压电叠层作动器驱动的直升机结构响应自适应控制
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摘要
直升机的高振动水平会严重影响直升机的飞行性能和飞行安全，降低直升机振动水平一直是直升机技术领域期待解决的难题。结构响应主动控制具有控制效果好、适应性强等优点，已成为直升机振动控制的最重要发展方向。直升机结构响应主动控制的核心是准确的机体结构/作动器耦合动力学模型、高性能的控制器和作动器，要求控制器具有快速、自适应的控制能力，要求作动器质量轻、输出力大、工作频带宽、响应速度快。本文根据直升机机身振动的稳态谐波特性、压电叠层作动器的驱动特性及直升机振动主动控制要求，深入研究了压电叠层作动器驱动的直升机结构响应自适应控制，有效克服了现有直升机振动主动控制中采用惯性作动器及由于控制器性能差所带来的附加重量大、工作频带窄、控制速度慢、适应性差等缺点，为有效提高振动主动控制系统的性能、有效降低直升机振动水平建立了新的直升机结构响应自适应控制方法。本文研究取得的创新点主要有以下四个方面：
（1）建立了直升机结构响应主动控制的机身/压电叠层作动器复合结构的耦合优化法，研究了压电叠层作动器安装对机身结构特性的影响，为直升机振动主动控制中建立准确的机体结构/作动器耦合动力学模型奠定了理论基础。通过建立直升机机身/压电叠层作动器复合结构的耦合频域方程及改进实数编码遗传算法，实现了同时优化作动器安装位置离散变量和控制器加权参数连续变量的混合优化，得到了在控制输入约束下的最有效振动控制。该耦合优化法与目前国际上把压电叠层作动器理想成力发生器的方法相比，得到的优化结果具有更好的振动控制效果。
（2）建立了直升机结构响应自适应控制的谐波同步识别-修正法，克服了现有直升机结构响应主动控制的频域法中信号时/频转换采用离散傅里叶变换及其逆变换所带来的缺点，为直升机振动主动控制系统中构建高性能的控制器奠定了理论基础。采用递推最小二乘算法和基于最陡梯度法的自适应谐波控制，实现了直升机结构响应自适应控制中控制误差响应谐波系数识别与控制输入谐波系数同步修正。基于作动器安装位置和控制器参数的优化结果，采用稳态谐波激励及幅值快速周期时变谐波激励研究了压电叠层作动器驱动的机身弹性线梁模型的多输入/多输出结构响应自适应控制，结果表明建立的直升机结构响应自适应控制的谐波同步识别-修正法能有效降低直升机的振动水平，且具有较强的自适应控制能力。
（3）把建立的直升机结构响应自适应控制的谐波同步识别-修正法用于控制器，建立了具有自适应控制能力的结构响应控制实验系统。把直升机机身结构模拟为自由-自由弹性梁，采用压电叠层作动器驱动梁模型，以控制点的加速度响应为控制目标，对由激振器模拟旋翼激励梁模型产生的稳态谐波振动和实测的某直升机机身振动进行了自适应控制的理论和实验研究，结果表明具有由谐波同步识别-修正法的控制器和由压电叠层作动器驱动的结构响应自适应控制系统能有效降低结构的振动水平，且具有较强的自适应控制能力。
（4）建立了结构响应自适应控制中压电叠层作动器迟滞非线性的谐波输入补偿法，解决了压电叠层作动器迟滞非线性对结构振动控制的影响问题，为直升机振动主动控制系统中构建高性能的作动器奠定了理论基础。基于控制通道传递函数矩阵的下三角特性，对单频、多频振动控制证明了压电叠层作动器驱动的振动自适应控制系统的收敛性并给出了收敛条件，并证明了在存在压电叠层作动器的迟滞非线性时，线性谐波控制与线性控制通道具有相同的收敛性质。通过对压电叠层作动器迟滞非线性影响的理论与实验研究，表明了该谐波输入补偿法的有效性。
The high vibration levels of helicopter will seriously affect the flight performanceand the flight safety of helicopter. To effectively reduce the vibration levels of helicopterhas been the difficult problem in the field of helicopter technology which has beenexpected to solve. Active control of structural response has the advantages such as thegood control effect and strong adaptability etc., and has become the most importantdevelopment direction in helicopter vibration control. The cores of active control ofhelicopter structural response are the accurate fuselage structure/actuator couplingdynamic model, high-performance controller and actuator, requiring the controller hasthe rapid and adaptive control ability, actuator has light weight, large output force, wideworking frequency range and fast response speed. Based on the steady harmoniccharacteristics of helicopter fuselage vibration, the driving characteristics of piezoelectricstack actuators and the requirements of active vibration control of helicopter, the adaptivecontrol of helicopter structural response driven by piezoelectric stack actuators has beendeeply investigated in this thesis, and has effectively overcome the shortcomings such asthe large additional weight, the narrow range of working frequency, slow speed of control,poor adaptability etc. brought by using the inertial actuator and the controller with poorperformance in the existing active vibration control of helicopter, establishing a newmethod for adaptive control of helicopter structural response to effectively improve theperformance of active vibration control system and to effectively reduce the vibrationlevels of helicopter. This investigation has made major innovation of the following fourareas:
(1) A coupling optimization method of fuselage/piezoelectric stack actuatorscomposite structure for active control of helicopter structural response has beenestablished, to solve the effect problems of installation of piezoelectric stack actuators onthe structural characteristics of fuselage and to lay a theoretical foundation forestablishing an accurate dynamic model of fuselage structure/actuators couplingstructure in the active vibration control of helicopter. Through the establishment of thecoupling frequency-domain equations of helicopter fuselage/piezoelectric stack actuators coupled composite structure and improvement of real-coded genetic algorithm,the hybrid optimization of simultaneously optimizing the discrete variables of theactuator installed positions and the continuous variables of the weighted parameters ofcontroller was achieved and the most effective vibration control was obtained in theconstraints of control input. Comparing with the current method in the world which thepiezoelectric stack actuator was idealized as a force generator, the coupling optimizationmethod can obtain the optimal results with better vibration control effect.
(2) A harmonic synchronous identification-updating method for adaptive control ofhelicopter structural response has been established, to overcome the drawbacks broughtby using the discrete Fourier transform and its inverse transform for time/frequencyconversion of signals in the existing frequency-domain method in the active control ofhelicopter structural response, and lay a theoretical foundation for building thehigh-performance controller in the active vibration control system of helicopter. Usingthe recursive least squares algorithm and the steepest gradient method based adaptiveharmonic control, the identification of control error response harmonic coefficients andsynchronous updating of control input harmonic coefficients in the adaptive control ofhelicopter structural response were achieved. Based on the optimization results ofactuator installed positions and the parameters of controller, the adaptive control ofmultiple input/multiple output responses of a fuselage elastic beam model driven bypiezoelectric stack actuators by using the steady harmonic excitation and the harmonicexcitation with fast cycle time-varying amplitude has been investigated. The resultsindicated that the established harmonic synchronous identification-updating method foradaptive control of helicopter structural response could effectively reduce the vibrationlevels of helicopter, and had strong adaptive control ability.
(3) An experimental control system of structural response with adaptive controlability has been set up by using the established harmonic synchronousidentification-updating method in the controller for adaptive control of helicopterstructural response. The helicopter fuselage structure was simulated a free-free elasticbeam. Using piezoelectric stack actuators to drive the beam model, taking theacceleration responses at the control points as the control objectives, the theoretical andexperimental investigations on adaptive control of the steady harmonic vibrationgenerated by the exciter simulating rotor to excite the beam and the vibration measured in a helicopter fuselage have been carried out. The results indicated that the system ofadaptive control of structural response with the controller made by the harmonicsynchronous identification-updating method and driven by piezoelectric stack actuatorscould effectively reduce the vibration level of structure, and had strong adaptive controlability.
(4) A harmonic input compensation method for the hysteresis nonlinearity ofpiezoelectric stack actuator in adaptive control of structural response has been established,to solve the effect of hysteresis nonlinearity of piezoelectric stack actuator on thevibration control of structure, and to lay a theoretical foundation for building thehigh-performance actuator in the system of active vibration control of helicopter. Basedon the lower triangular characteristics of transfer function matrix of control channel, forthe single-frequency, multi-frequency vibration control, the convergence of adaptivevibration control system driven by piezoelectric stack actuator was proved and theconvergence conditions were given, and it was proved that in the presence of hysteresisnonlinearity of piezoelectric stack actuator, the linear harmonic control and the linearcontrol channel have the same convergence properties. The theoretical and experimentalstudies on the effect of hysteresis nonlinearity of piezoelectric stack actuator verified theeffectiveness of the harmonic input compensation method.
（1）建立了直升机结构响应主动控制的机身/压电叠层作动器复合结构的耦合优化法，研究了压电叠层作动器安装对机身结构特性的影响，为直升机振动主动控制中建立准确的机体结构/作动器耦合动力学模型奠定了理论基础。通过建立直升机机身/压电叠层作动器复合结构的耦合频域方程及改进实数编码遗传算法，实现了同时优化作动器安装位置离散变量和控制器加权参数连续变量的混合优化，得到了在控制输入约束下的最有效振动控制。该耦合优化法与目前国际上把压电叠层作动器理想成力发生器的方法相比，得到的优化结果具有更好的振动控制效果。
（2）建立了直升机结构响应自适应控制的谐波同步识别-修正法，克服了现有直升机结构响应主动控制的频域法中信号时/频转换采用离散傅里叶变换及其逆变换所带来的缺点，为直升机振动主动控制系统中构建高性能的控制器奠定了理论基础。采用递推最小二乘算法和基于最陡梯度法的自适应谐波控制，实现了直升机结构响应自适应控制中控制误差响应谐波系数识别与控制输入谐波系数同步修正。基于作动器安装位置和控制器参数的优化结果，采用稳态谐波激励及幅值快速周期时变谐波激励研究了压电叠层作动器驱动的机身弹性线梁模型的多输入/多输出结构响应自适应控制，结果表明建立的直升机结构响应自适应控制的谐波同步识别-修正法能有效降低直升机的振动水平，且具有较强的自适应控制能力。
（3）把建立的直升机结构响应自适应控制的谐波同步识别-修正法用于控制器，建立了具有自适应控制能力的结构响应控制实验系统。把直升机机身结构模拟为自由-自由弹性梁，采用压电叠层作动器驱动梁模型，以控制点的加速度响应为控制目标，对由激振器模拟旋翼激励梁模型产生的稳态谐波振动和实测的某直升机机身振动进行了自适应控制的理论和实验研究，结果表明具有由谐波同步识别-修正法的控制器和由压电叠层作动器驱动的结构响应自适应控制系统能有效降低结构的振动水平，且具有较强的自适应控制能力。
（4）建立了结构响应自适应控制中压电叠层作动器迟滞非线性的谐波输入补偿法，解决了压电叠层作动器迟滞非线性对结构振动控制的影响问题，为直升机振动主动控制系统中构建高性能的作动器奠定了理论基础。基于控制通道传递函数矩阵的下三角特性，对单频、多频振动控制证明了压电叠层作动器驱动的振动自适应控制系统的收敛性并给出了收敛条件，并证明了在存在压电叠层作动器的迟滞非线性时，线性谐波控制与线性控制通道具有相同的收敛性质。通过对压电叠层作动器迟滞非线性影响的理论与实验研究，表明了该谐波输入补偿法的有效性。
The high vibration levels of helicopter will seriously affect the flight performanceand the flight safety of helicopter. To effectively reduce the vibration levels of helicopterhas been the difficult problem in the field of helicopter technology which has beenexpected to solve. Active control of structural response has the advantages such as thegood control effect and strong adaptability etc., and has become the most importantdevelopment direction in helicopter vibration control. The cores of active control ofhelicopter structural response are the accurate fuselage structure/actuator couplingdynamic model, high-performance controller and actuator, requiring the controller hasthe rapid and adaptive control ability, actuator has light weight, large output force, wideworking frequency range and fast response speed. Based on the steady harmoniccharacteristics of helicopter fuselage vibration, the driving characteristics of piezoelectricstack actuators and the requirements of active vibration control of helicopter, the adaptivecontrol of helicopter structural response driven by piezoelectric stack actuators has beendeeply investigated in this thesis, and has effectively overcome the shortcomings such asthe large additional weight, the narrow range of working frequency, slow speed of control,poor adaptability etc. brought by using the inertial actuator and the controller with poorperformance in the existing active vibration control of helicopter, establishing a newmethod for adaptive control of helicopter structural response to effectively improve theperformance of active vibration control system and to effectively reduce the vibrationlevels of helicopter. This investigation has made major innovation of the following fourareas:
(1) A coupling optimization method of fuselage/piezoelectric stack actuatorscomposite structure for active control of helicopter structural response has beenestablished, to solve the effect problems of installation of piezoelectric stack actuators onthe structural characteristics of fuselage and to lay a theoretical foundation forestablishing an accurate dynamic model of fuselage structure/actuators couplingstructure in the active vibration control of helicopter. Through the establishment of thecoupling frequency-domain equations of helicopter fuselage/piezoelectric stack actuators coupled composite structure and improvement of real-coded genetic algorithm,the hybrid optimization of simultaneously optimizing the discrete variables of theactuator installed positions and the continuous variables of the weighted parameters ofcontroller was achieved and the most effective vibration control was obtained in theconstraints of control input. Comparing with the current method in the world which thepiezoelectric stack actuator was idealized as a force generator, the coupling optimizationmethod can obtain the optimal results with better vibration control effect.
(2) A harmonic synchronous identification-updating method for adaptive control ofhelicopter structural response has been established, to overcome the drawbacks broughtby using the discrete Fourier transform and its inverse transform for time/frequencyconversion of signals in the existing frequency-domain method in the active control ofhelicopter structural response, and lay a theoretical foundation for building thehigh-performance controller in the active vibration control system of helicopter. Usingthe recursive least squares algorithm and the steepest gradient method based adaptiveharmonic control, the identification of control error response harmonic coefficients andsynchronous updating of control input harmonic coefficients in the adaptive control ofhelicopter structural response were achieved. Based on the optimization results ofactuator installed positions and the parameters of controller, the adaptive control ofmultiple input/multiple output responses of a fuselage elastic beam model driven bypiezoelectric stack actuators by using the steady harmonic excitation and the harmonicexcitation with fast cycle time-varying amplitude has been investigated. The resultsindicated that the established harmonic synchronous identification-updating method foradaptive control of helicopter structural response could effectively reduce the vibrationlevels of helicopter, and had strong adaptive control ability.
(3) An experimental control system of structural response with adaptive controlability has been set up by using the established harmonic synchronousidentification-updating method in the controller for adaptive control of helicopterstructural response. The helicopter fuselage structure was simulated a free-free elasticbeam. Using piezoelectric stack actuators to drive the beam model, taking theacceleration responses at the control points as the control objectives, the theoretical andexperimental investigations on adaptive control of the steady harmonic vibrationgenerated by the exciter simulating rotor to excite the beam and the vibration measured in a helicopter fuselage have been carried out. The results indicated that the system ofadaptive control of structural response with the controller made by the harmonicsynchronous identification-updating method and driven by piezoelectric stack actuatorscould effectively reduce the vibration level of structure, and had strong adaptive controlability.
(4) A harmonic input compensation method for the hysteresis nonlinearity ofpiezoelectric stack actuator in adaptive control of structural response has been established,to solve the effect of hysteresis nonlinearity of piezoelectric stack actuator on thevibration control of structure, and to lay a theoretical foundation for building thehigh-performance actuator in the system of active vibration control of helicopter. Basedon the lower triangular characteristics of transfer function matrix of control channel, forthe single-frequency, multi-frequency vibration control, the convergence of adaptivevibration control system driven by piezoelectric stack actuator was proved and theconvergence conditions were given, and it was proved that in the presence of hysteresisnonlinearity of piezoelectric stack actuator, the linear harmonic control and the linearcontrol channel have the same convergence properties. The theoretical and experimentalstudies on the effect of hysteresis nonlinearity of piezoelectric stack actuator verified theeffectiveness of the harmonic input compensation method.
引文
[1]张阿舟,姚起航.振动控制工程.北京:航空工业出版社,1989.
[2] Ver I L, Beranek I I. Noise and vibration control engineering: principles and application. HobokenN.J.: John Wiley&Sons,2006.
[3] Leoni R D. Black hawk: the story of a world class helicopter. Reston VA: AIAA,2007.
[4] Pearson J T, Goodall R M, Lyndon I. Active control of helicopter vibration. Computing&ControlEngineering Journal,1994,5(6):277-284.
[5] Johnson W. Helicopter theory. New York: Dover Publications, Inc.,1994.
[6] Loewy R G, Helicopter vibrations: a technological perspective. Journal of the American HelicopterSociety,1984,29(4):4-30.
[7] Crews S T. Rotorcraft vibration criteria: a new perspective. Proceedings of the43rdAnnual Forumof the American Helicopter Society, Alexandria, VA,1987.
[8] EU: Directive2002/44/EC of the European parliament and of the council. Physical Agents(Vibration), published in the Official Journal of the European Communities (L177vol45) of July6,2002.
[9] Ellis C W, Jones R. Application of an absorber to reduce helicopter vibration levels. Journal of theAmerican Helicopter Society,1963,8(3):30-42.
[10] Amer K B, Neff J R. Vertical-plane pendulum absorbers for minimizing helicopter vibratoryloads. Journal of the American Helicopter Society,1974,19(4):44-48.
[11] Miao W L, Mouzakis T. Nonlinear dynamic characteristics of rotor bifilar absorber. Proceedingsof the37thAnnual Forum of the American Helicopter Society, New Orleans,1981.
[12] Gabel R, Reed D. Evaluation of pylon focusing for reduced helicopter vibration [Report]. BoeingVertol Co. Philadelphia PA,1979.
[13] Flannelly W G. The dynamic anti-resonant vibration isolator. Proceedings of the22ndAnnualForum of the American Helicopter Society, Washington,1976.
[14] Friedmann P P, Millott T A. Vibration reduction in rotorcraft using active control: a comparisonof various approaches. Journal of Guidance, Control, and Dynamics,1995,18(4):664-672.
[15] Wood E R, Powers R W, Cline J H, et al. On developing and flight testing a higher harmoniccontrol system. Journal of the American Helicopter Society,1985,30(1):3-20.
[16] Shaw J N, Albion J, Hanker E, et al. Higher harmonic control: wind tunnel demonstration of fullyeffective vibratory hub force suppression. Journal of the American Helicopter Society,1989,31(1):14-25.
[17] Nguyen K, Betzina M, Kitaplioglu C. Full-scale demonstration of higher harmonic control fornoise and vibration reduction on the XV-15rotor. Proceedings of the56thAnnual Forum of theAmerican Helicopter Society, Virginia Beach, VA,2000.
[18] Ham H D. Helicopter individual blade control research at MIT1977-1985. Vertica.1986,11(1):831-843.
[19] Ham N D. Helicopter individual blade control: promising technology for the future helicopter.Proceedings of the American Helicopter Society Aeromechanics Conference, Bridgeport, CT,1995.
[20] Jacklin S A, Haber A, Simone G. Full-scale wind tunnel test of an individual blade control systemfor a UH-60Helicopter. Proceedings of the58thAnnual Forum of American Helicopter Society,Montreal, Canada,2002.
[21] McCloud III J L, Weisbrich A L. Wind tunnel test results of a full-scale multicyclic controllabletwist rotor. Proceedings of the34thAnnual Forum of the American Helicopter Society,Washington, DC,1978.
[22] Milgram J, Chapra I, Straub F. Rotors with trailing edge flaps: analysis and comparison withexperimental data. Journal of American Helicopter Society,1998,43(4):319-332.
[23] Friedmann P P, Terlizzi M. New developments in vibration reduction with actively controlledtrailing edge flaps. Mathematical and Computer Modelling,2001,33(10-11):1055-1083.
[24] Derham R C, Hagood N W. Rotor design using smart materials to actively twist blades.Proceedings of the52ndAnnual Forum of the American Helicopter Society. Washington, DC,1996.
[25] Chen P C, Chopra I, Wind tunnel test of a smart rotor model with individual blade twist control.Journal of Intelligent Material Systems and Structures,1997,8(5):414-425.
[26] Cesnik C E S, Shin S J, Wilbur M L. Dynamic response of active twist rotor blades. SmartMaterials and Structures,2001,10(1):62-76.
[27] King S P, Staple A E. Minimization of helicopter vibration through active control of structuralresponse. Rotorcraft Design Operations, AGARD-CP-423,1986.
[28] Staple A E. An evaluation of active control of structural response as a means of reducinghelicopter vibration. Proceedings of the15thEuropean Rotorcraft, Amsterdam, Netherlands,1987.
[29] Welsh W A, Staple A E. Test and evaluation of fuselage vibration utilizing active control ofstructural response (ACSR) optimized to ADS-27. Proceedings of the46thAnnual Forum of theAmerican Helicopter Society, Washington, DC,1990.
[30] Pearson T J, Goodall R M. Adaptive schemes for the active control of helicopter structuralresponse. IEEE Transactions on Control System Technology,1994,2(2):61-67.
[31] Teal R S, Mccorvey D L, Mailoy D. Active vibration suppression for the CH-47D. Proceedingsof the53rdAnnual Forum of the American Helicopter Society, Virginia Beach, Virginia,1997.
[32] Welsh W, Fredrickson C, Rauch C. Flight test of an active vibration control system on the UH-60Black Hawk helicopter. Proceedings of the51stAnnual Forum of the American HelicopterSociety, Fort Worth, TX,1995.
[33] Vignal B, Development and qualification of active vibration control system for the EurocopterEC225/EC725, Proceedings of the61stAnnual Forum of the American Helicopter Society,Grapevine, TX,2005.
[34] Blackwell R, Millott T. Dynamics design characteristics of the Sikorsky X2technologydemonstrator aircraft. Proceedings of the64thAnnual Forum of the American Helicopter Society,2008.
[35] Mahmood R S, Heverly D. In-flight demonstration of active vibration control technologies on theBell429helicopter. Proceedings of the68thAnnual Forum of the American Helicopter Society,Fort Worth, Texas,2012.
[36] Cribbs R C, Friedmann P P, Chiu T. Coupled helicopter rotor/flexible fuselage aeroelastic modelfor control of structural response. AIAA Journal2000,38(10):1777-1788.
[37] Chiu T, Friedmann P P. Vibration suppression in helicopter rotor/flexible fuselage system usingthe ACSR approach with disturbance rejection. Proceedings of the52ndAnnual Forum of theAmerican Helicopter Society, Washington, DC,1996.
[38] Cribbs R C, Friedmann P P. Vibration reduction in rotorcraft using an enhanced ACSR model.Proceedings of the AIAA/ASME/ASCE/AHS/ASC41st Structures, Structural Dynamics, andMaterials Conference, AIAA, Reston, VA,2000(AIAA Paper2000-1687).
[39] Heverly D, Wang K W, Smith E C. An optimal actuator placement methodology for activecontrol of helicopter airframe vibrations. Journal of American Helicopter Society,2001,46(4):251-261.
[40]杨铁军,顾仲权.基于误差通道在线辨识的直升机结构振动主动控制研究.航空学报,2004,25(1):36-40.
[41]鲁民月,雷凌云,顾仲权.结构振动的自适应反馈预测控制研究.振动工程学报,2004,17(3):258-262.
[42]鲁民月.直升机结构响应自适应预测控制研究[博士学位论文].南京:航空航天大学,航空宇航学院,2005.
[42]李明强.直升机机体动力学相似模型设计与结构响应主动控制[硕士学位论文].南京:航空航天大学,航空宇航学院,2008.
[44]赵灿峰,顾中权.直升机结构振动频率主动控制的时域仿真.系统仿真学报,2009,21(20):6347-6351.
[45]赵灿峰.直升机结构响应主动控制频率法研究[硕士学位论文].南京:航空航天大学,航空宇航学院,2010.
[46]陆洋,顾仲权,凌爱民.直升机结构响应主动控制飞行实验.振动工程学报,2012,25(1):24-29.
[47] Prouty R. Should we consider variable rotor speeds. Vertiflite,2004,50(4):24–27.
[48] Konstanzer P, Enenkl B, Aubourg P A. Recent advances in Eurocopter’s passive and activevibration control. Proceedings of the64thAnnual Forum of the American Helicopter Society,Montreal, Canada,2008
[49] Goodman R K, Millott T A. Design, development, and flight testing of the active vibrationcontrol system for the Sikorsky S-92. Proceedings of the56thAnnual Forum of the AmericanHelicopter Society, Virginia Beach, VA,2000.
[50]姚军.压电结构的主动振动控制[博士学位论文].南京：南京航空航天大学,航空宇航学院,1999.
[51] Jaffe B, Roth R S, Marzullo S. Piezoelectric properties of lead zirconate lead titanate solidsolution ceramics. Journal of Applied Physics,1954,25(6):809-810.
[52] Niezrecki C, Brei D, Balakrishnan S, et al. Piezoelectric actuation: state of the art. The Shock andVibration Digest,2001,33(4):269-280.
[53] Bailey T, Hubbard J E．Distributed piezoelectric polymeric active vibration control of a cantileverbeam．Journal of Guidance, Control, and Dynamics,1985,8(5):605-611.
[54] Crawley E F, Luis J D. Use of piezoelectric actuators elements of intelligent structures. AIAAJournal,1987,25(10):1375-1385.
[55] Devasia S, Meressi T, Paden B. Piezoelectric actuator design for vibration suppression:placement and sizing. Journal of Guidance, Control, and Dynamics,1993,16(5):859-864.
[56] Kim S, Jones D. Influence of piezo actuator thickness on the active vibration control of acantilever beam. Journal of Intelligent Material Systems and Structures,1995,6(5):610-623.
[57] Gaudenzi P, Carbonaro R, Benzi E. Control of beam vibrations by means of piezoelectric devices:theory and experiments. Composite Structures,2000,50(4):373-379.
[58] Han J H, Rew K H, Lee I. An experimental study of active vibration control of compositestructures with a piezo-ceramic actuator and a piezo-film sensor. Smart Materials and Structures,1997,6(5):549-558.
[59] Bruant I, Gallimard L, Nikoukar S. Optimal piezoelectric actuator and sensor location for activevibration control using genetic algorithm. Journal of Sound and Vibration,2010,329(10):1615-1635.
[60] Qiu J, Tani J. Vibration control of a shell using distributed piezoelectric sensor and actuators.Journal of Intelligent Material Systems and Structures,1995,6(7):474-481.
[61] Qiu J, Haraguchi M. Vibration control of a plate using a self-sensing piezoelectric actuator andan adaotive control approach. Journal of Intelligent Material Systems and Structures,2006,17(8-9):661-669.
[62] Miller S E, Oshman Y, Abramovich H. Modal control of piezolaminated anisotropic rectangularplates, Part1: Modal transducer theory. AIAA journal,1996,34(9):1868-1875.
[63] Miller S E, Oshman Y, Abramovich H. Modal control of piezolaminated anisotropic rectangularplates, Part2: Control theory. AIAA journal,1996,34(9):1876-1884.
[64] Tzou H S, Gadre M. Theoretical analysis of a multi-layered thin shell coupled with piezoelectricshell actuators for distributed vibration controls. Journal of Sound and Vibration,1989,132(3):433-450.
[65] Tzou H S, Tseng C I. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. Journal ofSound and Vibration,1990,138(1):17-34.
[66] Tzou H S. A new distributed sensor and actuator theory for “Intelligent” shells. Journal of Soundand Vibration1992,153(2):335-349.
[67] Maillard J P, Fuller C R. Active control of sound radiation from cylinders with piezoelectricactuators and structural acoustic sensing. Journal of Sound and Vibration,1999,222(3):363-387
[68] Ji H, Qiu J, Badel A. Semi-active vibration control of a composite beam using an adaptive SSDVapproach. Journal of intelligent material systems and structures,2009,20(4):401-412.
[69] Ji H, Qiu J, Zhu K. Two-mode vibration control of a beam using nonlinear synchronizedswitching damping based on the maximization of converted energy. Journal of Sound andVibration,2010,329(14):2751-2767.
[70] Fanson J L, Chu C, Lurie B J. Damping and structural control of the JPL phase0test bedstructure. Journal of Intelligent Material Systems and Structures,1991,2(3):281-300.
[71] Preumont A, Dufour J P, Malikian C. Active damping by local force feedback with piezoelectricactuators. Journal of Guidance, Control, and Dynamics,1992,15(2):390-395.
[72] Won C C, Sulla L, Sparks D W. Application of piezoelectric devices to vibration suppression.Journal of Guidance, Control, and Dynamics,1994,17(6):1333-1340.
[73] Song G, Vlattas J, Johnson S E, et al. Active vibration control of a space truss using a leadzirconate titanate stack actuator. Proceedings of the Institution of Mechanical Engineers, Part G,2001,215(1):355-361.
[74]李俊宝,张令弥.自适应桁架结构局部力反馈振动控制及其主动构件的配置研究.振动工程学报,1997,10(3):380-386.
[75] Gao W. Stochastically optimal active control of a smart truss structure under stationary randomexcitation. Journal of Sound and Vibration,2006,290(3-5):1256-1268
[76] Li W P, Huang H. Integrated optimization of actuator placement and vibration control forpiezoelectric adaptive trusses. Journal of Sound and Vibration,2013,332(1):17-32.
[77] Heeg J. Analytical and experimental investigation of flutter suppression by piezoelectricactuation [Report]. NASA,1993:1-43.
[78] Lin C Y, Crawley E F, Heeg J. Open-and closed-loop results of a strain-actuated activeaeroelastic wing. Journal of aircraft,1996,33(5):987-994.
[79] Lazarus K B, Crawley E F, Lin C Y. Multivariable active lifting surface control using strainactuation: analytical and experimental results. Journal of aircraft,1997,34(3):313-321.
[80] Kulkarmi M, Kumar G, Mujumdar P, et al. Active control of vibration modes of a wing box bypiezoelectric stack actuators. Proceeding of the51stAIAA/ASME/ASCE/AHS/ACS Structures,Structures Dynamics, and Material Conference, Orlando Florida, AIAA,2010:2010-2949.
[81] Hanagud S, Bayon de Noyer M, Luo H. Tail buffet alleviation of high-performance twin-tailaircraft using piezostack actuators. AIAA Journal,2002,40(4):619-627.
[82] Kermani M R, Patel R V, Moallem M. Flexure control using piezostack actuators: design andimplementation. IEEE/ASME Transsactions on Mechatronics,2005,10(2):181-188.
[83] Gerhard S, Peter L, Christian B, et al. Comfort enhancement by an active vibration reductionsystem for a flexible railway car body. Vehicle System Dynamics,2007,45(9):835-847
[84] Kozek M, Benatzky C, Schirrer A, et al. Vibration damping of a flexible car body structure usingpiezo-stack actuators. Control Engineering Practice,2009,19(3):298-310.
[85] Chen P P, Chopra I. Induced strain actuation of composite beams and rotor blades withembedded piezoceramic elements. Smart Materials and Structures,1996,5(1):35-48.
[86] Viswamurthy S R, Ganguli R. Optimal placement of piezoelectric actuated trailing-edge flaps forhelicopter vibration control. Journal of Aircraft,2009,46(1):244-253.
[87] Centolanza L R, Smith E C, Munsky B. Induced-shear piezoelectric actuators for rotor bladetrailing edge flaps. Smart Materials and Structures,2002,11(1):24–35.
[88] Hanagud S, Babu G L. Smart structures in the control of airframe vibrations. Journal of theAmerican Helicopter Society,1994,39(2):69-72.
[89] Heverly D. Optimal actuator placement and active structure design for control of helicopterairframe vibrations [PhD dissertation]. Pennsylvania: Department of Mechanical and NuclearEngineering, Pennsylvania State University,2002.
[90] Walchko J C, Kim J S, Wang K W. Hybrid feedforward-feedback control for active helicoptervibration suppression. Proceedings of the63rdAnnual Forum of the American Helicopter Society,Virginia Beach, VA,2007.
[91] Singhvi R, Vennkatesan C. Vibration control of an idealized helicoptor model using piezo stacksensor-actuator.46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics&Materials Conference, Austin, Texas,2005.
[92] Bouchilloux P, Claeyssen F, Letty R. Amplified piezoelectric actuators: from aerospace tounderwater applications. Proceedings of the SPIE Symposium on Smart Structures and Materials,SanDiego, CA,2004.
[93] IEEE standard on piezoelectricity, ANSI/IEEE standard176. New York: IEEE,1987.
[94] Arbel A. Controllability measures and actuator placement in oscillatory systems, InternationalJournal of Control,1981,33(3):565-574.
[95] Peng F J, Hu Y R. Actuator placement optimization and adaptive vibration control of plate smartstructures. Journal of Intelligent Material Systems and Structures,2005,16(3):263–271.
[96] Wang Q, Wang C. A controllability index for optimal design of piezoelectric actuators invibration control of beam structures. Journal of Sound and Vibration2001,242(3):507–518
[97] Gao W, Chen J J, Ma H B, et al. Optimal placement of active bars in active vibration control forpiezoelectric intelligent truss structures with random parameters. Computers and Structures2003,81(1):53–60.
[98] Yang Y, Jin Z, KiongSo C. Integrated optimal design of vibration control system for smart beamsusing genetic algorithms. Journal of Sound and Vibration,2005,282(3-5):1293–1307.
[99] Liu W, Hou Z, Demetriou M A. A computational scheme for the optimal sensor/actuatorplacement of flexible structures using spatial H2measures. Mechanical Systems and SignalProcessing,2006,20(4):881–895.
[100] Hiramoto K, Doki H, Obinata G. Optimal sensor/actuator placement for active vibration controlusing explicit solution of algebraic Riccati equation. Journal of Sound and Vibration,2000,229(5):1057–1075.
[101] Dhuri K D, Seshu P. Piezo actuator placement and sizing for good control effectiveness andminimal change in original system dynamics. Smart Materials and Structures,2006,15(6):1661-1672.
[102] Bruant I, Gallimard L, Nikoukar S. Optimal piezoelectric actuator and sensor location for activevibration control, using genetic algorithm. Journal of Sound and Vibration,2010,329(10):1615-1635.
[103] Roy T, Chakraborty D. Optimal vibration control of smart fiber reinforced composite shellstructures using improved genetic algorithm. Journal of Sound and Vibration,2009,319(1-2):15-40.
[104] Zhu Y, Qiu J, Tani J. Simultaneous optimization of structure and control for vibrationsuppression. Journal of vibration and acoustics,1999,121(2):237-243.
[105] Zhu Y, Qiu J, Du H. Simultaneous optimal design of structural topology, actuator locations andcontrol parameters for a plate structure. Computational mechanics,2002,29(2):89-97.
[106] Rao S S, Pan T S, Venkayya V B. Optimal placement of actuator in actively controlledstructures using genetic algorithms. AIAA Journal,1991,29(6):942-943.
[107] Yan S, Zheng K, Zhao Q, et al. Optimal placement of active members for truss structure usinggenetic algorithm. Lecture Notes in Computer Science,2005,3645:386-395.
[108] Kumar K R, Narayanan S, Active vibration control of beams with optimal placement ofpiezoelectric sensor/actuator pairs. Smart Materials and Structures,2008,17(5):1-15.
[109] Han J H, Lee L. Optimal placement of piezoelectric sensors and actuators for vibration controlof a composite plate using genetic algorithms. Smart Materials and Structures1999,8(2):257-267.
[110] Sadri A M, Wright J R, Wynne R. Modeling and optimal placement of piezoelectric actuators inisotropic plates using genetic algorithm. Smart Materials and Structures,1999,8(4):490-498.
[111]朱剑英.智能系统非经典数学方法.武汉：华中科技大学出版社，2001.
[112] Deep K, Singh K P, Kansal M L, et al. A real coded genetic algorithm for solving integer andmixed integer optimization problems. Applied Mathematics and Computation,2009,212(2):505-518.
[113] Bayon N M, Hanagud S V. Modal analysis and optimization of the offset piezoceramicstack actuator. Proceedings of the41stAIAA/ASME/ASCE/AHS/ASC Structure, StructuralDynamics, and Materials Conference, Atlanta, GA,2000, AIAA-2000-1792.
[114] Bauchau O A, Rodriguez J, Chen S Y, et al. Coupled rotor-fuselage analysis with finite motionsusing component mode synthesis. Journal of the American Helicopter Society,2004,49(2):201-211.
[115] Yeo H, Chopra I. Coupled rotor/fuselage vibration analysis for teetering rotor and test datacomparison. AIAA Journal of Aircraft,2001,38(1):111-121.
[116] Lu M Y, Gu Z Q. Decentralized adaptive generalized predictive control for structural vibration.Progress in Natural Science,2005,15(3):75-80.
[117]梅景瑞,孙洪杰,顾仲权.直升机结构振动鲁棒控制研究.振动、测试与诊断,2008,28(1):39-43.
[118] Patt D, Liu L, Chandrasekar J, et al. Higher harmonic control algorithm for helicopter vibrationreduction revisited. Journal of Guidance, Control, and Dynamics,2005,28(5):918-930.
[119] Mathews A, Sule V R, Venkatesan C. Order reduction and closed-loop vibration control inhelicopter fuselages. Journal of Guidance, Control, and Dynamics,2002,25(2):316-323.
[120] Gupta N, Du Val R. A new approach for active control of rotorcraft vibration. Journal ofGuidance, Control, and Dynamics,1992,5(2):143-150.
[121] Hugin C T, Hatch C, Shingle G W. Active vibration control of the Lynx helicopter airframe.Proceeding of the48thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, andMaterials Conformance, AIAA, Hoholulu, Hawaii,2007(AIAA2007-2222).
[122] Veres S M. Adaptive harmonic control. International Journal of Control,2001,74(12):1219-1225.
[123]戴华.矩阵论.北京：科学出版社，2005.
[124] Haykin S. Adaptive filter theory (4thedition). NJ: Prentice-Hall,2003.
[125] An F Y, Sun H L, Li X D. Adaptive active control of periodic vibration using maglev actuators.Journal of Sound and Vibration,2012,331(9):1971-1984.
[126] Konstanzer P, Grunewald M, Janker P. Aircraft interior noise reduction through a piezo tunablevibration absorber system. Proceedings of the25thInternational Congress of the AeronauticalSciences, Hamburg Germany,2006.
[127] Damnjanovic A, Parsley G M. Frequency domain modeling of hysteresis with superimposedorthogonalized polynomial functions. Journal of Applied Physics,2005,97(10):505(1-3)
[128] Gozen B A, Ozdoganlar O B. Characterization of three dimensional dynamics of piezo-stackactuators. Mechanical Systems and Signal Processing,2012,31:268-283
[129] Sutton T J, Elliott S J. Active attenuation of periodic vibration in nonlinear systems using anadaptive harmonic controller. Journal of Vibration and Acoustics,1995,117(3):355-362.
[130] Pasco Y, Berry A. Consideration of piezoceramic actuator nonlinearity in the active isolation ofdeterministic vibration. Journal of Sound and Vibration,2006,289(3):481-508.
[131] Viswamurthy S R, Rao A K, Ganguli R. Dynamic hysteresis of piezoceramic stack actuatorsused in helicopter vibration control: experiments and simulations. Smart Materials andStructures,2007,16(4):1109-1119.
[132] Viswamurthy S R, Ganguli R. Modeling and compensation of piezoceramic actuator hysteresisfor helicopter vibration control. Sensors and Actuators A: Physical.2007,135(2):801-810.
[133] Zhou Y L, Zhang Q Zh, Li X D. On the use of an SPSA-based model free feedback controller inactive noise control for periodic disturbances in a duct. Journal of Sound and Vibration,2008,317(5):456-472.
[2] Ver I L, Beranek I I. Noise and vibration control engineering: principles and application. HobokenN.J.: John Wiley&Sons,2006.
[3] Leoni R D. Black hawk: the story of a world class helicopter. Reston VA: AIAA,2007.
[4] Pearson J T, Goodall R M, Lyndon I. Active control of helicopter vibration. Computing&ControlEngineering Journal,1994,5(6):277-284.
[5] Johnson W. Helicopter theory. New York: Dover Publications, Inc.,1994.
[6] Loewy R G, Helicopter vibrations: a technological perspective. Journal of the American HelicopterSociety,1984,29(4):4-30.
[7] Crews S T. Rotorcraft vibration criteria: a new perspective. Proceedings of the43rdAnnual Forumof the American Helicopter Society, Alexandria, VA,1987.
[8] EU: Directive2002/44/EC of the European parliament and of the council. Physical Agents(Vibration), published in the Official Journal of the European Communities (L177vol45) of July6,2002.
[9] Ellis C W, Jones R. Application of an absorber to reduce helicopter vibration levels. Journal of theAmerican Helicopter Society,1963,8(3):30-42.
[10] Amer K B, Neff J R. Vertical-plane pendulum absorbers for minimizing helicopter vibratoryloads. Journal of the American Helicopter Society,1974,19(4):44-48.
[11] Miao W L, Mouzakis T. Nonlinear dynamic characteristics of rotor bifilar absorber. Proceedingsof the37thAnnual Forum of the American Helicopter Society, New Orleans,1981.
[12] Gabel R, Reed D. Evaluation of pylon focusing for reduced helicopter vibration [Report]. BoeingVertol Co. Philadelphia PA,1979.
[13] Flannelly W G. The dynamic anti-resonant vibration isolator. Proceedings of the22ndAnnualForum of the American Helicopter Society, Washington,1976.
[14] Friedmann P P, Millott T A. Vibration reduction in rotorcraft using active control: a comparisonof various approaches. Journal of Guidance, Control, and Dynamics,1995,18(4):664-672.
[15] Wood E R, Powers R W, Cline J H, et al. On developing and flight testing a higher harmoniccontrol system. Journal of the American Helicopter Society,1985,30(1):3-20.
[16] Shaw J N, Albion J, Hanker E, et al. Higher harmonic control: wind tunnel demonstration of fullyeffective vibratory hub force suppression. Journal of the American Helicopter Society,1989,31(1):14-25.
[17] Nguyen K, Betzina M, Kitaplioglu C. Full-scale demonstration of higher harmonic control fornoise and vibration reduction on the XV-15rotor. Proceedings of the56thAnnual Forum of theAmerican Helicopter Society, Virginia Beach, VA,2000.
[18] Ham H D. Helicopter individual blade control research at MIT1977-1985. Vertica.1986,11(1):831-843.
[19] Ham N D. Helicopter individual blade control: promising technology for the future helicopter.Proceedings of the American Helicopter Society Aeromechanics Conference, Bridgeport, CT,1995.
[20] Jacklin S A, Haber A, Simone G. Full-scale wind tunnel test of an individual blade control systemfor a UH-60Helicopter. Proceedings of the58thAnnual Forum of American Helicopter Society,Montreal, Canada,2002.
[21] McCloud III J L, Weisbrich A L. Wind tunnel test results of a full-scale multicyclic controllabletwist rotor. Proceedings of the34thAnnual Forum of the American Helicopter Society,Washington, DC,1978.
[22] Milgram J, Chapra I, Straub F. Rotors with trailing edge flaps: analysis and comparison withexperimental data. Journal of American Helicopter Society,1998,43(4):319-332.
[23] Friedmann P P, Terlizzi M. New developments in vibration reduction with actively controlledtrailing edge flaps. Mathematical and Computer Modelling,2001,33(10-11):1055-1083.
[24] Derham R C, Hagood N W. Rotor design using smart materials to actively twist blades.Proceedings of the52ndAnnual Forum of the American Helicopter Society. Washington, DC,1996.
[25] Chen P C, Chopra I, Wind tunnel test of a smart rotor model with individual blade twist control.Journal of Intelligent Material Systems and Structures,1997,8(5):414-425.
[26] Cesnik C E S, Shin S J, Wilbur M L. Dynamic response of active twist rotor blades. SmartMaterials and Structures,2001,10(1):62-76.
[27] King S P, Staple A E. Minimization of helicopter vibration through active control of structuralresponse. Rotorcraft Design Operations, AGARD-CP-423,1986.
[28] Staple A E. An evaluation of active control of structural response as a means of reducinghelicopter vibration. Proceedings of the15thEuropean Rotorcraft, Amsterdam, Netherlands,1987.
[29] Welsh W A, Staple A E. Test and evaluation of fuselage vibration utilizing active control ofstructural response (ACSR) optimized to ADS-27. Proceedings of the46thAnnual Forum of theAmerican Helicopter Society, Washington, DC,1990.
[30] Pearson T J, Goodall R M. Adaptive schemes for the active control of helicopter structuralresponse. IEEE Transactions on Control System Technology,1994,2(2):61-67.
[31] Teal R S, Mccorvey D L, Mailoy D. Active vibration suppression for the CH-47D. Proceedingsof the53rdAnnual Forum of the American Helicopter Society, Virginia Beach, Virginia,1997.
[32] Welsh W, Fredrickson C, Rauch C. Flight test of an active vibration control system on the UH-60Black Hawk helicopter. Proceedings of the51stAnnual Forum of the American HelicopterSociety, Fort Worth, TX,1995.
[33] Vignal B, Development and qualification of active vibration control system for the EurocopterEC225/EC725, Proceedings of the61stAnnual Forum of the American Helicopter Society,Grapevine, TX,2005.
[34] Blackwell R, Millott T. Dynamics design characteristics of the Sikorsky X2technologydemonstrator aircraft. Proceedings of the64thAnnual Forum of the American Helicopter Society,2008.
[35] Mahmood R S, Heverly D. In-flight demonstration of active vibration control technologies on theBell429helicopter. Proceedings of the68thAnnual Forum of the American Helicopter Society,Fort Worth, Texas,2012.
[36] Cribbs R C, Friedmann P P, Chiu T. Coupled helicopter rotor/flexible fuselage aeroelastic modelfor control of structural response. AIAA Journal2000,38(10):1777-1788.
[37] Chiu T, Friedmann P P. Vibration suppression in helicopter rotor/flexible fuselage system usingthe ACSR approach with disturbance rejection. Proceedings of the52ndAnnual Forum of theAmerican Helicopter Society, Washington, DC,1996.
[38] Cribbs R C, Friedmann P P. Vibration reduction in rotorcraft using an enhanced ACSR model.Proceedings of the AIAA/ASME/ASCE/AHS/ASC41st Structures, Structural Dynamics, andMaterials Conference, AIAA, Reston, VA,2000(AIAA Paper2000-1687).
[39] Heverly D, Wang K W, Smith E C. An optimal actuator placement methodology for activecontrol of helicopter airframe vibrations. Journal of American Helicopter Society,2001,46(4):251-261.
[40]杨铁军,顾仲权.基于误差通道在线辨识的直升机结构振动主动控制研究.航空学报,2004,25(1):36-40.
[41]鲁民月,雷凌云,顾仲权.结构振动的自适应反馈预测控制研究.振动工程学报,2004,17(3):258-262.
[42]鲁民月.直升机结构响应自适应预测控制研究[博士学位论文].南京:航空航天大学,航空宇航学院,2005.
[42]李明强.直升机机体动力学相似模型设计与结构响应主动控制[硕士学位论文].南京:航空航天大学,航空宇航学院,2008.
[44]赵灿峰,顾中权.直升机结构振动频率主动控制的时域仿真.系统仿真学报,2009,21(20):6347-6351.
[45]赵灿峰.直升机结构响应主动控制频率法研究[硕士学位论文].南京:航空航天大学,航空宇航学院,2010.
[46]陆洋,顾仲权,凌爱民.直升机结构响应主动控制飞行实验.振动工程学报,2012,25(1):24-29.
[47] Prouty R. Should we consider variable rotor speeds. Vertiflite,2004,50(4):24–27.
[48] Konstanzer P, Enenkl B, Aubourg P A. Recent advances in Eurocopter’s passive and activevibration control. Proceedings of the64thAnnual Forum of the American Helicopter Society,Montreal, Canada,2008
[49] Goodman R K, Millott T A. Design, development, and flight testing of the active vibrationcontrol system for the Sikorsky S-92. Proceedings of the56thAnnual Forum of the AmericanHelicopter Society, Virginia Beach, VA,2000.
[50]姚军.压电结构的主动振动控制[博士学位论文].南京：南京航空航天大学,航空宇航学院,1999.
[51] Jaffe B, Roth R S, Marzullo S. Piezoelectric properties of lead zirconate lead titanate solidsolution ceramics. Journal of Applied Physics,1954,25(6):809-810.
[52] Niezrecki C, Brei D, Balakrishnan S, et al. Piezoelectric actuation: state of the art. The Shock andVibration Digest,2001,33(4):269-280.
[53] Bailey T, Hubbard J E．Distributed piezoelectric polymeric active vibration control of a cantileverbeam．Journal of Guidance, Control, and Dynamics,1985,8(5):605-611.
[54] Crawley E F, Luis J D. Use of piezoelectric actuators elements of intelligent structures. AIAAJournal,1987,25(10):1375-1385.
[55] Devasia S, Meressi T, Paden B. Piezoelectric actuator design for vibration suppression:placement and sizing. Journal of Guidance, Control, and Dynamics,1993,16(5):859-864.
[56] Kim S, Jones D. Influence of piezo actuator thickness on the active vibration control of acantilever beam. Journal of Intelligent Material Systems and Structures,1995,6(5):610-623.
[57] Gaudenzi P, Carbonaro R, Benzi E. Control of beam vibrations by means of piezoelectric devices:theory and experiments. Composite Structures,2000,50(4):373-379.
[58] Han J H, Rew K H, Lee I. An experimental study of active vibration control of compositestructures with a piezo-ceramic actuator and a piezo-film sensor. Smart Materials and Structures,1997,6(5):549-558.
[59] Bruant I, Gallimard L, Nikoukar S. Optimal piezoelectric actuator and sensor location for activevibration control using genetic algorithm. Journal of Sound and Vibration,2010,329(10):1615-1635.
[60] Qiu J, Tani J. Vibration control of a shell using distributed piezoelectric sensor and actuators.Journal of Intelligent Material Systems and Structures,1995,6(7):474-481.
[61] Qiu J, Haraguchi M. Vibration control of a plate using a self-sensing piezoelectric actuator andan adaotive control approach. Journal of Intelligent Material Systems and Structures,2006,17(8-9):661-669.
[62] Miller S E, Oshman Y, Abramovich H. Modal control of piezolaminated anisotropic rectangularplates, Part1: Modal transducer theory. AIAA journal,1996,34(9):1868-1875.
[63] Miller S E, Oshman Y, Abramovich H. Modal control of piezolaminated anisotropic rectangularplates, Part2: Control theory. AIAA journal,1996,34(9):1876-1884.
[64] Tzou H S, Gadre M. Theoretical analysis of a multi-layered thin shell coupled with piezoelectricshell actuators for distributed vibration controls. Journal of Sound and Vibration,1989,132(3):433-450.
[65] Tzou H S, Tseng C I. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. Journal ofSound and Vibration,1990,138(1):17-34.
[66] Tzou H S. A new distributed sensor and actuator theory for “Intelligent” shells. Journal of Soundand Vibration1992,153(2):335-349.
[67] Maillard J P, Fuller C R. Active control of sound radiation from cylinders with piezoelectricactuators and structural acoustic sensing. Journal of Sound and Vibration,1999,222(3):363-387
[68] Ji H, Qiu J, Badel A. Semi-active vibration control of a composite beam using an adaptive SSDVapproach. Journal of intelligent material systems and structures,2009,20(4):401-412.
[69] Ji H, Qiu J, Zhu K. Two-mode vibration control of a beam using nonlinear synchronizedswitching damping based on the maximization of converted energy. Journal of Sound andVibration,2010,329(14):2751-2767.
[70] Fanson J L, Chu C, Lurie B J. Damping and structural control of the JPL phase0test bedstructure. Journal of Intelligent Material Systems and Structures,1991,2(3):281-300.
[71] Preumont A, Dufour J P, Malikian C. Active damping by local force feedback with piezoelectricactuators. Journal of Guidance, Control, and Dynamics,1992,15(2):390-395.
[72] Won C C, Sulla L, Sparks D W. Application of piezoelectric devices to vibration suppression.Journal of Guidance, Control, and Dynamics,1994,17(6):1333-1340.
[73] Song G, Vlattas J, Johnson S E, et al. Active vibration control of a space truss using a leadzirconate titanate stack actuator. Proceedings of the Institution of Mechanical Engineers, Part G,2001,215(1):355-361.
[74]李俊宝,张令弥.自适应桁架结构局部力反馈振动控制及其主动构件的配置研究.振动工程学报,1997,10(3):380-386.
[75] Gao W. Stochastically optimal active control of a smart truss structure under stationary randomexcitation. Journal of Sound and Vibration,2006,290(3-5):1256-1268
[76] Li W P, Huang H. Integrated optimization of actuator placement and vibration control forpiezoelectric adaptive trusses. Journal of Sound and Vibration,2013,332(1):17-32.
[77] Heeg J. Analytical and experimental investigation of flutter suppression by piezoelectricactuation [Report]. NASA,1993:1-43.
[78] Lin C Y, Crawley E F, Heeg J. Open-and closed-loop results of a strain-actuated activeaeroelastic wing. Journal of aircraft,1996,33(5):987-994.
[79] Lazarus K B, Crawley E F, Lin C Y. Multivariable active lifting surface control using strainactuation: analytical and experimental results. Journal of aircraft,1997,34(3):313-321.
[80] Kulkarmi M, Kumar G, Mujumdar P, et al. Active control of vibration modes of a wing box bypiezoelectric stack actuators. Proceeding of the51stAIAA/ASME/ASCE/AHS/ACS Structures,Structures Dynamics, and Material Conference, Orlando Florida, AIAA,2010:2010-2949.
[81] Hanagud S, Bayon de Noyer M, Luo H. Tail buffet alleviation of high-performance twin-tailaircraft using piezostack actuators. AIAA Journal,2002,40(4):619-627.
[82] Kermani M R, Patel R V, Moallem M. Flexure control using piezostack actuators: design andimplementation. IEEE/ASME Transsactions on Mechatronics,2005,10(2):181-188.
[83] Gerhard S, Peter L, Christian B, et al. Comfort enhancement by an active vibration reductionsystem for a flexible railway car body. Vehicle System Dynamics,2007,45(9):835-847
[84] Kozek M, Benatzky C, Schirrer A, et al. Vibration damping of a flexible car body structure usingpiezo-stack actuators. Control Engineering Practice,2009,19(3):298-310.
[85] Chen P P, Chopra I. Induced strain actuation of composite beams and rotor blades withembedded piezoceramic elements. Smart Materials and Structures,1996,5(1):35-48.
[86] Viswamurthy S R, Ganguli R. Optimal placement of piezoelectric actuated trailing-edge flaps forhelicopter vibration control. Journal of Aircraft,2009,46(1):244-253.
[87] Centolanza L R, Smith E C, Munsky B. Induced-shear piezoelectric actuators for rotor bladetrailing edge flaps. Smart Materials and Structures,2002,11(1):24–35.
[88] Hanagud S, Babu G L. Smart structures in the control of airframe vibrations. Journal of theAmerican Helicopter Society,1994,39(2):69-72.
[89] Heverly D. Optimal actuator placement and active structure design for control of helicopterairframe vibrations [PhD dissertation]. Pennsylvania: Department of Mechanical and NuclearEngineering, Pennsylvania State University,2002.
[90] Walchko J C, Kim J S, Wang K W. Hybrid feedforward-feedback control for active helicoptervibration suppression. Proceedings of the63rdAnnual Forum of the American Helicopter Society,Virginia Beach, VA,2007.
[91] Singhvi R, Vennkatesan C. Vibration control of an idealized helicoptor model using piezo stacksensor-actuator.46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics&Materials Conference, Austin, Texas,2005.
[92] Bouchilloux P, Claeyssen F, Letty R. Amplified piezoelectric actuators: from aerospace tounderwater applications. Proceedings of the SPIE Symposium on Smart Structures and Materials,SanDiego, CA,2004.
[93] IEEE standard on piezoelectricity, ANSI/IEEE standard176. New York: IEEE,1987.
[94] Arbel A. Controllability measures and actuator placement in oscillatory systems, InternationalJournal of Control,1981,33(3):565-574.
[95] Peng F J, Hu Y R. Actuator placement optimization and adaptive vibration control of plate smartstructures. Journal of Intelligent Material Systems and Structures,2005,16(3):263–271.
[96] Wang Q, Wang C. A controllability index for optimal design of piezoelectric actuators invibration control of beam structures. Journal of Sound and Vibration2001,242(3):507–518
[97] Gao W, Chen J J, Ma H B, et al. Optimal placement of active bars in active vibration control forpiezoelectric intelligent truss structures with random parameters. Computers and Structures2003,81(1):53–60.
[98] Yang Y, Jin Z, KiongSo C. Integrated optimal design of vibration control system for smart beamsusing genetic algorithms. Journal of Sound and Vibration,2005,282(3-5):1293–1307.
[99] Liu W, Hou Z, Demetriou M A. A computational scheme for the optimal sensor/actuatorplacement of flexible structures using spatial H2measures. Mechanical Systems and SignalProcessing,2006,20(4):881–895.
[100] Hiramoto K, Doki H, Obinata G. Optimal sensor/actuator placement for active vibration controlusing explicit solution of algebraic Riccati equation. Journal of Sound and Vibration,2000,229(5):1057–1075.
[101] Dhuri K D, Seshu P. Piezo actuator placement and sizing for good control effectiveness andminimal change in original system dynamics. Smart Materials and Structures,2006,15(6):1661-1672.
[102] Bruant I, Gallimard L, Nikoukar S. Optimal piezoelectric actuator and sensor location for activevibration control, using genetic algorithm. Journal of Sound and Vibration,2010,329(10):1615-1635.
[103] Roy T, Chakraborty D. Optimal vibration control of smart fiber reinforced composite shellstructures using improved genetic algorithm. Journal of Sound and Vibration,2009,319(1-2):15-40.
[104] Zhu Y, Qiu J, Tani J. Simultaneous optimization of structure and control for vibrationsuppression. Journal of vibration and acoustics,1999,121(2):237-243.
[105] Zhu Y, Qiu J, Du H. Simultaneous optimal design of structural topology, actuator locations andcontrol parameters for a plate structure. Computational mechanics,2002,29(2):89-97.
[106] Rao S S, Pan T S, Venkayya V B. Optimal placement of actuator in actively controlledstructures using genetic algorithms. AIAA Journal,1991,29(6):942-943.
[107] Yan S, Zheng K, Zhao Q, et al. Optimal placement of active members for truss structure usinggenetic algorithm. Lecture Notes in Computer Science,2005,3645:386-395.
[108] Kumar K R, Narayanan S, Active vibration control of beams with optimal placement ofpiezoelectric sensor/actuator pairs. Smart Materials and Structures,2008,17(5):1-15.
[109] Han J H, Lee L. Optimal placement of piezoelectric sensors and actuators for vibration controlof a composite plate using genetic algorithms. Smart Materials and Structures1999,8(2):257-267.
[110] Sadri A M, Wright J R, Wynne R. Modeling and optimal placement of piezoelectric actuators inisotropic plates using genetic algorithm. Smart Materials and Structures,1999,8(4):490-498.
[111]朱剑英.智能系统非经典数学方法.武汉：华中科技大学出版社，2001.
[112] Deep K, Singh K P, Kansal M L, et al. A real coded genetic algorithm for solving integer andmixed integer optimization problems. Applied Mathematics and Computation,2009,212(2):505-518.
[113] Bayon N M, Hanagud S V. Modal analysis and optimization of the offset piezoceramicstack actuator. Proceedings of the41stAIAA/ASME/ASCE/AHS/ASC Structure, StructuralDynamics, and Materials Conference, Atlanta, GA,2000, AIAA-2000-1792.
[114] Bauchau O A, Rodriguez J, Chen S Y, et al. Coupled rotor-fuselage analysis with finite motionsusing component mode synthesis. Journal of the American Helicopter Society,2004,49(2):201-211.
[115] Yeo H, Chopra I. Coupled rotor/fuselage vibration analysis for teetering rotor and test datacomparison. AIAA Journal of Aircraft,2001,38(1):111-121.
[116] Lu M Y, Gu Z Q. Decentralized adaptive generalized predictive control for structural vibration.Progress in Natural Science,2005,15(3):75-80.
[117]梅景瑞,孙洪杰,顾仲权.直升机结构振动鲁棒控制研究.振动、测试与诊断,2008,28(1):39-43.
[118] Patt D, Liu L, Chandrasekar J, et al. Higher harmonic control algorithm for helicopter vibrationreduction revisited. Journal of Guidance, Control, and Dynamics,2005,28(5):918-930.
[119] Mathews A, Sule V R, Venkatesan C. Order reduction and closed-loop vibration control inhelicopter fuselages. Journal of Guidance, Control, and Dynamics,2002,25(2):316-323.
[120] Gupta N, Du Val R. A new approach for active control of rotorcraft vibration. Journal ofGuidance, Control, and Dynamics,1992,5(2):143-150.
[121] Hugin C T, Hatch C, Shingle G W. Active vibration control of the Lynx helicopter airframe.Proceeding of the48thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, andMaterials Conformance, AIAA, Hoholulu, Hawaii,2007(AIAA2007-2222).
[122] Veres S M. Adaptive harmonic control. International Journal of Control,2001,74(12):1219-1225.
[123]戴华.矩阵论.北京：科学出版社，2005.
[124] Haykin S. Adaptive filter theory (4thedition). NJ: Prentice-Hall,2003.
[125] An F Y, Sun H L, Li X D. Adaptive active control of periodic vibration using maglev actuators.Journal of Sound and Vibration,2012,331(9):1971-1984.
[126] Konstanzer P, Grunewald M, Janker P. Aircraft interior noise reduction through a piezo tunablevibration absorber system. Proceedings of the25thInternational Congress of the AeronauticalSciences, Hamburg Germany,2006.
[127] Damnjanovic A, Parsley G M. Frequency domain modeling of hysteresis with superimposedorthogonalized polynomial functions. Journal of Applied Physics,2005,97(10):505(1-3)
[128] Gozen B A, Ozdoganlar O B. Characterization of three dimensional dynamics of piezo-stackactuators. Mechanical Systems and Signal Processing,2012,31:268-283
[129] Sutton T J, Elliott S J. Active attenuation of periodic vibration in nonlinear systems using anadaptive harmonic controller. Journal of Vibration and Acoustics,1995,117(3):355-362.
[130] Pasco Y, Berry A. Consideration of piezoceramic actuator nonlinearity in the active isolation ofdeterministic vibration. Journal of Sound and Vibration,2006,289(3):481-508.
[131] Viswamurthy S R, Rao A K, Ganguli R. Dynamic hysteresis of piezoceramic stack actuatorsused in helicopter vibration control: experiments and simulations. Smart Materials andStructures,2007,16(4):1109-1119.
[132] Viswamurthy S R, Ganguli R. Modeling and compensation of piezoceramic actuator hysteresisfor helicopter vibration control. Sensors and Actuators A: Physical.2007,135(2):801-810.
[133] Zhou Y L, Zhang Q Zh, Li X D. On the use of an SPSA-based model free feedback controller inactive noise control for periodic disturbances in a duct. Journal of Sound and Vibration,2008,317(5):456-472.