压电智能结构振动主动控制研究
|
摘要
压电材料作为一种新型的智能材料,以其良好的机电耦合特性,在结构振动主动控制领域得到了广泛应用。本文以压电悬臂梁振动系统为研究对象,利用压电材料的正、逆压电效应,分析压电元件和悬臂梁之间的相互耦合关系,建立压电悬臂梁的机电耦合动力学模型和基于闭环控制系统的状态方程,并应用ANSYS软件对系统进行静力学和动力学分析,为压电智能悬臂梁振动控制系统的设计提供依据。
确立压电传感器/驱动器的优化布置准则,即D优化设计准则,通过对结构振动特性的研究,将该优化准则简化到只需利用结构模态信息就能确定压电元件的最优位置。
针对压电智能结构的振动主动控制问题,考虑到布置压电元件对主体结构动力学特性的影响,采用线性二次型高斯(Linear Quadratic Gauss)最优控制方法,设计Kalman滤波器对结构模型噪声和量测噪声进行过滤,对系统的状态及输出做出比较精确的估计,从而达到最优的控制效果。
针对系统在不确定性因素作用下的控制问题,设计基于H_∞的鲁棒控制器,能够保证系统在模态参数摄动情况下,具有较强的鲁棒性以及较好的闭环动态性能,同样具有良好的振动抑制效果。
提出模态空间范数的概念和计算方法,建立控制系统模态空间的传递函数与状态方程,并利用模态空间范数作为各个模态对结构动力响应贡献大小的度量,给出一种基于所配置的驱动器对各个模态的控制能力大小,对压电柔性结构进行模态挑选而获得降阶模型的方法,并与常规方法进行比较研究。
以上方法均在MATLAB环境中进行了仿真研究,验证了其有效性。
The piezoelectric materials have been widely used in the field of structural active vibration control as a new type of smart materials because of their excellent mechanical-electrical coupling characteristics. With the positive and negative piezoelectric effect of the piezoelectric materials, a vibration system of piezoelectric cantilever beam is taken as the study object in the paper, the interaction coupling relations are analyzed between the piezoelectric elements and cantilever beam, the dynamical model of mechanical-electrical coupling and the state equation which based on the closed-loop control system are established, the static and dynamic analysis by the application of ANSYS software provides theoretical basis to the design of the vibration control system for piezoelectric cantilever beam.
The optimal collocation principle of piezoelectric sensor/actuator is established, namely the D optimum design principle. The principle is simplified by the study of the vibration characteristics of the system, and the optimal location of piezoelectric elements could be determined only by the modal information of the structure.
For the active vibration control of the piezoelectric flexible structures, the optimal control method of Linear Quadratic Gauss (LQG) is applied with the dynamical influence of piezoelectric elements to the main structure. A Kalman filter is designed to filtrate the model noise and measurement noise of the structure, therefore, the status and output of the system could be estimated more precisely, so as to achieve optimal control effect.
A robust controller is designed based on H_∞method in response to the control problem of the vibration system with uncertainty factors acted, the method could be able to guarantee the system has good robustness and better closed-loop dynamic performance when the modal parameters has some perturbation, also, it has a good effect of vibration suppression.
The concept and calculation method of modal space norm is put forward in this paper, the modal space transfer function and state equation of the control system is set up, and the modal space norm is used as the measurement of each modes contribute to the dynamical response of the structure, a model reduction method which based on the control ability of collocated actuators contributed to each modes is introduced in this paper, and it is compared with the conventional methods.
The simulation study of the above methods has been done in MATLAB, and improve the effectively of them.
确立压电传感器/驱动器的优化布置准则,即D优化设计准则,通过对结构振动特性的研究,将该优化准则简化到只需利用结构模态信息就能确定压电元件的最优位置。
针对压电智能结构的振动主动控制问题,考虑到布置压电元件对主体结构动力学特性的影响,采用线性二次型高斯(Linear Quadratic Gauss)最优控制方法,设计Kalman滤波器对结构模型噪声和量测噪声进行过滤,对系统的状态及输出做出比较精确的估计,从而达到最优的控制效果。
针对系统在不确定性因素作用下的控制问题,设计基于H_∞的鲁棒控制器,能够保证系统在模态参数摄动情况下,具有较强的鲁棒性以及较好的闭环动态性能,同样具有良好的振动抑制效果。
提出模态空间范数的概念和计算方法,建立控制系统模态空间的传递函数与状态方程,并利用模态空间范数作为各个模态对结构动力响应贡献大小的度量,给出一种基于所配置的驱动器对各个模态的控制能力大小,对压电柔性结构进行模态挑选而获得降阶模型的方法,并与常规方法进行比较研究。
以上方法均在MATLAB环境中进行了仿真研究,验证了其有效性。
The piezoelectric materials have been widely used in the field of structural active vibration control as a new type of smart materials because of their excellent mechanical-electrical coupling characteristics. With the positive and negative piezoelectric effect of the piezoelectric materials, a vibration system of piezoelectric cantilever beam is taken as the study object in the paper, the interaction coupling relations are analyzed between the piezoelectric elements and cantilever beam, the dynamical model of mechanical-electrical coupling and the state equation which based on the closed-loop control system are established, the static and dynamic analysis by the application of ANSYS software provides theoretical basis to the design of the vibration control system for piezoelectric cantilever beam.
The optimal collocation principle of piezoelectric sensor/actuator is established, namely the D optimum design principle. The principle is simplified by the study of the vibration characteristics of the system, and the optimal location of piezoelectric elements could be determined only by the modal information of the structure.
For the active vibration control of the piezoelectric flexible structures, the optimal control method of Linear Quadratic Gauss (LQG) is applied with the dynamical influence of piezoelectric elements to the main structure. A Kalman filter is designed to filtrate the model noise and measurement noise of the structure, therefore, the status and output of the system could be estimated more precisely, so as to achieve optimal control effect.
A robust controller is designed based on H_∞method in response to the control problem of the vibration system with uncertainty factors acted, the method could be able to guarantee the system has good robustness and better closed-loop dynamic performance when the modal parameters has some perturbation, also, it has a good effect of vibration suppression.
The concept and calculation method of modal space norm is put forward in this paper, the modal space transfer function and state equation of the control system is set up, and the modal space norm is used as the measurement of each modes contribute to the dynamical response of the structure, a model reduction method which based on the control ability of collocated actuators contributed to each modes is introduced in this paper, and it is compared with the conventional methods.
The simulation study of the above methods has been done in MATLAB, and improve the effectively of them.
引文
[1]刘春美.压电智能梁结构振动控制技术仿真与实验研究[D].山西:华北工学院硕士学位论文,2003
[2]宁淑荣.采用压电材料的振动主动控制[D].湖北:武汉科技大学硕士学位论文,2005
[3]王波.点式压电智能结构振动控制方法改进的研究[D].重庆:重庆大学博士学位论文,2004
[4]马治国,闻邦椿,颜云辉.智能结构的若干问题与进展[J].东北大学学报,1998,19(5):513~516
[5]骆英.正交异性压电复合材料功能元件的研究[D].江苏:南京航空航天大学博士学位论文,2000
[6]郑骥.基于改进遗传算法的主动柔性结构压电元件的位置优化[D].河北:河北工程大学硕士学位论文,2006
[7] E. F. Crawley, E. H. Anderson. Detailed modeling of piezoelectric actuation of beams [J].Proceeding of the 30th AIAA SDM Conference. 1989: 2000~2010
[8]殷学纲,李宾,李玉刚,黄尚廉.点式压电智能柔性板振动主动控制的建模与仿真[J].噪声与振动控制,1999,10(5):16~20
[9]秦荣,王涛,张永兵,涂远.压电智能梁振动主动控制分析的新方法[J].广西大学学报(自然科学版),2005,30(4):267~271
[10]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
[11] Gawronskiw. Balanced Control of Flexible Structures [M].Springer, 1996
[12] PreumentA, Elliot S J, Gardonia P. Responsive system for active vibration control [A].Proceeding of the NATO Advanced Study Institute[C], 2002
[13] S. O. R. Moheimani. Minimizing the out-of bandwidth dynamics in the model of reverberant system implication on spatial H∞control [J]. Automatica. 2000, 36:1023~1033
[14] Bailey T, Hubbard J E. Distributed piezoelectric-polymer active vibration control of a cantilever beam [J] AIAA Journal, 1985, 8(5):605~611
[15] Longman R.W. Actuator placement from degree of controllability criteria for regular slewing of flexible spacecraft [J]. ACTA.Astronautica, 1981, 8(7):703~718
[16] Harden A.M. Measure of modal controllability and observability for first and second order linear systems [J]. Control and Dynamics, 1989, 12(3):421~428
[17] Jae-Hung, Han and In, Lee, Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms [J]. Smart Materials and Structure, 1999, 8(2):257~267
[18] Maghami P.G., Joshi S.M. Sensor-actuator placement for flexible structures with actuatordynamics [J]. Control and Dynamics, 1993, 16(2):301~307
[19] Hongwei Zhang, Barry Lennox, Goulding, P. R. and Andrew, Leung, Y. T., A float encoded genetic algorithm technique for integrated optimization of piezoelectric actuator and sensor placement and feedback gains [J]. Smart Materials and Structure, 2000, 9:552~557
[20] Lee A.C., Chen S.T. Collocated sensor/actuator positioning and feedback design in the control of flexible structure system [J]. Transactions of ASME Journal of Vibration and Acoustics, 1994, 116:146~154
[21] Stieber M.E. Sensors/actuators and hygerstability of structures [J], AIAA, 1998, 88~4057
[22] Montgomery R.C., et al. Reliability considerations in the placement of control system components [J]. Control and Dynamics, 1985, 8(3):411~413
[23] Bayard D.S., Hadaegh F.Y., Meldrum D.R., Optimal Experiment Design for Identification of Large Space Structures [J]. Automatica, 1988, 24(3):357~364
[24]周刚,余跃庆,方道星,丁立.柔性机械臂振动压电抑振新方法[J].机械与电子,2007,(9):60~63
[25]吴振顺,肖原.零极点配置智能PID控制器在系统控制中的应用[J].哈尔滨工业大学学报,2008,40(1):54~57
[26]黄忠霖.控制系统MATLAB计算及仿真[M].北京:国防工业出版社,2004,424~440
[27]陈庆伟,郭健,王小华,胡维礼.基于状态反馈控制的柔性臂系统振动抑制[J].兵工学报,2006,27(1):184~187
[28] T.Cmanjunath. Multivariable control of a smart structure cantilever beam using fast output sampling feedback [J]. System identification and control problems SICPRO04, Mosocow, 2004,28~30
[29]唐凤,黄尚廉.机敏柔性梁的振动主动控制[J].应用力学学报,1999,16(1):131~136
[30]梅胜敏,陶宝棋.压电作动器用于振动主动控制技术的研究[J].航空学报,1997,18(1):100~103
[31]陈仁文,陶宝祺,陈勇.利用压电元件的空间挠性结构振动主动控制研究[J].数据采集与处理,1999,14(1):128~132
[32] Jessica M Yellin, Shen I Y.A self-sensing active constrained layer damping treatment for an Euler-Bernoulli beam [J]. Smart Mater Struct, 1996, 5:628~637
[33] Hossein Moini Concurrent design of a structure and its distributed piezoelectric actuators [J].Smart Mater.Struct, 1997, 6(2): 89~101
[34]吴大方,刘安成,麦汉超,房元鹏.压电智能柔性梁振动主动控制研究[J].北京航空航天大学学报,2004,30(2):160~163
[35]孙立宁,楚中毅,曲东升,崔晶.压电智能结构有限元动力模型及其振动主动控制的研究[J].高技术通讯,2004,12(11):120~125
[36]姚军,李岳锋,刘娟.压电薄板的建模和阻尼的准独立模态控制[J].航空学报,2000,21(2):159~163
[37]张付兴.压电陶瓷用于悬臂梁主动控制的仿真研究[J].中国力学学会学术大会,2005 (CCTAM2005)
[38]邱志成.压电智能挠性板的主动振动控制研究[J].压电与声光,2002,24(6):497~501
[39]王宗利,林启荣,刘正兴.压电智能梁的状态相关LQR振动控制[J].上海交通大学学报,2001,35(4):503~508
[40] S.Narayanana, V.Balamurugan. Finite element modeling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. Journal of Sound and Vibration, 2003, 262: 529~562
[41]常军,陈敏,刘正兴.基于能量准则的梁振动多模态主动控制的LQR法[J].固体力学学报,2004,25(4):423~429
[42]蒋建平,李东旭.压电复合梁高阶有限元模型与主动振动控制研究[J].动力学与控制学报,2007,5(2):141~146
[43]林嗣廉,徐博侯.柔性结构振动的独立模态H∞控制[J].浙江大学学报,2001,35(1):23~29
[44] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems [J]. Journal of Intelligent Material System &Structure, 2000, 11:311~323
[45]屈文忠,春安,孙进才,邱阳.宽带振动主动控制的模糊自适应控制方法[J].机械强度,2003,25(1):009~011
[46]徐亚兰,陈建军,谢永强,陈龙.几何非线性压电柔性板结构的模糊H∞振动控制[J].振动与冲击,2007,26(2):112~116
[47] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems [J]. Journal of Intelligent Material System & Structure, 2000, 11:311~323
[48]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[J].振动与冲击,1999,18(4):6~12
[49]任兴仑,童昕.压电智能梁振动控制的遗传算法优化设计[J].华侨大学学报(自然科学版),2002,23(1):81~86
[50] Chen C i.el al. Adaptive control using the modified independent modal space control [J]. J.of Intell.mater and struc. 1994, 5:550~558
[51] Yang S.M.eI a1.Vibration of smart structures by using neural networks transactions of the ASME [J]. J.of Dynamic Systems Measurement and Control. 1997, 119:34~39
[52]王玉辉.基于神经网络的悬臂梁振动主动控制研究[D].江苏:南京航空航天大学硕士学位论文,2005
[53] S.M.Yang and G.s.Lee. An Optimal Neural Network Design Method logy for Fast Convergence and Vibration Suppression [J]. J.of Intelligent Material Systems and Structure. 1998
[54] Ratneshwar, Jhan, Jacob, Rower. Experimental investigation of active vibration control using neural networks and piezoelectric actuators [J]. Smart Mater.Struct. 2002, 11:115~121
[55]张海峰.基于神经网络的压电智能结构控制方法的研究[D].陕西:西北工业大学硕士学位论文,2001
[56]陈传尧.智能结构及其在航空工业中的应用[R].航空工业部科技报告,1993
[57]陈永富.压电智能结构振动控制研究[D].陕西:西安建筑科技大学硕士学位论文,2004
[58]郝文化,肖新标.ANSYS7.0实例分析与应用[M].北京:清华大学出版社,2004,1~2
[59]王荣津.水声材料手册[M].北京:科学出版社,1983
[60] Saravanos D.A., Heyliger P.R. and Hopkins D.A., Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates [J]. J. Solid structure, 1997, 34: 359~378
[61] Bailey T., Hubbard J.E. Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam [J]. J. of Guidance, 1985, 8(5):605~611
[62]古渊,陈伟民,雷跃明等.压电减振机敏柔性板上的布片位置优化研究[J].压电与声光,1999,21(1):32~36
[63] Bayard D.S., Hadaegh F.Y., Meldrum D.R., Optimal Experiment Design for Identification of Large Space Structures [J]. Automatica, 1988, 24(3):357~364
[64]丁文镜.振动主动控制当前的主要研究课题[J].力学进展,1994,24(2):173~180
[65]王成亮.柔性板主动控制中压电元件的优化布置[D].江苏:南京航天航空大学硕士学位论文,2004
[66]黄忠霖.自动控制原理的MATLAB实现[M].北京:国防工业出版社,2007
[67]张静.MATLAB在控制系统中的应用[M].北京:电子工业出版社,2007
[68] Han Jae-Hung, Rew Keun-Ho, Lee In. An experimental study of active vibration control of composite structures with a piezo-ceramic actuator and a piezo-film sensor [J]. Smart Materials and Structures, 1997, 6(5):549~558
[69] Tzou, H.S. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameters system: A piezoelectric finite element approach [J]. Sound Vib, 1990, 138(1):17~34
[70]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005
[71]周克敏,Doyle J C, Glover K.鲁棒与最优控制[M].北京:国防工业出版社,2002
[72]彭程,王永.柔性梁降阶H∞控制实验研究[J].振动与冲击,2007,26(10):64~67
[73] Kneppova V, Kiffmeier U, Unbehauen. Weighting function selection in H∞-optimal control with application to a thyristor-driven DC-motor [C]. In the Proceedings of American Conference, Seattle, USA, 1995, 3002~3008
[74] Rabih Alkhatib, M. F. Golnaraghi. Active structural vibration control review [J]. The Shock and Vibration Digest. 2003, 35(5): 367~383
[75]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[J].工程力学,2006,23(5):20~23
[76] Andre preument, S. J. Elliot, P. Gardonia. Responsive system for active vibration control [J].Proceeding of the NATO Advanced Study Institute. 2002: 45~56
[77] S. O. R. Moheimani, M. Fu. Spatial H2 norms of flexible structures and its application in modelorder selection [J]. Proceedings of the 37th Conference on Decision and Control, 1998:3623~3624
[78] G. L. Bala. Control Design for variation in structural natural frequencies [J]. Journal of Guidance Control and Dynamics, 1995, 18(2): 325~332
[79] H. T. Banks, R. C. Smith, Y. Wang. Smart Material Structures: Modeling, Estimation and Control [M]. Paris, Wiley, 1996
[80] J. L. Fanson, C. C. Chu. Active member control of a precision structure with and H∞performance objective [J]. AIAA Dynamic Specialist Conference, 1990:322~333
[81] S. O. R. Moheimani. Minimizing the out of bandwidth dynamics in the model of reverberant system: Implication on Spatial H∞Control [J]. Automatica, 2000, 36:1023~1033
[2]宁淑荣.采用压电材料的振动主动控制[D].湖北:武汉科技大学硕士学位论文,2005
[3]王波.点式压电智能结构振动控制方法改进的研究[D].重庆:重庆大学博士学位论文,2004
[4]马治国,闻邦椿,颜云辉.智能结构的若干问题与进展[J].东北大学学报,1998,19(5):513~516
[5]骆英.正交异性压电复合材料功能元件的研究[D].江苏:南京航空航天大学博士学位论文,2000
[6]郑骥.基于改进遗传算法的主动柔性结构压电元件的位置优化[D].河北:河北工程大学硕士学位论文,2006
[7] E. F. Crawley, E. H. Anderson. Detailed modeling of piezoelectric actuation of beams [J].Proceeding of the 30th AIAA SDM Conference. 1989: 2000~2010
[8]殷学纲,李宾,李玉刚,黄尚廉.点式压电智能柔性板振动主动控制的建模与仿真[J].噪声与振动控制,1999,10(5):16~20
[9]秦荣,王涛,张永兵,涂远.压电智能梁振动主动控制分析的新方法[J].广西大学学报(自然科学版),2005,30(4):267~271
[10]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
[11] Gawronskiw. Balanced Control of Flexible Structures [M].Springer, 1996
[12] PreumentA, Elliot S J, Gardonia P. Responsive system for active vibration control [A].Proceeding of the NATO Advanced Study Institute[C], 2002
[13] S. O. R. Moheimani. Minimizing the out-of bandwidth dynamics in the model of reverberant system implication on spatial H∞control [J]. Automatica. 2000, 36:1023~1033
[14] Bailey T, Hubbard J E. Distributed piezoelectric-polymer active vibration control of a cantilever beam [J] AIAA Journal, 1985, 8(5):605~611
[15] Longman R.W. Actuator placement from degree of controllability criteria for regular slewing of flexible spacecraft [J]. ACTA.Astronautica, 1981, 8(7):703~718
[16] Harden A.M. Measure of modal controllability and observability for first and second order linear systems [J]. Control and Dynamics, 1989, 12(3):421~428
[17] Jae-Hung, Han and In, Lee, Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms [J]. Smart Materials and Structure, 1999, 8(2):257~267
[18] Maghami P.G., Joshi S.M. Sensor-actuator placement for flexible structures with actuatordynamics [J]. Control and Dynamics, 1993, 16(2):301~307
[19] Hongwei Zhang, Barry Lennox, Goulding, P. R. and Andrew, Leung, Y. T., A float encoded genetic algorithm technique for integrated optimization of piezoelectric actuator and sensor placement and feedback gains [J]. Smart Materials and Structure, 2000, 9:552~557
[20] Lee A.C., Chen S.T. Collocated sensor/actuator positioning and feedback design in the control of flexible structure system [J]. Transactions of ASME Journal of Vibration and Acoustics, 1994, 116:146~154
[21] Stieber M.E. Sensors/actuators and hygerstability of structures [J], AIAA, 1998, 88~4057
[22] Montgomery R.C., et al. Reliability considerations in the placement of control system components [J]. Control and Dynamics, 1985, 8(3):411~413
[23] Bayard D.S., Hadaegh F.Y., Meldrum D.R., Optimal Experiment Design for Identification of Large Space Structures [J]. Automatica, 1988, 24(3):357~364
[24]周刚,余跃庆,方道星,丁立.柔性机械臂振动压电抑振新方法[J].机械与电子,2007,(9):60~63
[25]吴振顺,肖原.零极点配置智能PID控制器在系统控制中的应用[J].哈尔滨工业大学学报,2008,40(1):54~57
[26]黄忠霖.控制系统MATLAB计算及仿真[M].北京:国防工业出版社,2004,424~440
[27]陈庆伟,郭健,王小华,胡维礼.基于状态反馈控制的柔性臂系统振动抑制[J].兵工学报,2006,27(1):184~187
[28] T.Cmanjunath. Multivariable control of a smart structure cantilever beam using fast output sampling feedback [J]. System identification and control problems SICPRO04, Mosocow, 2004,28~30
[29]唐凤,黄尚廉.机敏柔性梁的振动主动控制[J].应用力学学报,1999,16(1):131~136
[30]梅胜敏,陶宝棋.压电作动器用于振动主动控制技术的研究[J].航空学报,1997,18(1):100~103
[31]陈仁文,陶宝祺,陈勇.利用压电元件的空间挠性结构振动主动控制研究[J].数据采集与处理,1999,14(1):128~132
[32] Jessica M Yellin, Shen I Y.A self-sensing active constrained layer damping treatment for an Euler-Bernoulli beam [J]. Smart Mater Struct, 1996, 5:628~637
[33] Hossein Moini Concurrent design of a structure and its distributed piezoelectric actuators [J].Smart Mater.Struct, 1997, 6(2): 89~101
[34]吴大方,刘安成,麦汉超,房元鹏.压电智能柔性梁振动主动控制研究[J].北京航空航天大学学报,2004,30(2):160~163
[35]孙立宁,楚中毅,曲东升,崔晶.压电智能结构有限元动力模型及其振动主动控制的研究[J].高技术通讯,2004,12(11):120~125
[36]姚军,李岳锋,刘娟.压电薄板的建模和阻尼的准独立模态控制[J].航空学报,2000,21(2):159~163
[37]张付兴.压电陶瓷用于悬臂梁主动控制的仿真研究[J].中国力学学会学术大会,2005 (CCTAM2005)
[38]邱志成.压电智能挠性板的主动振动控制研究[J].压电与声光,2002,24(6):497~501
[39]王宗利,林启荣,刘正兴.压电智能梁的状态相关LQR振动控制[J].上海交通大学学报,2001,35(4):503~508
[40] S.Narayanana, V.Balamurugan. Finite element modeling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. Journal of Sound and Vibration, 2003, 262: 529~562
[41]常军,陈敏,刘正兴.基于能量准则的梁振动多模态主动控制的LQR法[J].固体力学学报,2004,25(4):423~429
[42]蒋建平,李东旭.压电复合梁高阶有限元模型与主动振动控制研究[J].动力学与控制学报,2007,5(2):141~146
[43]林嗣廉,徐博侯.柔性结构振动的独立模态H∞控制[J].浙江大学学报,2001,35(1):23~29
[44] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems [J]. Journal of Intelligent Material System &Structure, 2000, 11:311~323
[45]屈文忠,春安,孙进才,邱阳.宽带振动主动控制的模糊自适应控制方法[J].机械强度,2003,25(1):009~011
[46]徐亚兰,陈建军,谢永强,陈龙.几何非线性压电柔性板结构的模糊H∞振动控制[J].振动与冲击,2007,26(2):112~116
[47] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems [J]. Journal of Intelligent Material System & Structure, 2000, 11:311~323
[48]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[J].振动与冲击,1999,18(4):6~12
[49]任兴仑,童昕.压电智能梁振动控制的遗传算法优化设计[J].华侨大学学报(自然科学版),2002,23(1):81~86
[50] Chen C i.el al. Adaptive control using the modified independent modal space control [J]. J.of Intell.mater and struc. 1994, 5:550~558
[51] Yang S.M.eI a1.Vibration of smart structures by using neural networks transactions of the ASME [J]. J.of Dynamic Systems Measurement and Control. 1997, 119:34~39
[52]王玉辉.基于神经网络的悬臂梁振动主动控制研究[D].江苏:南京航空航天大学硕士学位论文,2005
[53] S.M.Yang and G.s.Lee. An Optimal Neural Network Design Method logy for Fast Convergence and Vibration Suppression [J]. J.of Intelligent Material Systems and Structure. 1998
[54] Ratneshwar, Jhan, Jacob, Rower. Experimental investigation of active vibration control using neural networks and piezoelectric actuators [J]. Smart Mater.Struct. 2002, 11:115~121
[55]张海峰.基于神经网络的压电智能结构控制方法的研究[D].陕西:西北工业大学硕士学位论文,2001
[56]陈传尧.智能结构及其在航空工业中的应用[R].航空工业部科技报告,1993
[57]陈永富.压电智能结构振动控制研究[D].陕西:西安建筑科技大学硕士学位论文,2004
[58]郝文化,肖新标.ANSYS7.0实例分析与应用[M].北京:清华大学出版社,2004,1~2
[59]王荣津.水声材料手册[M].北京:科学出版社,1983
[60] Saravanos D.A., Heyliger P.R. and Hopkins D.A., Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates [J]. J. Solid structure, 1997, 34: 359~378
[61] Bailey T., Hubbard J.E. Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam [J]. J. of Guidance, 1985, 8(5):605~611
[62]古渊,陈伟民,雷跃明等.压电减振机敏柔性板上的布片位置优化研究[J].压电与声光,1999,21(1):32~36
[63] Bayard D.S., Hadaegh F.Y., Meldrum D.R., Optimal Experiment Design for Identification of Large Space Structures [J]. Automatica, 1988, 24(3):357~364
[64]丁文镜.振动主动控制当前的主要研究课题[J].力学进展,1994,24(2):173~180
[65]王成亮.柔性板主动控制中压电元件的优化布置[D].江苏:南京航天航空大学硕士学位论文,2004
[66]黄忠霖.自动控制原理的MATLAB实现[M].北京:国防工业出版社,2007
[67]张静.MATLAB在控制系统中的应用[M].北京:电子工业出版社,2007
[68] Han Jae-Hung, Rew Keun-Ho, Lee In. An experimental study of active vibration control of composite structures with a piezo-ceramic actuator and a piezo-film sensor [J]. Smart Materials and Structures, 1997, 6(5):549~558
[69] Tzou, H.S. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameters system: A piezoelectric finite element approach [J]. Sound Vib, 1990, 138(1):17~34
[70]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005
[71]周克敏,Doyle J C, Glover K.鲁棒与最优控制[M].北京:国防工业出版社,2002
[72]彭程,王永.柔性梁降阶H∞控制实验研究[J].振动与冲击,2007,26(10):64~67
[73] Kneppova V, Kiffmeier U, Unbehauen. Weighting function selection in H∞-optimal control with application to a thyristor-driven DC-motor [C]. In the Proceedings of American Conference, Seattle, USA, 1995, 3002~3008
[74] Rabih Alkhatib, M. F. Golnaraghi. Active structural vibration control review [J]. The Shock and Vibration Digest. 2003, 35(5): 367~383
[75]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[J].工程力学,2006,23(5):20~23
[76] Andre preument, S. J. Elliot, P. Gardonia. Responsive system for active vibration control [J].Proceeding of the NATO Advanced Study Institute. 2002: 45~56
[77] S. O. R. Moheimani, M. Fu. Spatial H2 norms of flexible structures and its application in modelorder selection [J]. Proceedings of the 37th Conference on Decision and Control, 1998:3623~3624
[78] G. L. Bala. Control Design for variation in structural natural frequencies [J]. Journal of Guidance Control and Dynamics, 1995, 18(2): 325~332
[79] H. T. Banks, R. C. Smith, Y. Wang. Smart Material Structures: Modeling, Estimation and Control [M]. Paris, Wiley, 1996
[80] J. L. Fanson, C. C. Chu. Active member control of a precision structure with and H∞performance objective [J]. AIAA Dynamic Specialist Conference, 1990:322~333
[81] S. O. R. Moheimani. Minimizing the out of bandwidth dynamics in the model of reverberant system: Implication on Spatial H∞Control [J]. Automatica, 2000, 36:1023~1033