J]. IEEE Transactions on Aerospace and Electronic Systems.2011,47(4):2423-2434.
[4]Ramos F, Feliu V, Payo I. Design of trajectories with physical constraints for very lightweight single link flexible arms[J]. Journal of Vibration and Control.2008,14(8): 1091-1110.
[5]张祥通.基于视觉的智能柔性结构的振动测量及控制研究[D].华南理工大学,2012.
[6]http://www.nasa.gov/multimedia/imagegallery/iss032e016906.html[Z].
[7]洪嘉振,刘铸永.刚柔耦合动力学的建模方法[J].上海交通大学学报.2008(11)：1922-1926.
[8]Krishnamurthy K, Chao M C. Active Vibration Control during Deployment of Space Structures[J]. Journal of Sound and Vibration.1992,152(2):205-218.
[9]褚明.空间柔性机械臂的动力学特性与主动控制研究[D].北京邮电大学,2010.
[10]黄文虎,王心清,张景绘,et al.航天柔性结构振动控制的若干新进展[J].力学进展.1997(01)：6-19.
[11]杨大智.智能材料与智能系统[M].天津：天津大学出版社,2000.
[12]Gurses K, Buckham B J, Park E J. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators[J]. Mechatronics.2009,19(2): 167-177.
[13]陆佑方,冯冠民,齐朝晖.柔性机械臂动力学与控制建模的若干基本问题[J].机器人.1993(05)：52-59.
[14]Dwivedy S K, Eberhard P. Dynamic analysis of flexible manipulators, a literature review[J]. Mechanism and Machine Theory.2006,41(7):749-777.
[15]洪嘉振,尤超蓝.刚柔耦合系统动力学研究进展[J].动力学与控制学报.2004(02)：3-8.
[16]Sakawa Y, Matsuno F, Fukushima S. Modeling and Feedback-Control of A Flexible arm [J].Journal of Robotic Systems.1985,2(4):453-472.
[17]Lee H H. New dynamic modeling of flexible-link robots[J]. Journal of Dynamic Systems Measurement and Control.2005,127(2):307-309.
[18]Chanron V, Singh T, Lewis K. Equilibrium stability in decentralized design systems[J]. International Journal of Systems Science.2005,36(10):651-662.
[19]邱志成,韩建达,王越超.基于复合喷气压电驱动器的柔性机械臂振动控制[J].机械工程学报.2009(05)：184-192.
[20]陈炜,余跃庆,张绪平,et al.欠驱动柔性机器人的动力学建模与耦合特性[J].机械工程学报.2006(06)：16-23.
[21]Martins J M, Mohamed Z, Tokhi M O, et al. Approaches for dynamic modelling of flexible manipulator systems[J]. IEEE Proceedings Control Theory and Applications.2003, 150(4):401-411.
[22]Ge S S, Lee T H, Zhu G. A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model [J].Journal of Robotic Systems.1997,14(3): 165-178.
[23]Meghdari A, Fahimi F. On the first-order decoupling of dynamical equations of motion for elastic multibody systems as applied to a two-link flexible manipulator[J]. Multibody System Dynamics.2001,5(1):1-20.
[24]Yue S G, Tso S K, Xu W L. Maximum-dynamic-payload trajectory for flexible robot manipulators with kinematic redundancy [J]. Mechanism and Machine theory.2001,36(6SI): 785-800.
[25]崔玲丽,张建宇,高立新,et al.柔性机械臂系统动力学建模的研究[J].系统仿真学报.2007(06)：1205-1208.
[26]Hong Z, Yun C, Chen L. Modeling and Trajectory Tracking Control of a Free-Floating Space Robot with Flexible Manipulators [J]. Robot.2007,29:92-96.
[27]褚明,贾庆轩,叶平,et al.关节驱动柔性臂非最小相位系统的全局终端滑模控制[J].机械工程学报.2012(03)：41-49.
[28]Sun D, Mills J K, Shan J J, et al. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement[J]. Mechatronics.2004, 14(4):381-401.
[29]Gurses K, Buckham B J, Park E J. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators[J]. Mechatronics.2009,19(2): 167-177.
[30]Spong M W. Modeling and Control of Elastic Joint Robots[J] Journal of Dynamic Systems Measurement and Control.1987,109(4):310-319.
[31]Seyfferth W, Maghzal A J, Angeles J. Nonlinear modeling and parameter identification of harmonic drive robotic transmissions:IEEE International Conference on Robotics and Automation[Z]. Nagoya:1995,3027-3032.
[32]邱志成.基于特征模型的柔性关节机械臂的控制[J].系统仿真学报.2002(08)：971-974.
[33]孙汉旭,褚明,贾庆轩.柔性关节摩擦和不确定补偿的小波神经——鲁棒复合控制[J].机械工程学报.2010(13)：68-75.
[34]Pereira E, Aphale S S, Feliu V, et al. Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator[J]. IEEE-ASME Transactions on Mechatronics.2011,16(2):232-240.
[35]Diaz I M, Pereira E, Feliu V, et al. Concurrent Design of Multimode Input Shapers and Link Dynamics for Flexible Manipulators[J]. IEEE-ASME Transactions on Mechatronics.2010, 15(4):646-651.
[36]Becedas J, Trapero J R, Sira-Ramirez H, et al. Fast identification method to control a flexible manipulator with parameter uncertainties[M].2007,3445-3450.
[37]Becedas J, Feliu V, Sira-Ramirez H. Control of flexible manipulators affected by non-linear friction torque based on the generalized proportional integral concept[J].2007 IEEE International Symposium on Industrial Electronics, Proceedings, VOLS 1-8.2007:12-17.
[38]Baroudi M, Saad M, Ghie W. State-Feedback and Linear Quadratic Regulator Applied to a Single-Link Flexible Manipulator[J].2009 IEEE International Conference on Robotics and Biomimetics (ROBIO2009), VOLS 1-4.2009:1381-1386.
[39]Payo I, Feliu V, Daniel Cortazar O. Force control of a very lightweight single-link flexible arm based on coupling torque feedback[J]. Mechatronics.2009,19(3):334-347.
[40]Bossi L, Rottenbacher C, Mimmi G, et al. Multivariable predictive control for vibrating structures:An application[J]. Control Engineering Practice.2011,19(10):1087-1098.
[41]褚明.空间柔性机械臂的动力学特性与主动控制研究[D].北京邮电大学,2010.
[42]李传兵,廖昌荣,张玉磷,et al.压电智能结构的研究进展[J].压电与声光.2002(01)：42-46.
[43]叶春德.智能柔性结构建模及控制研究[D].华南理工大学,2010.
[44]Robert C H, Schmitz E. Initial experiments on end-point control of a flexible one-link robot[J]. International Journal of Robotics Research.1984(3):62-75.
[45]刘福强,张令弥.作动器/传感器优化配置的研究进展[J].力学进展.2000(04)：506-516.
[46]顾仲权,马扣根,陈卫东.振动主动控制[M].北京：国防工业出版社,1997.
[47]Choe K, Baruh H. Actuator Placement in Structural Control[J], Journal of Guidance Control and Dynamics.1992,15(1):40-48.
[48]Ning H H, Optimal number and placements of piezoelectric patch actuators in structural active vibration control[J]. Engineering Computations.2004,21(5-6):651-665.
[49]詹训慧.分布式压电智能结构的建模与振动控制[D].中国科学技术大学,2007.
[50]方水良.现代控制理论及其MATLAB实践[M].杭州：浙江大学出版社,2006.
[51]潘继.结构作动器/传感器的优化配置及其主动控制研究[D].上海交通大学,2008.
[52]Qiu Z, Zhang X, Wu H, et al. Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate[J]. Journal of Sound and Vibration.2007,301(3-5): 521-543.
[53]Gawronski W, Lim K B. Balanced actuator and sensor placement for flexible structures[J]. International Journal of Control.1996,65(1):131-145.
[54]Leleu S, Abou-Kandil H, Bonnassieux Y. Piezoelectric actuators and sensors location for active control of flexible structures [J]. IEEE Transactions on Instrumentation and Measurement. 2001,50(6):1577-1582.
[55]陈光.密集模态挠性结构的多变量实验辨识及自适应逆控制[D].中国科学技术大学,2006.
[56]吴印泽.挠性体振动控制中传感器/致动器位置的优化配置[D].南京理工大学,2004.
[57]刘福强,张令弥.作动器/传感器优化配置的研究进展[J].力学进展.2000(04)：506-516.
[58]Yang Y W, Jin Z L, Soh C K. Integrated optimal design of vibration control system for smart beams using genetic algorithms [J]. Journal of Sound and Vibration.2005,282(3-5): 1293-1307.
[59]程耀东,顾荣荣,童忠钫.挠性结构主动减振中传感器和激振器的优化布置[J].振动与冲击.1995(03)：12-18.
[60]Lee A C, Chen S T. Collocated Sensor Actuator Positioning and Feedback Design in the Control of Flexible Structure-System[J]. Journal of Cibration and Acoustics-Transactions of the ASME.1994,116(2):146-154.
[61]Kumar K R, Narayanan S. The optimal location of piezoelectric actuators and sensors for vibration control of plates[J]. Smart Materials & Structures.2007,16(6):2680-2691.
[62]朱灯林,吕蕊,俞洁.压电智能悬臂梁的压电片位置、尺寸及控制融合优化设计[J].机械工程学报.2009(02)：262-267.
[63]黄全振.压电智能结构自适应滤波振动主动控制研究[D].上海大学,2012.
[64]Rang Y K, Park H C, Hwang W B, et al. Optimum placement of piezoelectric sensor/actuator for vibration control of laminated beams[J]. AIAA Journal.1996,34(9): 1921-1926.
[65]周星德,汪凤泉.基于可靠性的框架结构作动器/传感器最优配置[J].东南大学学报(自然科学版).2003(06)：746-749.
[66]Ryou J K, Park K Y, Kim S J. Electrode pattern design of piezoelectric sensors and actuators using genetic algorithms[J]. AIAA Journal.1998,36(2):227-233.
[67]Spier C, Jr Bruch J C, Sloss J M, et al. Study of optimal locations of piezo-patch actuators and sensors on a cantilever beam for maximum frequency gaps[M].2006:6166.
[68]吕永桂,魏燕定,吕存养,et al.悬臂板振动控制传感器/致动器优化配置[J].兵工学报.2006(01)：88-92.
[69]Lindberg R E, Longman R W. On the Number and Placement of Actuators for Independent Modal Space Control[J]. Journal of Guidance Control and Dynamics.1984,7(2): 215-221.
[70]Hakim S, Fuchs M B. Quasistatic optimal actuator placement with minimum worst case distortion criterion[J]. AIAA Journal.1996,34(7):1505-1511.
[71]Chen S T, Fan Y H, Lee A C. Effective Active Damping Design for Suppression of Vibration in Flexible Systems Via Dislocated Sensor Actuator Positioning[J]. JSME International Journal Series dynamics Control Robotics Design and Manufacturing.1994,37(2): 252-259.
[72]陈龙祥.结构振动的时滞反馈控制及其实验研究[D].上海交通大学,2009.
[73]田莉,陈换过,祝俊,et al.基于自适应模拟退火遗传算法的传感器优化配置研究[J].振动工程学报.2012(03)：238-243.
[74]吴立成,孙富春,孙增圻.空间机器人建模、规划与控制研究现状分析[C].中国青岛：2005.
[75]吴立成,孙富春,孙增圻,et al.柔性空间机器人振动抑制轨迹规划算法[J].机器人2003(03)：250-254.
[76]Park K, Park Y. Fourier-Based Optimal-Design of a Flexible Manipulator Path to Reduce Residual Vibration of the End-Point[J]. ROBOTICA.1993,11(3):263-272.
[77]Sarkar P K, Yamamoto M, Mohri A. Significance of spline curve in path planning of flexible manipulator:IEEE International Conference on Robotics and Automation [Z]. New Mexico:19972535-2540.
[78]Mohri A, Sarkar P K, Yamamoto M. An efficient motion planning of flexible manipulator along specified path[M].1998,1104-1109.
[79]Yue S G, Yu Y G, Bai S X. Flexible rotor beam element for the manipulators with joint and link flexibility[J]. Mechanism and Machine theory.1997,32(2):209-219.
[80]Kojima H, Kibe T. Optimal trajectory planning of a two-link flexible robot arm based on genetic algorithm for residual vibration reduction[J]. IROS 2001:Proceedings of the 2001 IEEE/ International Conference on Intelligent Robots and Systems,2001:2276-2281.
[81]Korayem M H, Davarzani E, Bamdad M. Optimal Trajectory Planning with the Dynamic Load Carrying Capacity of a Flexible Cable-Suspended Manipulator[J]. Scientia Iranica Transaction B-Mechanical Engineering.2010,17(4):315-326.
[82]吴立成,孙富春,孙增圻,et al.柔性空间机器人振动抑制轨迹规划算法[J].机器人.2003(03)：250-254.
[83]邵君奕,张传清,刘召,et al.考虑振动抑制的多冗余度特种操作机器人轨迹优化方法[J].机械工程学报.2012(01)：13-18.
[84]黎田.柔性关节机械臂及其运动学标定和振动抑制的研究[D].哈尔滨工业大学,2012.
[85]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[86]Reis J C P, Da Costa J S. Motion planning and actuator specialization in the control of active-flexible link robots[J]. Journal of Sound and Vibration.2012,331(14):3255-3270.
[87]张晓东.空间柔性机械臂控制策略研究[D].北京邮电大学,2009.
[88]Alberts T E, Dickerson S L, Book W J. On the transfer function modeling of flexible structures with distributed damping:ASME[Z].1986.
[89]孔宪仁,杨正贤,叶东,et al.基于输入成形的柔性航天器振动闭环抑制方法研究[J].振动与冲击.2010(03)：72-76.
[90]柳硕.输入整形技术对柔性臂结构振动抑制的研究[D].哈尔滨工业大学,2010.
[91]W S. Command gcneration for flexible systems[D]. Cambridge:MIT,1997.
[92]Chatlatanagulchai W, Beazel V M, Meckl P H. Command shaping applied to a flexible robot with configuration-dependent resonance[M].2006:1-12,1766-1771.
[93]Hyde J M, Seering W P. Inhibiting Multiple Mode Vibration in Controlled Flexible Systems:American Control Conference[Z]. Boston:19912449-2454.
[94]Pai M. Closed-loop input shaping control of vibration in flexible structures via adaptive sliding mode control[J]. SHOCK AND VIBRATION.2012,19(2):221-233.
[95]Yan A Z, Wang G Q, Xu H, et al. Reduction of residual vibration in a rotating flexible beam[J]. ACTA MECHANICA.2004,171(3-4):137-149.
[96]董明晓,梅雪松.时滞滤波理论及其工程应用[M].北京：科学出版社,2008.
[97]滕悠优.柔性机械臂的主动控制与实验研究[D].上海交通大学,2007.
[98]Wang D, Vidyasagar M. Modeling a Class of Multilink Manipulators with the last Link Flexible[J]. IEEE Transactions on Robotics and Automation.1992,8(1):33-41.
[99]Chapnik B V, Heppler G R, Aplevich J D. Controlling the Impact Response of a One-link Flexible Robotic arm[J]. IEEE Transactions on Robotics and Automation.1993,9(3):346-351.
[100]毕士华,费从宇,黄文虎,et al.柔性机械臂的两种逆动力学方法[J].应用力学学报.1996(03)：22-29.
[101]Morris A S, Madani A. Quadratic optimal control of a two-flexible-link robot manipulator[J]. Robotica.1998,16(1):97-108.
[102]戈新生,崔玮,赵秋玲.刚柔性耦合机械臂轨迹跟踪与振动抑制[J].工程力学.2005(06)：188-191.
[103]Yang J H, Lian F L, Fu L C. Nonlinear adaptive control for flexible-link manipulators[J]. IEEE Transactions on Robotics and Automation.1997,13(1):140-148.
[104]Shawky A, Ordys A, Grimble M J. End-point control of a flexible-link manipulator using H(infinity) nonlinear control via a state-dependent Riccati equation[J]. proceedings of the 2002 IEEE Tnternational Conference on Control Applications, VOLS 1 & 2.2002:501-506.
[105]吴立成,陆震,于守谦,et al.一种柔性机器人的神经网络控制方法[J].北京航空航天大学学报.2002(03)：316-318.
[106]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[107]K T, I Y. The study control based on neural network in flexible structure and its application in single-link flexible arm[J]. ASME Transactions on Measurement and control .1994,16(4):792-795.
[108]Yesildirek A, Vandegrift M W, Lewis F L. A neural network controller for flexible-link robots[J]. Journal of Intelligent & Robotic Systems.1996,17(4):327-349.
[109]黄登峰,陈力.具有外部扰动的参数未知漂浮基柔性空间机械臂的对角递归神经网络控制[J].机械工程学报.2012(01)：91-97.
[110]谢立敏,陈力.控制力矩受限情况下漂浮基柔性空间机械臂鲁棒自适应控制[J].机械工程学报.2012(21)：41-46.
[111]洪昭斌,陈力.漂浮基柔性空间机械臂基于奇异摄动法的模糊控制和柔性振动主动控制[J].机械工程学报.2010(07)：35-41.
[112]Baz A, Poh S. Performance of an Active Control-System with Piezoelectric Actuators[J]. Journal of Sound and Vibration.1988,126(2):327-343.
[113]Sun D, Mills J K, Shan J J, et al. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement[J]. Mechatronics.2004, 14(4):381-401.
[114]陈岩.利用压电陶瓷对柔性悬臂梁进行主动控制试验研究[J].甘肃联合大学学报(自然科学版).2008(06)：43-45.
[115]魏燕定,吕永桂,吕存养,et a1.机器人柔性臂的扭转振动主动控制研究[J].浙江大学学报(工学版).2005(11)：1761-1764.
[116]吕永桂,魏燕定,陈子辰.空间两连杆柔性构件弯扭耦合振动主动控制[J].浙江大学学报(工学版).2007(05)：715-719.
[117]Kermani M R, Moallem M, Patel R V. Study of system parameters and control design for a flexible manipulator using piezoelectric transducers [J]. Smart materials & Structures.2005, 14(4):843-849.
[118]邱志成.刚柔耦合系统的振动主动控制[J].机械工程学报.2006(11)：26-33.
[119]Hu Q, Ma G. Manoeuvring and vibration reduction of a flexible spacecraft integrating optimal sliding mode controller and distributed piezoelectric sensors/actuators[J]. International Journal of Adaptive Control and Signal Processing.2007,21(6):452-476.
[120]杜欣.双连杆柔性机械臂的主动控制研究[D].上海交通大学,2009.
[121]刘延柱,陈立群.振动力学[M].北京：高等教育出版社,2011.
[122]历虹,杨黎明,艾红.伺服技术[M].北京：国防工业出版社,2008.
[123]Becedas J, Payo I, Feliu V. Generalised proportional integral torque control for single-link flexible manipulators[J]. let Control Theory and Applications.2010,4(5):773-783.
[124]Mamani G, Becedas J, Feliu V. Sliding mode tracking control of a very lightweight single-link flexible robot robust to pay load changes and motor friction [J]. Journal of Vibration and Control.2012,18(8):1141-1155.
[125]胡庆雷.挠性航天器姿态机动的主动振动控制[D].哈尔滨工业大学,2006.
[126]张春良,梅德庆,陈子辰.振动主动控制及应用[M].哈尔滨：哈尔滨工业大学出版社,2011.
[127]Dhuri K D, Seshu P. Piezo actuator placement and sizing for good control effectiveness and minimal change in original system dynamics[J]. Smart materials & Structures.2006,15(6): 1661-1672.
[128]陆锋,吕刚,张景绘.结构振动控制中主、被动构件的优化配置[J].强度与环境.1998(03)：13-20.
[129]Crawley E F, Deluis J. Use of Piezoelectric Actuators as Elements of Intelligent Structures[J]. AIAA Journal.1987,25(10):1373-1385.
[130]李磊.压电柔性梁的振动主动控制研究[D].浙江大学,2008.
[131]刘其超.柔性臂系统主动控制研究[D].南京理工大学,2008.
[132]朱灯林,吕蕊,俞洁.压电智能悬臂梁的压电片位置、尺寸及控制融合优化设计[J].机械工程学报.2009(02)：262-267.
[133]王小平.遗传算法：理论应用与软件实现[M].西安：西安交通大学出版社,2002.
[134]王四春.遗传程序设计技术及应用研究[M].长沙：中南大学出版社,2006.
[135]石秀华,孟祥众,杜向党,et a1.基于多岛遗传算法的振动控制传感器优化配置[J].振动、测试与诊断.2008(01)：62-65.
[136]魏承.空间柔性机器人在轨抓取与转移目标动力学与控制[D].哈尔滨工业大学,2010.
[137]黎田.柔性关节机械臂及其运动学标定和振动抑制的研究[D].哈尔滨工业大学,2012.
[138]Ghariblu H, Korayem M H. Trajectory optimization of flexible mobile manipulators[J]. Robotica.2006,24(3):333-335.
[139]Korayem M H, Nohooji H R. Trajectory Optimization of Flexible Mobile Manipulators Using Open-Loop Optimal Control Method[M].2008:5314,54-63.
[140]丰保民.自由漂浮空间机器人轨迹规划与轨迹跟踪问题研究[D].哈尔滨工业大学,2007.
[141]吴立成,杨国胜,郐新凯,et al.柔性臂机器人：建模、分析与控制[M].北京：高等教育出版社,2012.
[142]Abe A. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation[J]. Mechanism and Machine theory.2009,44(9): 1627-1639.
[143]Ge S S, Tee K P, Vahhi I E, et al. Tracking and vibration control of flexible robots using shape memory alloys[J]. IEEE-ASME Transactions on Mechatronics.2006,11(6):690-698.
[144]Vakil M, Fotouhi R, Nikiforuk P N. Maneuver control of the multilink flexible manipulators[J]. International Journal of Non-Linear Mechanics.2009,44(8):831-844.
[145]Siciliano B, Book W J. A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators[J]. International Journal of Robotics Research.1988,7(4):79-90.
[146]钱伟长.奇异摄动理论及其在力学中的应用[M].北京：科学出版社,1981.
[147]Mirzaee E, Eghtesad M, Fazelzadeh S A. Maneuver control and active vibration suppression of a two-link flexible arm using a hybrid variable structure/Lyapunov control design[J]. Acta Astronautica.2010,67(9-10):1218-1232.
[148]奥马利RE,江福汝,尚汉冀,et al. Introduction to singular perturbations[M].北京：科学出版社,1983.
[149]许可康.控制系统中的奇异摄动[M].北京：科学出版社,1986.
[150]唐志国.机械臂操作柔性负载系统分布参数建模与控制方法研究[D].吉林大学,2011.
[151]Subudhi B, Morris A S. Singular perturbation based neuro-H-infinity control scheme for a manipulator with flexible links and joints[J]. Robotica.2006,24(2):151-161.
[152]Subudhi B, Morris A S. On the singular perturbation approach to trajectory control of a multilink manipulator with flexible links and joints[J]. Proceedings of the Institution of Mechanical Engineers part i-Journal of Systems and Control Engineering.2001,215(16): 587-598.
[153]张昌凡,何静.滑模变结构的智能控制理论与应用研究[M].北京：科学出版社,2005.
[154]张晓东.空间柔性机械臂控制策略研究[D].北京邮电大学,2009.
[155]罗战武.自由浮动空间柔性双臂机器人系统的动力学控制研究[D].南京航空航天大学,2008.
[156]Bazzi B A, Chalhoub N G. Fuzzy sliding mode controller for a flexible single-link robotic manipulator[J]. Journal of Vibration and Control.2005,11(2):295-314.
[157]Kwok N M, Lee C K. Control of a flexible manipulator using a sliding mode controller with a fuzzy-like weighting factor[J]. ISIE 2001:IEEE International Symposium onIndustrial
Electronics Proceedings, VOLS Ⅰ-Ⅲ.2001:52-57.[158]王艳敏.柔性机械手非奇异终端滑模控制方法的研究[D].哈尔滨工业大学,2009.
[159]Kovacic Z, Bogdan S,胡玉玲.模糊控制器设计理论与应用：Fuzzy controller design theory and applications[Z].北京：机械工业出版社,2010.
[160]白志刚.自动调节系统解析与PID整定[M].北京：化学工业出版社,2012.
[161]刘金琨.先进PID控制及其MATLAB仿真[M].北京：电子工业出版社,2011.
[162]梁捷,陈力.柔性空间机械臂系统的双环积分滑模控制[J].中国机械工程.2011(16)：1906-1912.