一种压电智能结构的颤振主动控制研究
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摘要
压电智能结构的气动弹性主动控制是当前国际上气动弹性领域内的研究热点之一。本文以压电智能复合材料盒型机翼为研究对象,对气动弹性主动控制系统的结构特性以及开闭环颤振特性进行了较为深入地分析。
对压电智能复合材料盒型机翼结构,按照经典层合板理论,采用20个位移自由度和8个电自由度的四边形板单元,利用Hamilton变分原理,详细推导了压电智能复合材料盒型机翼的有限元运动方程,并通过算例验证本文有限元程序是可行的。
利用偶极格子网法计算空气动力影响系数矩阵,利用子空间法将空气动力影响系数矩阵拟合成时域有理函数形式,建立了压电智能复合材料盒型机翼的状态空间颤振方程。依次利用模态截断法、最小实现、平衡降阶法对系统方程进行了降阶处理。
以提高颤振速度为目标,利用H∞控制理论对于降阶后的系统方程求解出能抑制外界干扰力的动态输出反馈控制器,并与降阶后的状态空间方程相结合,形成闭环控制系统。
最后,对建立单输入单输出系统和多输入多输出系统模型等多种情况进行了理论分析。讨论了压电片的放置位置对颤振速度的影响。计算结果表明,通过主动控制律的实施,达到了颤振主动抑制的目的。
Active aeroelastic control of piezoelectric smart structure is one of the hotspot in the field of aeroelasticity. The main task of this paper is to study the flutter characteristics of piezoelectric smart box wing. The flutter characteristics of open-loop and close-loop as well as structure characteristics of active aeroelastic control system are deeply analyzed.
Based on the classical laminate theory, the quadrilateral plate element which contains 20 displacement DOF and 8 electrical DOF is used to study the structure of piezoelectric smart composite box wing. This paper also deduces the finite element equations of piezoelectric smart box wing via Hamilton principle and an example is presented to demonstrate the validity of the finite element program.
The aerodynamic influence coefficient (AIC) matrice is calculated by using the Doublet Lattice Method and approximated as a rational function in time domain by using the new state-space method. The state space equations of the aeroservoelastic system are formulated and the reduction of system equations uses the following process in turn: Model truncation, Minimal realization and Balancing reduction.
To increase the flutter speed, H∞-control theory is used to design dynamic output feedback controller which can suppress the disturbance for the reduced system, and the close-loop system is formed by integrating the controller with the reduced system.
At last, a single input/single ouput model and a multi input/multi output model of close-loop system are analyzed respectively. The influences of the location of piezoelectric material on the flutter speed are simply discussed. The results indicate that the flutter can be suppressed through active aeroelastic control law design.
对压电智能复合材料盒型机翼结构,按照经典层合板理论,采用20个位移自由度和8个电自由度的四边形板单元,利用Hamilton变分原理,详细推导了压电智能复合材料盒型机翼的有限元运动方程,并通过算例验证本文有限元程序是可行的。
利用偶极格子网法计算空气动力影响系数矩阵,利用子空间法将空气动力影响系数矩阵拟合成时域有理函数形式,建立了压电智能复合材料盒型机翼的状态空间颤振方程。依次利用模态截断法、最小实现、平衡降阶法对系统方程进行了降阶处理。
以提高颤振速度为目标,利用H∞控制理论对于降阶后的系统方程求解出能抑制外界干扰力的动态输出反馈控制器,并与降阶后的状态空间方程相结合,形成闭环控制系统。
最后,对建立单输入单输出系统和多输入多输出系统模型等多种情况进行了理论分析。讨论了压电片的放置位置对颤振速度的影响。计算结果表明,通过主动控制律的实施,达到了颤振主动抑制的目的。
Active aeroelastic control of piezoelectric smart structure is one of the hotspot in the field of aeroelasticity. The main task of this paper is to study the flutter characteristics of piezoelectric smart box wing. The flutter characteristics of open-loop and close-loop as well as structure characteristics of active aeroelastic control system are deeply analyzed.
Based on the classical laminate theory, the quadrilateral plate element which contains 20 displacement DOF and 8 electrical DOF is used to study the structure of piezoelectric smart composite box wing. This paper also deduces the finite element equations of piezoelectric smart box wing via Hamilton principle and an example is presented to demonstrate the validity of the finite element program.
The aerodynamic influence coefficient (AIC) matrice is calculated by using the Doublet Lattice Method and approximated as a rational function in time domain by using the new state-space method. The state space equations of the aeroservoelastic system are formulated and the reduction of system equations uses the following process in turn: Model truncation, Minimal realization and Balancing reduction.
To increase the flutter speed, H∞-control theory is used to design dynamic output feedback controller which can suppress the disturbance for the reduced system, and the close-loop system is formed by integrating the controller with the reduced system.
At last, a single input/single ouput model and a multi input/multi output model of close-loop system are analyzed respectively. The influences of the location of piezoelectric material on the flutter speed are simply discussed. The results indicate that the flutter can be suppressed through active aeroelastic control law design.
引文
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[25]张妃二,娆立宁,复合材料层合板智能结构主动振动控制的边界元法,振动与冲击,2003,22(1):40-43。
[26]钱振东,黄卫,朱德懋,主动减振板的数值分析,工程力学,2000,17(2):58-65。
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[31]Changho Nam,Youndan Kim and Jeffrey B.Layton,Active Aeroelastic Wing Design for Gust Load Alleviation and Flutter Suppression,AIAA-97-1265.
[32]Zhou R.C., Mei C. And Huang J.K., Suppression of nonlinear panel flutter at supersonic speeds and elevated temperature, AIAA Journal, 1996, 34(2): 347-354.
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[34]S.Raja,A.A.Pashilkar, R.Sreedeep, J.V.Kamesh, Flutter control of a composite plate with Piezoelectric multilayered actuatiors,Aerospace Science and Technology 2006,10:435-411.
[35]Seong Hwan Moon,Joon Seok Hwang,Panel flutter suppression with an optimal controller based on the the nonlinear model using piezoelectric materials,Composite Structures ,2005,68:371-379.
[36]I.K. Oh, I,Lee,Supersonic flutter suppression of piezolaminated cylindrical panels based on multifield layerwise theory,Journal of sound and Vibration ,2006,291:1186-1201.
[37]Ratneshwar Jha and Aditi Chattopadhyay,Smart composite wing design for optimal aeroelastic control,AIAA-99-1514.
[38]Seong Hwan Moon,Finite element analysis and design of control system with feedback output using piezoelectric sensor/actuator for panel flutter suppression,Finite Elements in Analysis and Design 2006,42:1071-1078.
[39]Jae-Hung Han,Junji Tani,Jinhao Qiu,Active flutter suppression of a lifting surface using piezoelectric actuation and modern control theory,Journal of Sound and Vibration ,2006,291: 706-722.
[40]Doyle J.Glove K.Khargonekar P.State-space solution to standard H∞control problem,IEEE Transaction on Automatic Control,1989,34(8):831-842.
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[43]谢石林,张景绘,H∞方法在振动主动鲁棒控制中的应用,机械强度,1998,20(4):284-289。
[44]徐亚兰,陈建军等,具有极点约束的不确定压电柔性结构鲁棒H∞振动控制,应用基础与工程科学学报,2007,15(3):332-341。
[45]谢光华,曾庆福,基于LMI的航空发动机鲁棒H∞控制器设计,航空学报,2000,21(2):175-178。
[46]李普,孙庆鸿,陈南,振动系统复合摄动的鲁棒H∞控制,振动工程学报,2001,14(1):118-121。
[47]于明礼,文浩,胡海岩,二维翼段颤振的H∞控制,振动工程学报,2006,19(3):326-330。
[48]马清亮,胡昌华,基于参数相关Lyapunov函数的鲁棒H 2 /H∞控制,系统仿真学报,2007,19(10):2244-2247。
[49]夸克工作室,有限元分析基础篇ANSYS与Mathematica,北京,清华大学出版社,2002。
[50]舒小平,复合材料板壳理论及其应用,徐州,中国矿业大学出版社,2004。
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[60]王小兵,压电智能板结构的H∞振动控制,[硕士学位论文],西安,西安电子科技大学,2004。
[2]陶宝祺,智能材料结构,北京:国防工业出版社,1997。
[3]吴克恭,埋入压电材料的智能复合材料结构振动主动控制理论和实验研究,[博士学位论文] ,西安,西北工业大学,2003。
[4]钱振东,压电耦合板主动减振技术研究,[博士学位论文] ,南京,南京航空航天大学,1998。
[5] Tzou,H.S,Fu,H.Q.,A Study on Segmentation of Distributed Piezoelectric Sensors and Actuators:Part I-Theoretical Analysis,Journal of Sound and Vibration, 1994,172(2):247-260.
[6] Ha S.K.,Keilers C.,Chang F.K.,Finite Element Analysis of Composite Structures Containing Distributed Piezoceramic Sensors and Actuators,AIAA Journal , 1992,30(3):772-780.
[7] Hwang W.S.,Park H.C.,Finite Element Modeling of Piezoelectric Sensors and Actuators,AIAA , 1993,31(5):930-937.
[8] Lee J.S,Jiang L.Z.,Exact electroelastic analysis of piezoelectric laminate via state space approach,Int J of Solid and Structures,1996,33(7):977-990.
[9] Brooks S,Heyliger P,Static behavior of piezoelectric laminates with distuributed and patched actuators,J of intelligent Material Systems and Structures,1994,5:635-646.
[10]Batra RC,Liang XQ,The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators,Computer & Structures,1997,63:203-216.
[11]A.Chattopadhyay,H.Gu,Q.Liu,Modeling of smart composite box beams with nonlinear induced strain,Composites,1999, Part B 30:603-612.
[12]Mira Mitra,S.Gopalakrishnan,M.Seetharama Bhat,A new super convergent thin walled composite beam element for analysis of box beam structures,International Journal of Solids and Structures 2004,41:1491-1518.
[13]吕胜利,吕国志,压电控制层合梁的振动分析,振动与冲击,1997,16(1):20-23。
[14]闫云聚,姜节胜,袁振宇,复合材料层合板振动衰减主动控制力学模型,振动与冲击,1997,16(4): 54-59。
[15]曹宗杰,闻邦椿,陈塑寰,含压电材料智能结构动态特性的研究,计算力学学报,2001,18(3):267-272。
[16]金江,陶宝祺,压电自适应层合板的有限元法分析,南京航空航天大学学报,1997,29(2):196-201。
[17]尹林,王晓明,沈亚鹏,用压电元件实现复合材料层合板振动控制的数值分析,振动工程学报,1996,9(2):107-115。
[18]姚林泉,俞焕然,具有压电材料薄板弯曲控制的有限元法,计算力学学报,1999,16(3):330-333。
[19]高坚新,沈亚鹏,王子昆,有限长压电层合简支板自由振动的三维精确解,力学学报,1998,30(2):167-176。
[20]贾建援,王卫东等,压电致动式圆片驱动装置结构分析与设计,西安电子科技大学学报,2003,30(1):42-46。
[21]Bailey T. , Hubbard Jr. E. , Distributed Piezoelectric-Polymer Active Vibration Control of a cantilever Beam,J. Guidance,control and control,1985, 8(5):605-611.
[22]John J.M. ,Gareth J.K., The Multimodal Damping of Piezo-coupled Plate Structures, AIAA,97,13(6):1352-1360.
[23]Maghami PG, Juang J-N.Efficient eigenvalue assignment for large space structures. Journal of Guidance, Control, and Dynamics, 1990, 13(6): 1033-1039.
[24]梅胜敏,陶宝祺,压电作动器用于振动主动控制技术研究,航空学报,1997,18(1):125:132。
[25]张妃二,娆立宁,复合材料层合板智能结构主动振动控制的边界元法,振动与冲击,2003,22(1):40-43。
[26]钱振东,黄卫,朱德懋,主动减振板的数值分析,工程力学,2000,17(2):58-65。
[27]钱振东,朱德懋,陈国平等,压电耦合板主动控制及稳定性分析,振动与冲击,2000,19(1):1-4。
[28]蔡炜,李由青,杨耀文等,压电层合板结构振动控制的有限元法,固体力学学报,1998,19(1):45-32。
[29]P.Hajela,Application of Piezoelectric Element in Supersonic Panel Flutter Suppression,AIAA-91-3191.
[30]Scott R.C.,Controlling Panel Flutter Using Adaptive Materials, AIAA-91-1067-CP.
[31]Changho Nam,Youndan Kim and Jeffrey B.Layton,Active Aeroelastic Wing Design for Gust Load Alleviation and Flutter Suppression,AIAA-97-1265.
[32]Zhou R.C., Mei C. And Huang J.K., Suppression of nonlinear panel flutter at supersonic speeds and elevated temperature, AIAA Journal, 1996, 34(2): 347-354.
[33]Jennifer Heeg,Analytical and Experimental Investigation of Flutter Suppression by Piezoelectric Actuation ,NASA Technical Paper 3241,Feb,1993.
[34]S.Raja,A.A.Pashilkar, R.Sreedeep, J.V.Kamesh, Flutter control of a composite plate with Piezoelectric multilayered actuatiors,Aerospace Science and Technology 2006,10:435-411.
[35]Seong Hwan Moon,Joon Seok Hwang,Panel flutter suppression with an optimal controller based on the the nonlinear model using piezoelectric materials,Composite Structures ,2005,68:371-379.
[36]I.K. Oh, I,Lee,Supersonic flutter suppression of piezolaminated cylindrical panels based on multifield layerwise theory,Journal of sound and Vibration ,2006,291:1186-1201.
[37]Ratneshwar Jha and Aditi Chattopadhyay,Smart composite wing design for optimal aeroelastic control,AIAA-99-1514.
[38]Seong Hwan Moon,Finite element analysis and design of control system with feedback output using piezoelectric sensor/actuator for panel flutter suppression,Finite Elements in Analysis and Design 2006,42:1071-1078.
[39]Jae-Hung Han,Junji Tani,Jinhao Qiu,Active flutter suppression of a lifting surface using piezoelectric actuation and modern control theory,Journal of Sound and Vibration ,2006,291: 706-722.
[40]Doyle J.Glove K.Khargonekar P.State-space solution to standard H∞control problem,IEEE Transaction on Automatic Control,1989,34(8):831-842.
[41]吴敏,桂卫华,何勇,现代鲁棒控制,长沙,中南大学出版社,2006。
[42]毛维杰,孙优贤,不确定线性系统的输出反馈鲁棒H∞控制,信息与控制,1997,26(3):174-180。
[43]谢石林,张景绘,H∞方法在振动主动鲁棒控制中的应用,机械强度,1998,20(4):284-289。
[44]徐亚兰,陈建军等,具有极点约束的不确定压电柔性结构鲁棒H∞振动控制,应用基础与工程科学学报,2007,15(3):332-341。
[45]谢光华,曾庆福,基于LMI的航空发动机鲁棒H∞控制器设计,航空学报,2000,21(2):175-178。
[46]李普,孙庆鸿,陈南,振动系统复合摄动的鲁棒H∞控制,振动工程学报,2001,14(1):118-121。
[47]于明礼,文浩,胡海岩,二维翼段颤振的H∞控制,振动工程学报,2006,19(3):326-330。
[48]马清亮,胡昌华,基于参数相关Lyapunov函数的鲁棒H 2 /H∞控制,系统仿真学报,2007,19(10):2244-2247。
[49]夸克工作室,有限元分析基础篇ANSYS与Mathematica,北京,清华大学出版社,2002。
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