压电柔性结构的建模、参数辨识与振动主动控制
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摘要
本文以压电智能柔性结构为研究对象,对其模型的建立以及振动主动控制问题进行了全面而系统的研究;提出了对结构进行模型降阶、模态参数辨识的新方法;针对具有不确定性和几何非线性的压电智能柔性结构,建立了结构的模态状态空间表示,对结构的振动主动控制进行了研究。主要内容如下:
1.提出了模态空间范数的概念和计算方法,以压电柔性梁、板结构为对象,建立了其模态空间的传递函数与状态方程;利用模态空间范数作为各个模态对压电柔性结构动力响应贡献大小的度量,给出了一种对带有压电作动器、输出为空间分布的柔性结构进行模态挑选而获得降阶模型的方法。仿真结果表明,随着压电作动器的配置不同,结构的降阶模型中应保留的模态也应随之发生变化,利用所提出的方法获得的降阶模型保留了相对较重要的模态,它比直接模态截断方法更逼近原系统,是一种适用于结构全局振动控制的模型降阶方法;因其考虑了配置的作动器对各个模态的控制能力,将会提高压电柔性结构振动主动控制的控制效果。
2.利用小波变换所具有的特性,分析了在众多小波基函数中Morlet小波更适合对结构振动系统进行模态分析的原因,结合Morlet小波的性质和结构振动系统自由响应信号的特性,构造了一组小波族,实现了利用小波变换对多自由度系统进行模态解耦、以及对压电智能柔性结构、时变系统进行模态参数辨识。仿真结果表明,所提方法的正确性和有效性,它比直接利用Morlet小波更为直观、方便和准确;对压电柔性结构的低频密集模态频率和振型能够很好地进行辨识。
3.以不确定压电柔性结构为对象,考虑其被控模态参数的不确定性以及剔除残余模态所引起的模型误差,建立了模态空间内结构的不确定线性分式模型;根据所建立的不确定模型,设计了一个对结构进行振动控制的非同位动态输出反馈控制器,使结构的闭环系统满足多个性能要求;并利用线性矩阵不等式方法,将具有多个性能约束的振动控制问题转化为一个具有线性矩阵不等式约束和线性目标函数的凸优化问题。仿真结果表明,所建立的模态不确定模型和在此基础上
The research is concentrated on the modeling analysis and active vibration control for piezoelectric flexible structures in this dissertation. The new methods are developed for model reduction and modal parameters identification in Chapters 2 and 3. Robust vibration control laws are designed for flexible structures with either model uncertainties or non-linearity in Chapters 4 to 7. The dissertation consists of the following six parts.
1. For flexible structures with multi-input and spatially distributed output, the contribution of modes to the dynamic response of systems may change with the location of piezoelectric actuator patches and the ability of actuators to control vibration modes has to be taken into account in developing a relatively low-order dynamic modal equation. Mode spatial norms, serving as a measure of the intensity of modes to system response, are used to pick relatively important modes for piezoelectric flexible structures. The simulation result shows that the low-order model obtained by using mode norms, which keeps relatively important modes, is the better approximation of the original system than that of direct mode truncation, and is helpful to suppress the vibration of structures better.
2. The method of modal analysis for piezoelectric flexible structures using wavelet transform is introduced. The reasons why Morlet wavelet is attractive for analyzing signals that are generated by dynamical vibration systems are given, although there are a multitude of wavelets that could be used. Based on the characteristics of transient responses of vibration system and Morlet wavelet, a family of wavelet functions are introduced and used in the parameter identification of modal frequencies and mode shapes for piezoelectric flexible structures. The simulation results are straightforward and satisfactory.
3. The linear fractional representation is developed for flexible structures with piezoelectric material as actuators and sensors, taking into account uncertainties due to modal parameters variation and un-modeled residual modes. Based on Linear matrix inequality, the vibration control problem with conflicting performance specifications, such as robust stability, damping ratio and decay rate requirement, disturbance rejection, actuator saturation constraints and so on, is converted into an linear convex optimization problem. The results show that the modal-based multi-objective vibration control law can suppress the low-frequency modes without exciting the high-frequency
1.提出了模态空间范数的概念和计算方法,以压电柔性梁、板结构为对象,建立了其模态空间的传递函数与状态方程;利用模态空间范数作为各个模态对压电柔性结构动力响应贡献大小的度量,给出了一种对带有压电作动器、输出为空间分布的柔性结构进行模态挑选而获得降阶模型的方法。仿真结果表明,随着压电作动器的配置不同,结构的降阶模型中应保留的模态也应随之发生变化,利用所提出的方法获得的降阶模型保留了相对较重要的模态,它比直接模态截断方法更逼近原系统,是一种适用于结构全局振动控制的模型降阶方法;因其考虑了配置的作动器对各个模态的控制能力,将会提高压电柔性结构振动主动控制的控制效果。
2.利用小波变换所具有的特性,分析了在众多小波基函数中Morlet小波更适合对结构振动系统进行模态分析的原因,结合Morlet小波的性质和结构振动系统自由响应信号的特性,构造了一组小波族,实现了利用小波变换对多自由度系统进行模态解耦、以及对压电智能柔性结构、时变系统进行模态参数辨识。仿真结果表明,所提方法的正确性和有效性,它比直接利用Morlet小波更为直观、方便和准确;对压电柔性结构的低频密集模态频率和振型能够很好地进行辨识。
3.以不确定压电柔性结构为对象,考虑其被控模态参数的不确定性以及剔除残余模态所引起的模型误差,建立了模态空间内结构的不确定线性分式模型;根据所建立的不确定模型,设计了一个对结构进行振动控制的非同位动态输出反馈控制器,使结构的闭环系统满足多个性能要求;并利用线性矩阵不等式方法,将具有多个性能约束的振动控制问题转化为一个具有线性矩阵不等式约束和线性目标函数的凸优化问题。仿真结果表明,所建立的模态不确定模型和在此基础上
The research is concentrated on the modeling analysis and active vibration control for piezoelectric flexible structures in this dissertation. The new methods are developed for model reduction and modal parameters identification in Chapters 2 and 3. Robust vibration control laws are designed for flexible structures with either model uncertainties or non-linearity in Chapters 4 to 7. The dissertation consists of the following six parts.
1. For flexible structures with multi-input and spatially distributed output, the contribution of modes to the dynamic response of systems may change with the location of piezoelectric actuator patches and the ability of actuators to control vibration modes has to be taken into account in developing a relatively low-order dynamic modal equation. Mode spatial norms, serving as a measure of the intensity of modes to system response, are used to pick relatively important modes for piezoelectric flexible structures. The simulation result shows that the low-order model obtained by using mode norms, which keeps relatively important modes, is the better approximation of the original system than that of direct mode truncation, and is helpful to suppress the vibration of structures better.
2. The method of modal analysis for piezoelectric flexible structures using wavelet transform is introduced. The reasons why Morlet wavelet is attractive for analyzing signals that are generated by dynamical vibration systems are given, although there are a multitude of wavelets that could be used. Based on the characteristics of transient responses of vibration system and Morlet wavelet, a family of wavelet functions are introduced and used in the parameter identification of modal frequencies and mode shapes for piezoelectric flexible structures. The simulation results are straightforward and satisfactory.
3. The linear fractional representation is developed for flexible structures with piezoelectric material as actuators and sensors, taking into account uncertainties due to modal parameters variation and un-modeled residual modes. Based on Linear matrix inequality, the vibration control problem with conflicting performance specifications, such as robust stability, damping ratio and decay rate requirement, disturbance rejection, actuator saturation constraints and so on, is converted into an linear convex optimization problem. The results show that the modal-based multi-objective vibration control law can suppress the low-frequency modes without exciting the high-frequency
引文
[1]Wodek Gawronski. Balanced control of flexible structures. Springer, 1996.
[2]Rabih Alkhatib, M. F. Golnaraghi. Active structural vibration control: a review. The Shock and Vibration Digest. 2003, 35(5): 367-383.
[3]M. Porfiri, F. dell’Isolaand, F. M. Frattale Mascioli. Circuit analog of a beam and its application to multimodal vibration damping using piezoelectric transducers. International Journal of Circuit Theory and Applications. 2004, 32: 167-198.
[4]丁文镜. 振动主动控制当前的主要研究课题. 力学进展. 1992, 24(2): 173-180.
[5]B. C. Nakra, Vibration control in machines and structures using viscoelastic damping. Journal of Sound and Vibration. 1998, 211(3): 449-465.
[6]Y. Zhu, J. Qiu, H. Du. Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure. Archive of Applied Mechanics. 2004, 73: 718-733.
[7]胡海岩. 动力学、振动与控制学科未来的发展趋势. 力学进展. 2002, 32(2): 194-306.
[8]刘少军, 李艳. 基于1/2车辆模型主动悬架预先控制方法的研究. 信息与控制. 2000, 29(1): 6-13.
[9]S. Ikenaga, F. L. Lewis, J. Campos. Active suspension control of ground vehicle based on a full-vehicle model. American Control Conference. Chicago, USA, 2000: 1327-1339.
[10]Zhang Yisheng, Alleyne. A new approach to half-car active suspension control. American Control Conference. Denver, Colorado, 2003: 1420-1431.
[11]T. Kobori. Past, present and future in seismic response control of civil engineering structures. Proceedings of the Third World Conference on Structural Control. Como, Italy, 2002, 1: 9-14.
[12]Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited Structures. Engineering Structures. 2004, 26: 279-289.
[13]M. Aldawod, B. Samali, F Naghdy. Active control of wind response of tall building using a fuzzy controller. Engineering Structures. 2001, 23(11) 1512-1522.
[14]W. J. Book. New concepts in lightweight arms. Proceedings of the Second International Symposium on Robotic Research. 1984, 1: 203-205.
[15]Z. Su, K. Khorasani. Neural network controller for single-link flexible manipulator based on the inverse dynamics structure. Proceeding of the International Joint Conference on Neural Network. 2000, 5: 311-316.
[16]De Luca. Closed-form dynamic model of planar multilink lightweight robots. IEEE Trans. Systems, Man & Cybernetics. 1991, 21: 826-839.
[17]H. A. Talebi. Inverse dynamics control of flexible-link manipulators using neural networks. IEEE International Conference on Robotics and Automation. 1998, 1: 806-811.
[18]De luca. Inversion-based nonlinear control of robot arms with flexible links. Journal of Guidance, Control and Dynamics. 1993, 16: 1669-1176.
[19]Afzal Suleman, Antonio P. Costa. Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators. Computers and Structures. 2004, 82: 1303-1314.
[20]E. F. Crawley. Intelligent structures for aerospace: a technology overview and assessment. AIAA Journal. 1994, 32: 1689-1699.
[21]牟全臣, 黄文虎, 郑钢铁等. 航天结构主、被动一体化振动控制技术的研究现状和进展. 应用力学学报. 2001, 18(3): 1-7.
[22]黄文虎, 王心清, 张景绘等. 航天柔性结构振动控制的若干新进展. 力学进展. 1997, 27(1): 5-18.
[23]E. F. Crawley, De Luis. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 1987, 25(10): 1373-1385.
[24]E. F. Crawley, E. H. Anderson. Detailed modeling of piezoelectric actuation of beams. Proceeding of the 30th AIAA SDM Conference. 1989: 2000-2010.
[25]S. B. Choi. Vibration control of a smart beam structure subjected to actuator uncertainty: Experimental verification. Acta Mechanica. 2006, 181: 19-30.
[26]H. T. Banks, R. C. Smith, Y. Wang. Smart Material Structures: Modeling, Estimation and Control. Paris, Wiley, 1996.
[27]W. S. Hwang, H. C. Park. Finite element modeling of piezoelectric sensors and actuators. AIAA Journal. 1993, 31(5): 930-937.
[28]T. Kamada, T. Fujita. Active vibration control of structures with smart structures using piezoeelectric actuators. Journal of Intelligent Material Systems and Structures. 1997, 8(6): 447-456.
[29]李传兵, 廖昌荣, 张玉等. 压电智能结构的研究进展. 压电与声光. 2002, 24(1): 42-60.
[30]李俊宝, 张景绘, 任勇生等. 振动工程中智能结构的研究进展. 力学进展. 1999, 29(2): 177-185.
[31]吴大方, 刘安成, 麦汉超等. 压电智能柔性梁振动主动控制研究. 北京航空航天大学学报. 2004, 30(12): 160-163.
[32]Ha Sung, K. Keilers. Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA Journal. 1992, 30(3): 772-780.
[33]Wenwu Cao, Harley. Smart materials and structures. Proceeding of national Academic Science. USA ,1999: 1013-1024.
[34]Z. K. Kusculuoglu, B. Fallahi. Finite element model of a beam with a piezoceramic patch actuator. Journal of Sound and Vibration. 2004, 275: 27-44.
[35]I. S. Grewal, W. Szyszkowski. Optimal vibration control of continuous structures by FEM: Part II-the computer implementation. Communications in Numeriacal Methods in Engineering. 2002, 18: 869-876.
[36]Xing-Jian Dong, Guang Meng, Juan-Chun Peng. Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study. Journal of Sound and Vibration. 2006, 297: 680-693.
[37]Chyanbin Hwu, W.C. Chang, H.S. Gai. Vibration suppression of composite sandwich beams. Journal of Sound and Vibration. 2004, 272: 1-20.
[38]S. Raja, P. K. Sinha, G. RaThap. Influence of one and two dimensional piezoelectric actuation: an active vibration control of smart panels. Aerospace Science and Technology. 2002, 6(3): 209-216.
[39]M. J. Balas. Direct velocity feedback control of large space structures. Journal of Guidance. 1979, 2(3): 252-253.
[40]M. J. Balas. Feedback control of flexible systems. IEEE Trans. on Automatic Control. 1978, 23(4): 673-679.
[41]C. J. Goh, T. K. Caughey. On the stability problem caused by finite actuator dynamics in the collocated control of large space structures. International Journal of Control. 1985, 41(3): 787-802.
[42]Fanson J. L, Caugher T. K. Positive position feedback control for large space structures. AIAA Journal. 1990, 28(4): 712-724.
[43]Meirovitch L, Baruh H. A comparison of control techniques for large flexible systems. Journal of Guidance. 1983, 6(4): 302-310.
[44]Baz A, Poh S, Fedo J. Independent modal space control with positive position feedback. Trans. of the ASME. 1992, 114: 96-103.
[45]S.P. Singh, Harpreet Singh Pruthi, V.P. Agarwal. Efficient modal control strategies for active control of vibrations. Journal of Sound and Vibration. 2003, 262: 563-575.
[46]陈大跃, 胡宗武, 范祖尧. 振动控制的特征结构配置. 振动工程学报. 1991, 4(2): 75-81.
[47]马扣根, 顾仲权. 最优极点配置法在梁式结构振动主动控制中的应用. 振动与冲击. 1991, 3: 85-89.
[49]顾仲权. 振动主动控制中低阶控制器的优化设计. 振动工程学报. 1990, 3(3): 1-8.
[50]谭善光, 汪希宣. 结构强迫振动最优响应和模态主动控制. 振动工程学报. 1989, 2(4): 76-81.
[48]M. A. Vasques, J. Dias Rodrigues. Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Computers and Structures. 2006, 84: 1402-1414.
[51]俞文伯, 丁文镜. 悬臂梁随机振动的最优控制. 建筑结构学报. 1995, 17(5): 49-58.
[52]P. K. Kwakuo, C. C. Kevin. The application of multi-channel design methods for vibration control of an active structure. Smart Material and Structures. 1994, 3: 329-343.
[53]D. S. Scott, T. Nobuo. Modification to overall system response when using narrow band adaptive feedforward control system. Journal of Dynamic Systems, Measurement, and Control. 1993, 115: 612-626.
[54]J. S. Vipperman, R. A. Burdisso, C. R. Fuller. Active control of broadband structural vibration using the LMS adaptive algorithm. Journal of Sound and Vibration. 1993, 166(2): 283-299.
[55]孙朝晖, 王冲, 戴扬等. 结构振动主动控制理论及实验研究. 振动工程学报. 1994, 7(2): 154-160.
[56]刘季, 滕军. 结构在地震作用下的主动自校正控制计算方法. 地震工程与工程振动. 1991, 11(2): 73-84.
[57]刘季, 滕军. 地震作用下结构振型组合自校正控制. 地震工程与工程振动. 1992, 12(2): 48-58.
[58]C. H. Charles, D. S. Bayard. Experimental study of robustness in adaptive control for large flexible structures. AIAA Guidance, Navigation and Control Conference. 1990: 1645-1656.
[59]马扣根, 顾仲权. 结构振动的一种离散自适应控制策略. 中国振动工程学会噪声与振动控制学术年会论文集. 北京, 1991: 260-267.
[60]Matthew Allen, Franco Bernelli-Zazzera, Riccardo Scattolini. Sliding mode control of a large flexible space structure. Control Engineering Practice. 2000, 8: 861-871.
[61]M. H. Kim. Reduction of observation spillover in vibration suppression using a sliding mode observer. Journal of Vibration and Control. 2002, 7(7): 1087-1150.
[62]周军, 陈新海. 大型柔性空间结构的变结构模型参考自适应控制. 航空学报. 1992, 13(4): 158-163.
[63]J. C. Doyle. State-space solution to standard / control. American Control Conference. 1988: 817-823. H 2H∞
[64]I. N. Kar, K. Seto, F. Doi. Multimode vibration control of a flexible structure using H-based robust control. IEEE Trans. Mechatronics. 2000, 5(1): 23-31.
[65]林嗣廉, 徐博侯. 柔性结构振动的独立模态 H2控制. 浙江大学学报. 2001, 35(1): 23-29.
[66]X. Zhang, C. Shao. Robust vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators. H∞Journal of Sound and Vibration. 2001, 243(1): 145-155.
[67]J. Qiu, J. Tani. Vibration control of a cylindrical shell using distributed piezoelectric sensors and actuators. Journal of Intelligent Material Systems and Structures. 1995, 6: 474-481.
[68]J. L. Fanson, C. C. Chu. Active member control of a precision structure with and performance objective. AIAA Dynamic Specialist Conference. 1990: 322-333. H∞
[69]C. C. Chu, R. Smith, J. Fanson. Robust control of an active precision truss structure. Proceeding of the American Control Conference. 1990: 2490-2495.
[70]C. C. Chu, R. Smith, J. Fanson. The design of controllers for an experimental non-collocated flexible structure problem. IEEE Trans. Control System Technology. 1994, 2(2): 101-109. H∞
[71]Carten Scherer, Pascal Gahinet. Multiobjective output-feedback control via LMI optimization. IEEE Trans. on Automatic Control. 1997, 42(7): 896-910.
[72]俞立. 鲁棒控制. 北京, 清华大学出版社, 2002.
[73]Qinglei Hu, Guangfu Ma. Active vibration control of a flexible plate structure using LMI-based output feedback control law. Proceedings of the 5th World Congress on Intelligent Control and Automation. 2004: 2021-2032. H∞
[74]Sridhar Sana, Vittal S. Rao. Application of linear matrix inequalities in the control of smart structural systems. Journal of Intelligent Material System & Structure. 2000, 11: 311-323.
[75]Y. Y. Li, L. H. Yam. A robust design method of active controller for uncertain vibration systems. Journal of Vibration and Control. 2001, 7: 453-466.
[76]Y. Y. Li, L. H. Yam. Robust vibration control of uncertain systems using variable parameter feedback and model-based fuzzy strategies. Computers and Structures. 2001, 79(11): 1109-1119.
[77]R. W. James, J. H. John. Distributed fuzzy control of a flexible structure. SPIE Proceedings of Smart Structures and Materials. 1994, 1: 488-499.
[78]D. Park. Genetic-based new fuzzy reasoning models with application to fuzzy control. IEEE Trans. System, man and Cybernetics. 1994, 224(1): 185-191.
[79]Casciati F. Application of fuzzy to active structural control. The Second conference on Smart Structures and Material. Glasgow, 1994, 5: 206-209.
[80]Kubica E. E, Wang D. A fuzzy-control strategy for a flexible single link robot. American Control Conference. 1993: 236-241.
[81]Shiuhjer Huang, Weicheng Lin. Adaptive fuzzy controller with sliding surface for vehicle suspension control. IEEE Trans. Fuzzy Systems. 2003, 11(4): 550-560.
[82]Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited structures. Engineering Structures. 2004, 26: 279-289.
[83]M. K. Kwak, D. Sciulli. Fuzzy-logic Based Vibration Suppression Control Experiments on Active Structures. Journal of Sound and Vibration. 1996, 191(1): 17-28.
[84]刘华, 黄田, 曾子平. 一类非线性振动的智能主动控制方法. 非线性动力学报. 1994, 1(3): 288-292.
[85]R. Jha, J. Rower. Experimental investigation of active vibration control using neural networks and piezoelectric actuators. Smart Materials and Structures. 2002, 11: 115-121.
[86]Y. N. Nassar, M. Siddiqui, A. Z. Garni. Artificial neural networks in vibration control of rotor bearing systems. Simulation Practice and Theory. 2000, 7(8): 729-740.
[87]M. T. Valoor, K. Chandrashekhara, S Agarwal. Active vibration control of smart composite plates using self-adaptive neuro-controller. Smart Material and Structures. 2000. 9: 197-204.
[88]C. P. Smyser, K. Chandrashekharay. Robust vibration control of composite beams using piezoelectric devices and neural networks. Smart Material and Structures. 1997, 6: 178-189.
[89]Van Tsai Liu, Chun Liang Lin, Gean Pao Lee. Neural-network-based identification and control of a thin plate using piezoelectric actuators and sensors. International Journal of Systems Science. 2004, 35(6): 355-373.
[90]傅志方, 周炎. 非线性结构系统的模态分析、建模及参数辨识: 研究综述. 振动与冲击. 1992, 1(2): 100-114.
[91]付志方. 振动模态分析与参数辨识. 北京: 机械工业出版社, 1990.
[92]P. Verboven, P. Guillaume, B. Cauberghe. Modal parameter estimation from input–output Fourier data using frequency-domain maximum likelihood identification. Journal of Sound and Vibration. 2004, 276: 957-979.
[93]Thien-Phu Le, Pierre Argoul. Continuous wavelet transform for modal identification using free decay response. Journal of Sound and Vibration. 2004, 277: 73-100.
[94]续秀忠. 结构模态参数辨识的时频分析方法. 噪声与振动控制. 2002, 22(5): 3-7.
[95]R. Lind, K. Snyder , M. Brenner. Wavelet analysis to characterize non-linearities and predict limit cycles of an elastic system. Mechanical Systems and Signal Processing. 2001, 15(2): 337-356.
[96]W. J. Staszewski. Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform. Journal of Sound and Vibration. 1998, 214: 639-658.
[97]续秀忠. 基于环境激励的模态参数辨识方法综述. 振动与冲击. 2002, 21(35): 1-5.
[98]J. Awrejcewicz, A. V. Krysko. Wavelet-based analysis of parametric vibrations of flexible structures. International Applied Mechanics. 2003, 39(9): 997-1029.
[99]S. Pernot, C. H. Lamarque. A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems. Nonlinear Dynamics. 2003, 32: 33–70.
[100]刘一武, 张洪华, 吴宏鑫. 基于小波方法的挠性空间结构模态参数的辨识. 中国空间科学技术. 2001, 4: 1-10.
[101]C. Pislaru, J.M. Freeman, D.G. Ford. Modal parameter identification for CNC machine tools using wavelet transform. International Journal of Machine Tools and Manufacture. 2003, 43: 987-993.
[102]B. F. Yana, A. Miyamotoa, E. Bruhwiler. Wavelet transform-based modal parameter identification considering uncertainty. Journal of Sound and Vibration. 2006, 291: 285-301.
[103]Joseph Lardies. Stephane Gouttebroze. Identication of modal parameters using the wavelet transform. International Journal of Mechanical Sciences. 2002, 266: 2263-2283.
[104]李鹤, 姚红良, 闻邦椿. 基于小波变换方法的高层建筑模态参数辨识. 振动与冲击. 2005, 25(4): 96-103.
[105]J. Lardies, M. N. Ta, M. Berthillier. Modal parameter estimation based on the wavelet transform of output data. Archive of Applied Mechanics. 2004, 73: 718-731.
[106]Z.Y. Zhang, H. X. Hua, X.Z. Xu. Modal parameter identification through Gabor expansion of response signals. Journal of Sound and Vibration. 2003, 266: 943-955.
[107]张建华, 刘建军, 张庆国. 基于平衡降阶法的结构振动模态预测控制. 工程力学. 2006, 23(5): 20-23.
[108]M. I. Friswell, S.D. Garvey, J. E. T. Penny. Model reduction usingDynamic and iterated IRS techniques. Journal of sound and Vibration. 1995, 186(2): 311-323.
[109]Andre preument, S. J. Elliot, P. Gardonia. Responsive system for active vibration control. Proceeding of the NATO Advanced Study Institute. 2002: 45-56.
[110]S. O. R. Moheimani, M. Fu. Spatial norms of flexible structures and its application in model order selection. Proceedings of the 37th Conference on Decision and Control. 1998: 3623-3624. H2
[111]S. O. R. Moheimani. Minimizing the out-of bandwidth dynamics in the model of reverberant system: Implication on Spatial H∞ control. Automatica. 2000, 36: 1023-1033.
[112]G. L. Bala. Control Design for variation in structural natural frequencies. Journal of Guidance, control and Dynamics. 1995, 18(2): 325-332.
[113]W. Gao, J. J. Chen. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Computers and Structures. 2003, 81(1): 53-60.
[114]S. Narayanan, V. Balamurugan. Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. Journal of Sound and Vibration. 2003, 262: 529-562.
[115]J. Osama. Optimal size and location of piezielectric actuator/sensor. Journal of Guidance, Control and Dynamics, 2000, 23(3): 509-515.
[116]Chien Yu Lu, Jason Sheng, Hong Tsai. An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Trans. Automatic Control. 2003, 48(2): 286-289.
[117]X. Zhang, C. Shao. Robust vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators. H∞Journal of Sound and Vibration. 2001, 243(1): 145-155.
[118]Van-Tsai Liu, Chun-liang Lin, Gean-pao Lee. Neural-network-based identification and control of a thin plate using piezoelectric actuators and sensors. International Journal of Systems Science. 2004, 35(6): 355-373.
[119]Yan-Ru Hu, Alfred Ng. Active robust vibration control of flexible structures. Journal of Sound and Vibration. 2005, 288: 43-56.
[120]C. Scherer, P. Gahinet, M. Chiali. Multiobjective output feedback control via LMI optimization. IEEE Trans. Automatic Control. 1997, 42(7): 896-911.
[121]Chen Hong, Guo Konghui. Constrained control of active suspensions: an LMI approach. IEEE Trans. Control Systems and Technology. 2005, 13(3): 412-421. H∞
[122]Samuel da silva, Vicente lopes junio. Design of a control system using linear matrix inequalities for the active vibration control of a plate. Journal of Intelligent Material Systems and Structures. 2006, 17(1): 81-93.
[123]张家凡, 郑晓. 具有极点约束的线性振动系统的一种主动控制设计. 振动与冲击. 2002, 21(3): 66-70.
[124]潘伟, 王学勇, 井元伟. 基于遗传算法的混合 / 状态反馈控制器. 控制与决策. 2005, 20(2): 132-136. H 2H∞
[125]Yang CianDong, Sun YunPing. Mixed / state-feedback design for microsatellite attitude control. Control Engineering Practice. 2002, 10: 951-97. H 2H∞
[126]Caracciolo, D. Richiedei, A. Trevisani. Robust mixed-norm position and vibration control of flexible link mechanisms. Mechatronics. 2005, 15: 767-791.
[127]张宏伟, 徐世杰, 黄文虎. 一种混合遗传算法在压电智能结构振动控制全局优化设计中的应用. 振动与冲击. 1999, 18(4): 6-11.
[128]D. B. Fogel. An introduction to simulated evolutionary optimization. IEEE Trans. Neural Networks. 1994, 5(1): 3-14.
[129]J. C. Doyle. Mixed and performance objective: optimal control. IEEE Trans. Automatic Control. 1994, 39(8): 1575-1587. H 2H∞
[130]杨冬梅, 张庆灵, 沙成满. 基于LMI的广义系统混合 / 优化控制. 控制与决策. 2003, 18(3): 320-323. H 2H∞
[131]Wu Huaining, Fei Yuanchun. Mixed / Robust output feedback control for uncertain linear systems. Control Theory and Application. 2000, 17(3): 367-377. H 2H∞
[132]Giovanni Caruso, Sergio Galeani, Laura Menini. Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators. Simulation Modelling Practice and Theory. 2003, 11: 403-419
[133]刘晓东, 张庆灵. 模糊系统控制器设计的LMI方法. 控制理论与应用. 2004, 21(1): 102-124.
[134]Paulo Tabuada, George J. Pappas. From nonlinear to hamiltonian via feedback. IEEE Trans. Automatic Control. 2003, 48(8), 1439-1445.
[135]Gregory S. Agines, Daniel J. Inman. Performance of nonlinear vibration absorbers for multi-degrees-of-freedom systems using nonlinear normal modes. Nonlinear Dynamics. 2001, 25: 275-292.
[136]P. F. Pai, M. J. Schulz. A refined nonlinear vibration absorber. International Journal of Mechanical Sciences. 2000, 42(3): 537-560.
[137]L. Q. Yao, J. G. Zhang, L. Lu. Nonlinear extension and bending of piezoelectric laminated plate under large applied field actuation. Smart Material and Structures. 2004, 13: 404-414.
[138]A. Kuai, K. Schlacher, H. Irschik. Infinite-dimensional control of nonlinear beam vibrations by piezoelectric actuator and sensor layers. Nonlinear Dynamics. 1999, 19: 71-91.
[139]Amit Kumar Onkar, D. Yadav. Non-linear free vibration of laminated composite plate with random material properties. Journal of Sound and Vibration. 2004, 272: 627-641.
[140]Santosh Kapuria, P.C. Dumir. Geometrically nonlinear axisymmetric response of thin circular plate under piezoelectric actuation. Communications in Nonlinear Science and Numerical Simulation. 2005, 10: 411-423.
[141]Xiao Lin Huang, Hui Shen Shen. Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators. International Journal of Mechanical Sciences. 2005, 47: 187-208.
[142]Yuan Chang Chang, Song Shyong Chen, Shun Feng Su. Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach. Fuzzy Sets and Systems. 2004, 148: 395-410.
[143]Wu Huaining, Cai. Kaiyuan. Mode-independent robust stabilization for uncertain markovian jump nonlinear systems via fuzzy Control. IEEE Trans. Systems, Man and Cybernetics. 2006, 36(3): 509-512.
[144]J. X. Gao, Y. P. Shen. Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators. Journal of Sound and Vibration. 2003, 264: 911-928.
[145]Zhou Youhe, Wan Jizeng. Vbration control of piezoelectric beam-type plates with geometrically nonlinear deformation. International Journal of Non-Linear Mechanics. 2004, 39: 909-920.
[146]Qu Wenzhong, Sun Jincai, Qiu Yang. Active control of vibration using a fuzzy control method. Journal of Sound and Vibration. 2004, 275: 917-930.
[147]Y. Y. Lee, H. Y. Sun, J. N. Reddy. Non-linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates. International Journal of Numerical Method in Engineering. 2006, 65: 45-61.
[148]Kougen Ma, Adaptive non-linear control of a clamped rectangular plate with PZT patches. Journal of Sound and Vibration. 2003, 264: 835-850.
[149]H. O. Wang, K. Tanaka, M. F. Griffin. An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy System. 1996, 4(1): 14-23.
[150]Bor-Sen Chen, Chung-Shi Tseng, Huey-Jian Uang. Mixed fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach. IEEE Trans. Fuzzy Systems. 2000, 8(3): 249-256.
[151]Amit Kumar Onkar, D. Yadav. Forced nonlinear vibration of laminated composite plates with random material properties. Composite Structures. 2005, 70: 334-342.
[152]李卓球, 董文堂. 非线性弹性理论. 北京: 科学出版社, 2004.
[153]K. Renganathan, Nageswara Rao, T. Manoj. Moderately large deflection of laminated thin rectangular plates. Mathematics and Mechanics. 2002, 82(5): 352-360.
[154]M. Amabili. Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments. Computers and Structures. 2004, 82: 2587–2605.
[155]M. Amabili. Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. Journal of Sound and Vibration. 2006, 291: 539–565.
[156]Federico Cuesta, Francisco Gordillo, Javier Aracil. Stability analysis of nonlinear multivariable Takagi–Sugeno fuzzy Control Systems. IEEE Trans. Fuzzy System. 1999, 7(5): 508-520.
[157]Chun-Hsiung Fang, Yung-Sheng Liu, Shih-Wei Kau. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems. IEEE Trans. Fuzzy Sysems. 2006, 14(3): 386-398.
[158]王磊, 王为民. 模糊控制理论及应用. 北京: 国防工业出版社, 1997.
[159]Wudhichai Assawinchaichote, Sing Kiong Nguang. Fuzzy control dsign for nonlinear singularly perturbed systems with pole placement constraints: an LMI Approach. IEEE Trans. System, Man, and Cybernetics-Part B: Cybernetics. 2004, 34(1): 579-588.
[160]Kuang-Yow Lian, Jeih-Jang Liou, Chien-Yu Huang. LMI-based integral fuzzy control of DC-DC converters. IEEE Trans. Fuzzy System. 2006, 14(1): 71-80.
[161]N. G. Chalhoub, G. A. Kfoury, B. A. Bazzi. Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator. Journal of Sound and Vibration. 2006, 291: 437-461.
[162]Dong Sun, James K. Mills, Jinjun Shan. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement. Mechatronics. 2004, 14: 381-401.
[163]Lianfang Tian, Curtis Collins. Adaptive neuro-fuzzy control of a flexible manipulator. Mechatronics. 2005, 115: 1305-1320.
[164]Santosha Kumar Dwivedy, Peter Eberhard. Dynamic analysis of flexible manipulators: a literature review. Mechanism and Machine Theory. 2006, 41: 749-777.
[165]Yuangang Tang, Fuchun Sun, Zengqi Sun. Neural network control of flexible-link manipulators using sliding mode. Neurocomputing. 2006, 70: 288-295.
[166]Luca Bascetta, Paolo Rocco. End-point vibration sensing of planar flexible manipulators through visual servoing. Mechatronics. 2006, 16: 221-232.
[2]Rabih Alkhatib, M. F. Golnaraghi. Active structural vibration control: a review. The Shock and Vibration Digest. 2003, 35(5): 367-383.
[3]M. Porfiri, F. dell’Isolaand, F. M. Frattale Mascioli. Circuit analog of a beam and its application to multimodal vibration damping using piezoelectric transducers. International Journal of Circuit Theory and Applications. 2004, 32: 167-198.
[4]丁文镜. 振动主动控制当前的主要研究课题. 力学进展. 1992, 24(2): 173-180.
[5]B. C. Nakra, Vibration control in machines and structures using viscoelastic damping. Journal of Sound and Vibration. 1998, 211(3): 449-465.
[6]Y. Zhu, J. Qiu, H. Du. Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure. Archive of Applied Mechanics. 2004, 73: 718-733.
[7]胡海岩. 动力学、振动与控制学科未来的发展趋势. 力学进展. 2002, 32(2): 194-306.
[8]刘少军, 李艳. 基于1/2车辆模型主动悬架预先控制方法的研究. 信息与控制. 2000, 29(1): 6-13.
[9]S. Ikenaga, F. L. Lewis, J. Campos. Active suspension control of ground vehicle based on a full-vehicle model. American Control Conference. Chicago, USA, 2000: 1327-1339.
[10]Zhang Yisheng, Alleyne. A new approach to half-car active suspension control. American Control Conference. Denver, Colorado, 2003: 1420-1431.
[11]T. Kobori. Past, present and future in seismic response control of civil engineering structures. Proceedings of the Third World Conference on Structural Control. Como, Italy, 2002, 1: 9-14.
[12]Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited Structures. Engineering Structures. 2004, 26: 279-289.
[13]M. Aldawod, B. Samali, F Naghdy. Active control of wind response of tall building using a fuzzy controller. Engineering Structures. 2001, 23(11) 1512-1522.
[14]W. J. Book. New concepts in lightweight arms. Proceedings of the Second International Symposium on Robotic Research. 1984, 1: 203-205.
[15]Z. Su, K. Khorasani. Neural network controller for single-link flexible manipulator based on the inverse dynamics structure. Proceeding of the International Joint Conference on Neural Network. 2000, 5: 311-316.
[16]De Luca. Closed-form dynamic model of planar multilink lightweight robots. IEEE Trans. Systems, Man & Cybernetics. 1991, 21: 826-839.
[17]H. A. Talebi. Inverse dynamics control of flexible-link manipulators using neural networks. IEEE International Conference on Robotics and Automation. 1998, 1: 806-811.
[18]De luca. Inversion-based nonlinear control of robot arms with flexible links. Journal of Guidance, Control and Dynamics. 1993, 16: 1669-1176.
[19]Afzal Suleman, Antonio P. Costa. Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators. Computers and Structures. 2004, 82: 1303-1314.
[20]E. F. Crawley. Intelligent structures for aerospace: a technology overview and assessment. AIAA Journal. 1994, 32: 1689-1699.
[21]牟全臣, 黄文虎, 郑钢铁等. 航天结构主、被动一体化振动控制技术的研究现状和进展. 应用力学学报. 2001, 18(3): 1-7.
[22]黄文虎, 王心清, 张景绘等. 航天柔性结构振动控制的若干新进展. 力学进展. 1997, 27(1): 5-18.
[23]E. F. Crawley, De Luis. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 1987, 25(10): 1373-1385.
[24]E. F. Crawley, E. H. Anderson. Detailed modeling of piezoelectric actuation of beams. Proceeding of the 30th AIAA SDM Conference. 1989: 2000-2010.
[25]S. B. Choi. Vibration control of a smart beam structure subjected to actuator uncertainty: Experimental verification. Acta Mechanica. 2006, 181: 19-30.
[26]H. T. Banks, R. C. Smith, Y. Wang. Smart Material Structures: Modeling, Estimation and Control. Paris, Wiley, 1996.
[27]W. S. Hwang, H. C. Park. Finite element modeling of piezoelectric sensors and actuators. AIAA Journal. 1993, 31(5): 930-937.
[28]T. Kamada, T. Fujita. Active vibration control of structures with smart structures using piezoeelectric actuators. Journal of Intelligent Material Systems and Structures. 1997, 8(6): 447-456.
[29]李传兵, 廖昌荣, 张玉等. 压电智能结构的研究进展. 压电与声光. 2002, 24(1): 42-60.
[30]李俊宝, 张景绘, 任勇生等. 振动工程中智能结构的研究进展. 力学进展. 1999, 29(2): 177-185.
[31]吴大方, 刘安成, 麦汉超等. 压电智能柔性梁振动主动控制研究. 北京航空航天大学学报. 2004, 30(12): 160-163.
[32]Ha Sung, K. Keilers. Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA Journal. 1992, 30(3): 772-780.
[33]Wenwu Cao, Harley. Smart materials and structures. Proceeding of national Academic Science. USA ,1999: 1013-1024.
[34]Z. K. Kusculuoglu, B. Fallahi. Finite element model of a beam with a piezoceramic patch actuator. Journal of Sound and Vibration. 2004, 275: 27-44.
[35]I. S. Grewal, W. Szyszkowski. Optimal vibration control of continuous structures by FEM: Part II-the computer implementation. Communications in Numeriacal Methods in Engineering. 2002, 18: 869-876.
[36]Xing-Jian Dong, Guang Meng, Juan-Chun Peng. Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study. Journal of Sound and Vibration. 2006, 297: 680-693.
[37]Chyanbin Hwu, W.C. Chang, H.S. Gai. Vibration suppression of composite sandwich beams. Journal of Sound and Vibration. 2004, 272: 1-20.
[38]S. Raja, P. K. Sinha, G. RaThap. Influence of one and two dimensional piezoelectric actuation: an active vibration control of smart panels. Aerospace Science and Technology. 2002, 6(3): 209-216.
[39]M. J. Balas. Direct velocity feedback control of large space structures. Journal of Guidance. 1979, 2(3): 252-253.
[40]M. J. Balas. Feedback control of flexible systems. IEEE Trans. on Automatic Control. 1978, 23(4): 673-679.
[41]C. J. Goh, T. K. Caughey. On the stability problem caused by finite actuator dynamics in the collocated control of large space structures. International Journal of Control. 1985, 41(3): 787-802.
[42]Fanson J. L, Caugher T. K. Positive position feedback control for large space structures. AIAA Journal. 1990, 28(4): 712-724.
[43]Meirovitch L, Baruh H. A comparison of control techniques for large flexible systems. Journal of Guidance. 1983, 6(4): 302-310.
[44]Baz A, Poh S, Fedo J. Independent modal space control with positive position feedback. Trans. of the ASME. 1992, 114: 96-103.
[45]S.P. Singh, Harpreet Singh Pruthi, V.P. Agarwal. Efficient modal control strategies for active control of vibrations. Journal of Sound and Vibration. 2003, 262: 563-575.
[46]陈大跃, 胡宗武, 范祖尧. 振动控制的特征结构配置. 振动工程学报. 1991, 4(2): 75-81.
[47]马扣根, 顾仲权. 最优极点配置法在梁式结构振动主动控制中的应用. 振动与冲击. 1991, 3: 85-89.
[49]顾仲权. 振动主动控制中低阶控制器的优化设计. 振动工程学报. 1990, 3(3): 1-8.
[50]谭善光, 汪希宣. 结构强迫振动最优响应和模态主动控制. 振动工程学报. 1989, 2(4): 76-81.
[48]M. A. Vasques, J. Dias Rodrigues. Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Computers and Structures. 2006, 84: 1402-1414.
[51]俞文伯, 丁文镜. 悬臂梁随机振动的最优控制. 建筑结构学报. 1995, 17(5): 49-58.
[52]P. K. Kwakuo, C. C. Kevin. The application of multi-channel design methods for vibration control of an active structure. Smart Material and Structures. 1994, 3: 329-343.
[53]D. S. Scott, T. Nobuo. Modification to overall system response when using narrow band adaptive feedforward control system. Journal of Dynamic Systems, Measurement, and Control. 1993, 115: 612-626.
[54]J. S. Vipperman, R. A. Burdisso, C. R. Fuller. Active control of broadband structural vibration using the LMS adaptive algorithm. Journal of Sound and Vibration. 1993, 166(2): 283-299.
[55]孙朝晖, 王冲, 戴扬等. 结构振动主动控制理论及实验研究. 振动工程学报. 1994, 7(2): 154-160.
[56]刘季, 滕军. 结构在地震作用下的主动自校正控制计算方法. 地震工程与工程振动. 1991, 11(2): 73-84.
[57]刘季, 滕军. 地震作用下结构振型组合自校正控制. 地震工程与工程振动. 1992, 12(2): 48-58.
[58]C. H. Charles, D. S. Bayard. Experimental study of robustness in adaptive control for large flexible structures. AIAA Guidance, Navigation and Control Conference. 1990: 1645-1656.
[59]马扣根, 顾仲权. 结构振动的一种离散自适应控制策略. 中国振动工程学会噪声与振动控制学术年会论文集. 北京, 1991: 260-267.
[60]Matthew Allen, Franco Bernelli-Zazzera, Riccardo Scattolini. Sliding mode control of a large flexible space structure. Control Engineering Practice. 2000, 8: 861-871.
[61]M. H. Kim. Reduction of observation spillover in vibration suppression using a sliding mode observer. Journal of Vibration and Control. 2002, 7(7): 1087-1150.
[62]周军, 陈新海. 大型柔性空间结构的变结构模型参考自适应控制. 航空学报. 1992, 13(4): 158-163.
[63]J. C. Doyle. State-space solution to standard / control. American Control Conference. 1988: 817-823. H 2H∞
[64]I. N. Kar, K. Seto, F. Doi. Multimode vibration control of a flexible structure using H-based robust control. IEEE Trans. Mechatronics. 2000, 5(1): 23-31.
[65]林嗣廉, 徐博侯. 柔性结构振动的独立模态 H2控制. 浙江大学学报. 2001, 35(1): 23-29.
[66]X. Zhang, C. Shao. Robust vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators. H∞Journal of Sound and Vibration. 2001, 243(1): 145-155.
[67]J. Qiu, J. Tani. Vibration control of a cylindrical shell using distributed piezoelectric sensors and actuators. Journal of Intelligent Material Systems and Structures. 1995, 6: 474-481.
[68]J. L. Fanson, C. C. Chu. Active member control of a precision structure with and performance objective. AIAA Dynamic Specialist Conference. 1990: 322-333. H∞
[69]C. C. Chu, R. Smith, J. Fanson. Robust control of an active precision truss structure. Proceeding of the American Control Conference. 1990: 2490-2495.
[70]C. C. Chu, R. Smith, J. Fanson. The design of controllers for an experimental non-collocated flexible structure problem. IEEE Trans. Control System Technology. 1994, 2(2): 101-109. H∞
[71]Carten Scherer, Pascal Gahinet. Multiobjective output-feedback control via LMI optimization. IEEE Trans. on Automatic Control. 1997, 42(7): 896-910.
[72]俞立. 鲁棒控制. 北京, 清华大学出版社, 2002.
[73]Qinglei Hu, Guangfu Ma. Active vibration control of a flexible plate structure using LMI-based output feedback control law. Proceedings of the 5th World Congress on Intelligent Control and Automation. 2004: 2021-2032. H∞
[74]Sridhar Sana, Vittal S. Rao. Application of linear matrix inequalities in the control of smart structural systems. Journal of Intelligent Material System & Structure. 2000, 11: 311-323.
[75]Y. Y. Li, L. H. Yam. A robust design method of active controller for uncertain vibration systems. Journal of Vibration and Control. 2001, 7: 453-466.
[76]Y. Y. Li, L. H. Yam. Robust vibration control of uncertain systems using variable parameter feedback and model-based fuzzy strategies. Computers and Structures. 2001, 79(11): 1109-1119.
[77]R. W. James, J. H. John. Distributed fuzzy control of a flexible structure. SPIE Proceedings of Smart Structures and Materials. 1994, 1: 488-499.
[78]D. Park. Genetic-based new fuzzy reasoning models with application to fuzzy control. IEEE Trans. System, man and Cybernetics. 1994, 224(1): 185-191.
[79]Casciati F. Application of fuzzy to active structural control. The Second conference on Smart Structures and Material. Glasgow, 1994, 5: 206-209.
[80]Kubica E. E, Wang D. A fuzzy-control strategy for a flexible single link robot. American Control Conference. 1993: 236-241.
[81]Shiuhjer Huang, Weicheng Lin. Adaptive fuzzy controller with sliding surface for vehicle suspension control. IEEE Trans. Fuzzy Systems. 2003, 11(4): 550-560.
[82]Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited structures. Engineering Structures. 2004, 26: 279-289.
[83]M. K. Kwak, D. Sciulli. Fuzzy-logic Based Vibration Suppression Control Experiments on Active Structures. Journal of Sound and Vibration. 1996, 191(1): 17-28.
[84]刘华, 黄田, 曾子平. 一类非线性振动的智能主动控制方法. 非线性动力学报. 1994, 1(3): 288-292.
[85]R. Jha, J. Rower. Experimental investigation of active vibration control using neural networks and piezoelectric actuators. Smart Materials and Structures. 2002, 11: 115-121.
[86]Y. N. Nassar, M. Siddiqui, A. Z. Garni. Artificial neural networks in vibration control of rotor bearing systems. Simulation Practice and Theory. 2000, 7(8): 729-740.
[87]M. T. Valoor, K. Chandrashekhara, S Agarwal. Active vibration control of smart composite plates using self-adaptive neuro-controller. Smart Material and Structures. 2000. 9: 197-204.
[88]C. P. Smyser, K. Chandrashekharay. Robust vibration control of composite beams using piezoelectric devices and neural networks. Smart Material and Structures. 1997, 6: 178-189.
[89]Van Tsai Liu, Chun Liang Lin, Gean Pao Lee. Neural-network-based identification and control of a thin plate using piezoelectric actuators and sensors. International Journal of Systems Science. 2004, 35(6): 355-373.
[90]傅志方, 周炎. 非线性结构系统的模态分析、建模及参数辨识: 研究综述. 振动与冲击. 1992, 1(2): 100-114.
[91]付志方. 振动模态分析与参数辨识. 北京: 机械工业出版社, 1990.
[92]P. Verboven, P. Guillaume, B. Cauberghe. Modal parameter estimation from input–output Fourier data using frequency-domain maximum likelihood identification. Journal of Sound and Vibration. 2004, 276: 957-979.
[93]Thien-Phu Le, Pierre Argoul. Continuous wavelet transform for modal identification using free decay response. Journal of Sound and Vibration. 2004, 277: 73-100.
[94]续秀忠. 结构模态参数辨识的时频分析方法. 噪声与振动控制. 2002, 22(5): 3-7.
[95]R. Lind, K. Snyder , M. Brenner. Wavelet analysis to characterize non-linearities and predict limit cycles of an elastic system. Mechanical Systems and Signal Processing. 2001, 15(2): 337-356.
[96]W. J. Staszewski. Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform. Journal of Sound and Vibration. 1998, 214: 639-658.
[97]续秀忠. 基于环境激励的模态参数辨识方法综述. 振动与冲击. 2002, 21(35): 1-5.
[98]J. Awrejcewicz, A. V. Krysko. Wavelet-based analysis of parametric vibrations of flexible structures. International Applied Mechanics. 2003, 39(9): 997-1029.
[99]S. Pernot, C. H. Lamarque. A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems. Nonlinear Dynamics. 2003, 32: 33–70.
[100]刘一武, 张洪华, 吴宏鑫. 基于小波方法的挠性空间结构模态参数的辨识. 中国空间科学技术. 2001, 4: 1-10.
[101]C. Pislaru, J.M. Freeman, D.G. Ford. Modal parameter identification for CNC machine tools using wavelet transform. International Journal of Machine Tools and Manufacture. 2003, 43: 987-993.
[102]B. F. Yana, A. Miyamotoa, E. Bruhwiler. Wavelet transform-based modal parameter identification considering uncertainty. Journal of Sound and Vibration. 2006, 291: 285-301.
[103]Joseph Lardies. Stephane Gouttebroze. Identication of modal parameters using the wavelet transform. International Journal of Mechanical Sciences. 2002, 266: 2263-2283.
[104]李鹤, 姚红良, 闻邦椿. 基于小波变换方法的高层建筑模态参数辨识. 振动与冲击. 2005, 25(4): 96-103.
[105]J. Lardies, M. N. Ta, M. Berthillier. Modal parameter estimation based on the wavelet transform of output data. Archive of Applied Mechanics. 2004, 73: 718-731.
[106]Z.Y. Zhang, H. X. Hua, X.Z. Xu. Modal parameter identification through Gabor expansion of response signals. Journal of Sound and Vibration. 2003, 266: 943-955.
[107]张建华, 刘建军, 张庆国. 基于平衡降阶法的结构振动模态预测控制. 工程力学. 2006, 23(5): 20-23.
[108]M. I. Friswell, S.D. Garvey, J. E. T. Penny. Model reduction usingDynamic and iterated IRS techniques. Journal of sound and Vibration. 1995, 186(2): 311-323.
[109]Andre preument, S. J. Elliot, P. Gardonia. Responsive system for active vibration control. Proceeding of the NATO Advanced Study Institute. 2002: 45-56.
[110]S. O. R. Moheimani, M. Fu. Spatial norms of flexible structures and its application in model order selection. Proceedings of the 37th Conference on Decision and Control. 1998: 3623-3624. H2
[111]S. O. R. Moheimani. Minimizing the out-of bandwidth dynamics in the model of reverberant system: Implication on Spatial H∞ control. Automatica. 2000, 36: 1023-1033.
[112]G. L. Bala. Control Design for variation in structural natural frequencies. Journal of Guidance, control and Dynamics. 1995, 18(2): 325-332.
[113]W. Gao, J. J. Chen. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Computers and Structures. 2003, 81(1): 53-60.
[114]S. Narayanan, V. Balamurugan. Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. Journal of Sound and Vibration. 2003, 262: 529-562.
[115]J. Osama. Optimal size and location of piezielectric actuator/sensor. Journal of Guidance, Control and Dynamics, 2000, 23(3): 509-515.
[116]Chien Yu Lu, Jason Sheng, Hong Tsai. An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Trans. Automatic Control. 2003, 48(2): 286-289.
[117]X. Zhang, C. Shao. Robust vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators. H∞Journal of Sound and Vibration. 2001, 243(1): 145-155.
[118]Van-Tsai Liu, Chun-liang Lin, Gean-pao Lee. Neural-network-based identification and control of a thin plate using piezoelectric actuators and sensors. International Journal of Systems Science. 2004, 35(6): 355-373.
[119]Yan-Ru Hu, Alfred Ng. Active robust vibration control of flexible structures. Journal of Sound and Vibration. 2005, 288: 43-56.
[120]C. Scherer, P. Gahinet, M. Chiali. Multiobjective output feedback control via LMI optimization. IEEE Trans. Automatic Control. 1997, 42(7): 896-911.
[121]Chen Hong, Guo Konghui. Constrained control of active suspensions: an LMI approach. IEEE Trans. Control Systems and Technology. 2005, 13(3): 412-421. H∞
[122]Samuel da silva, Vicente lopes junio. Design of a control system using linear matrix inequalities for the active vibration control of a plate. Journal of Intelligent Material Systems and Structures. 2006, 17(1): 81-93.
[123]张家凡, 郑晓. 具有极点约束的线性振动系统的一种主动控制设计. 振动与冲击. 2002, 21(3): 66-70.
[124]潘伟, 王学勇, 井元伟. 基于遗传算法的混合 / 状态反馈控制器. 控制与决策. 2005, 20(2): 132-136. H 2H∞
[125]Yang CianDong, Sun YunPing. Mixed / state-feedback design for microsatellite attitude control. Control Engineering Practice. 2002, 10: 951-97. H 2H∞
[126]Caracciolo, D. Richiedei, A. Trevisani. Robust mixed-norm position and vibration control of flexible link mechanisms. Mechatronics. 2005, 15: 767-791.
[127]张宏伟, 徐世杰, 黄文虎. 一种混合遗传算法在压电智能结构振动控制全局优化设计中的应用. 振动与冲击. 1999, 18(4): 6-11.
[128]D. B. Fogel. An introduction to simulated evolutionary optimization. IEEE Trans. Neural Networks. 1994, 5(1): 3-14.
[129]J. C. Doyle. Mixed and performance objective: optimal control. IEEE Trans. Automatic Control. 1994, 39(8): 1575-1587. H 2H∞
[130]杨冬梅, 张庆灵, 沙成满. 基于LMI的广义系统混合 / 优化控制. 控制与决策. 2003, 18(3): 320-323. H 2H∞
[131]Wu Huaining, Fei Yuanchun. Mixed / Robust output feedback control for uncertain linear systems. Control Theory and Application. 2000, 17(3): 367-377. H 2H∞
[132]Giovanni Caruso, Sergio Galeani, Laura Menini. Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators. Simulation Modelling Practice and Theory. 2003, 11: 403-419
[133]刘晓东, 张庆灵. 模糊系统控制器设计的LMI方法. 控制理论与应用. 2004, 21(1): 102-124.
[134]Paulo Tabuada, George J. Pappas. From nonlinear to hamiltonian via feedback. IEEE Trans. Automatic Control. 2003, 48(8), 1439-1445.
[135]Gregory S. Agines, Daniel J. Inman. Performance of nonlinear vibration absorbers for multi-degrees-of-freedom systems using nonlinear normal modes. Nonlinear Dynamics. 2001, 25: 275-292.
[136]P. F. Pai, M. J. Schulz. A refined nonlinear vibration absorber. International Journal of Mechanical Sciences. 2000, 42(3): 537-560.
[137]L. Q. Yao, J. G. Zhang, L. Lu. Nonlinear extension and bending of piezoelectric laminated plate under large applied field actuation. Smart Material and Structures. 2004, 13: 404-414.
[138]A. Kuai, K. Schlacher, H. Irschik. Infinite-dimensional control of nonlinear beam vibrations by piezoelectric actuator and sensor layers. Nonlinear Dynamics. 1999, 19: 71-91.
[139]Amit Kumar Onkar, D. Yadav. Non-linear free vibration of laminated composite plate with random material properties. Journal of Sound and Vibration. 2004, 272: 627-641.
[140]Santosh Kapuria, P.C. Dumir. Geometrically nonlinear axisymmetric response of thin circular plate under piezoelectric actuation. Communications in Nonlinear Science and Numerical Simulation. 2005, 10: 411-423.
[141]Xiao Lin Huang, Hui Shen Shen. Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators. International Journal of Mechanical Sciences. 2005, 47: 187-208.
[142]Yuan Chang Chang, Song Shyong Chen, Shun Feng Su. Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach. Fuzzy Sets and Systems. 2004, 148: 395-410.
[143]Wu Huaining, Cai. Kaiyuan. Mode-independent robust stabilization for uncertain markovian jump nonlinear systems via fuzzy Control. IEEE Trans. Systems, Man and Cybernetics. 2006, 36(3): 509-512.
[144]J. X. Gao, Y. P. Shen. Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators. Journal of Sound and Vibration. 2003, 264: 911-928.
[145]Zhou Youhe, Wan Jizeng. Vbration control of piezoelectric beam-type plates with geometrically nonlinear deformation. International Journal of Non-Linear Mechanics. 2004, 39: 909-920.
[146]Qu Wenzhong, Sun Jincai, Qiu Yang. Active control of vibration using a fuzzy control method. Journal of Sound and Vibration. 2004, 275: 917-930.
[147]Y. Y. Lee, H. Y. Sun, J. N. Reddy. Non-linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates. International Journal of Numerical Method in Engineering. 2006, 65: 45-61.
[148]Kougen Ma, Adaptive non-linear control of a clamped rectangular plate with PZT patches. Journal of Sound and Vibration. 2003, 264: 835-850.
[149]H. O. Wang, K. Tanaka, M. F. Griffin. An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy System. 1996, 4(1): 14-23.
[150]Bor-Sen Chen, Chung-Shi Tseng, Huey-Jian Uang. Mixed fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach. IEEE Trans. Fuzzy Systems. 2000, 8(3): 249-256.
[151]Amit Kumar Onkar, D. Yadav. Forced nonlinear vibration of laminated composite plates with random material properties. Composite Structures. 2005, 70: 334-342.
[152]李卓球, 董文堂. 非线性弹性理论. 北京: 科学出版社, 2004.
[153]K. Renganathan, Nageswara Rao, T. Manoj. Moderately large deflection of laminated thin rectangular plates. Mathematics and Mechanics. 2002, 82(5): 352-360.
[154]M. Amabili. Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments. Computers and Structures. 2004, 82: 2587–2605.
[155]M. Amabili. Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. Journal of Sound and Vibration. 2006, 291: 539–565.
[156]Federico Cuesta, Francisco Gordillo, Javier Aracil. Stability analysis of nonlinear multivariable Takagi–Sugeno fuzzy Control Systems. IEEE Trans. Fuzzy System. 1999, 7(5): 508-520.
[157]Chun-Hsiung Fang, Yung-Sheng Liu, Shih-Wei Kau. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems. IEEE Trans. Fuzzy Sysems. 2006, 14(3): 386-398.
[158]王磊, 王为民. 模糊控制理论及应用. 北京: 国防工业出版社, 1997.
[159]Wudhichai Assawinchaichote, Sing Kiong Nguang. Fuzzy control dsign for nonlinear singularly perturbed systems with pole placement constraints: an LMI Approach. IEEE Trans. System, Man, and Cybernetics-Part B: Cybernetics. 2004, 34(1): 579-588.
[160]Kuang-Yow Lian, Jeih-Jang Liou, Chien-Yu Huang. LMI-based integral fuzzy control of DC-DC converters. IEEE Trans. Fuzzy System. 2006, 14(1): 71-80.
[161]N. G. Chalhoub, G. A. Kfoury, B. A. Bazzi. Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator. Journal of Sound and Vibration. 2006, 291: 437-461.
[162]Dong Sun, James K. Mills, Jinjun Shan. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement. Mechatronics. 2004, 14: 381-401.
[163]Lianfang Tian, Curtis Collins. Adaptive neuro-fuzzy control of a flexible manipulator. Mechatronics. 2005, 115: 1305-1320.
[164]Santosha Kumar Dwivedy, Peter Eberhard. Dynamic analysis of flexible manipulators: a literature review. Mechanism and Machine Theory. 2006, 41: 749-777.
[165]Yuangang Tang, Fuchun Sun, Zengqi Sun. Neural network control of flexible-link manipulators using sliding mode. Neurocomputing. 2006, 70: 288-295.
[166]Luca Bascetta, Paolo Rocco. End-point vibration sensing of planar flexible manipulators through visual servoing. Mechatronics. 2006, 16: 221-232.