基于PPF的柔性悬臂梁主动振动控制研究
|
摘要
随着空间技术的发展,大型的空间结构在航天领域得到了广泛的应用,成为空间技术研究的焦点。但是,现有的大型空间结构的模态频率一般都比较低、阻尼较小,因此在受到外界扰动后所需的振动衰减时间很长;而且这种空间结构大多数是基于分布式参数系统,即,高阶受控系统,具有很多振动模态,所以当以降阶模型为基础所设计的控制器作用于这些高阶受控系统时,将会产生溢出和引起闭环系统稳定裕度变小。
由于已有的主动振动控制算法很难满足空间结构精确性的要求,本文采用PPF(Positive Position Feedback)控制算法对柔性悬臂梁进行研究。虽然以前所用到的直接速度反馈算法是无条件稳定的,但是它是一种理想化算法,在实际应用中受到很大限制,而PPF算法是非动态稳定的,且对溢出不敏感,同时此算法可以通过根轨迹中的谐振点或固有频率与特征根负实部的关系实现作动器参数的最优化设计。本文利用PPF这些优点,首先通过结构频率与特征方程根之间的关系进行最优化参数选取,得到最适合系统的作动器频率和增益,然后改变作动器的不同的频率值和增益的大小,证明最优化参数能够使振动衰减的振幅和时间都达到最小,从而对振动抑制起到很好的作用。本文还做了进一步的研究,将一阶模态扩展为高阶模态,通过仿真证明,将PPF算法应用于高阶模态系统中,仍然能都得到较理想的振动抑制效果,从而体现了PPF算法的优越性和实用性。
With the development of space technology, large space structure has been widely used in the field of aerospace as the focus of the study of space technology. However, the modal frequency of the existing large space structure is relatively low in general and the damping is always small, so if there is a disturbance outside, the vibration will last a very long time. Large space structures are always distributed parameter systems, we call these the high-controlled systems, this kind of system has many vibration modes, when we design the controller based on a reduced order model in these high-controlled system will result in spillover and make the closed-loop system stability margin smaller.
As the active vibration control algorithm can not meet the requirements of accuracy of spatial structure, we do some study on a flexible cantilever beam system based on PPF (Positive Position Feedback) algorithm in this paper. Although the direct velocity feedback algorithm which previously used is unconditionally stable, it is an ideal algorithm and has a lot of limits in practical application. The PPF algorithm is non-dynamic stability and is not sensitive to overflow, and this algorithm can be root-locus and have the relationship between inherent resonant frequency and negative real part of the characteristic equation root to achieve the most optimal design of the actuator parameters. We make use of these advantages of PPF algorithm, first of all, through the relationship between structural frequency and characteristic equation root we select the optimal parameters, get the most suitable actuator frequency and gain for the system and then change the frequency and gain of different values, we prove that the most optimal parameters enable the amplitude of vibration attenuation and the decay time to a minimum, thereby they play a very good role in vibration suppression. This paper also do further studies, expand single-mode state to multi-mode, through experiments apply PPF algorithm to high-modal system could still have better vibration suppression effect, so as to show the superiority and practicality of PPF algorithm .
由于已有的主动振动控制算法很难满足空间结构精确性的要求,本文采用PPF(Positive Position Feedback)控制算法对柔性悬臂梁进行研究。虽然以前所用到的直接速度反馈算法是无条件稳定的,但是它是一种理想化算法,在实际应用中受到很大限制,而PPF算法是非动态稳定的,且对溢出不敏感,同时此算法可以通过根轨迹中的谐振点或固有频率与特征根负实部的关系实现作动器参数的最优化设计。本文利用PPF这些优点,首先通过结构频率与特征方程根之间的关系进行最优化参数选取,得到最适合系统的作动器频率和增益,然后改变作动器的不同的频率值和增益的大小,证明最优化参数能够使振动衰减的振幅和时间都达到最小,从而对振动抑制起到很好的作用。本文还做了进一步的研究,将一阶模态扩展为高阶模态,通过仿真证明,将PPF算法应用于高阶模态系统中,仍然能都得到较理想的振动抑制效果,从而体现了PPF算法的优越性和实用性。
With the development of space technology, large space structure has been widely used in the field of aerospace as the focus of the study of space technology. However, the modal frequency of the existing large space structure is relatively low in general and the damping is always small, so if there is a disturbance outside, the vibration will last a very long time. Large space structures are always distributed parameter systems, we call these the high-controlled systems, this kind of system has many vibration modes, when we design the controller based on a reduced order model in these high-controlled system will result in spillover and make the closed-loop system stability margin smaller.
As the active vibration control algorithm can not meet the requirements of accuracy of spatial structure, we do some study on a flexible cantilever beam system based on PPF (Positive Position Feedback) algorithm in this paper. Although the direct velocity feedback algorithm which previously used is unconditionally stable, it is an ideal algorithm and has a lot of limits in practical application. The PPF algorithm is non-dynamic stability and is not sensitive to overflow, and this algorithm can be root-locus and have the relationship between inherent resonant frequency and negative real part of the characteristic equation root to achieve the most optimal design of the actuator parameters. We make use of these advantages of PPF algorithm, first of all, through the relationship between structural frequency and characteristic equation root we select the optimal parameters, get the most suitable actuator frequency and gain for the system and then change the frequency and gain of different values, we prove that the most optimal parameters enable the amplitude of vibration attenuation and the decay time to a minimum, thereby they play a very good role in vibration suppression. This paper also do further studies, expand single-mode state to multi-mode, through experiments apply PPF algorithm to high-modal system could still have better vibration suppression effect, so as to show the superiority and practicality of PPF algorithm .
引文
[1]张义民.机械振动.北京:清华大学出版社,2007,3.
[2]戴德沛.阻尼技术的工程应用.北京:清华大学出版社,1991,10.
[3]顾仲权,马扣根,陈卫东等.振动主动控制.北京:国防工业出版社,1997.
[4]毛剑琴,卜庆忠,张杰,等.结构振动控制的新进展.控制理论与应用. 2001,18(5):647-652.
[5] Balas M. J. Direct Velocity Feedback control of Large Space Structures. Journal Guidance, control, and Dynamics. 1979, 2(3):252-253.
[6] Fanson J.L., Caughey T. K. Positive Position Feedback Control for Large Space Structures. AIAA Journal. 1990, 28(4):717-724.
[7]左振雷.柴油机双层隔振台架测试及振动有源控制仿真.哈尔滨工程大学硕士论文. 2000.
[8]黄金娥.基于神经网络的振动主动控制技术的研究.哈尔滨工程大学硕士论文. 2001.
[9] Blanco A., Beltran F., Silva G. On-Line Algebraic Identification of Eccentricity in Active Vibration Control of Rotor-Bearing Systems. Electrical and Electronics Engineering, 2007. ICEEE 2007. 4th International Conference on 5-7 Sept. 2007, Page(s):253– 256.
[10] Piroddi L., Leva A., Casaro F., Modelling and active vibration control of a turbomolecular vacuum pump. Control Applications, 2006 IEEE International Conference on Oct. 2006, Page(s):1103 - 1108.
[11] Yu-Chen Lin, Chun-Liang Lin, Chih-Chieh Yang. Robust Active Vibration Control for Rail Vehicle Pantograph. Vehicular Technology, IEEE Transactions on Volume 56, Issue 4, Part 2, July 2007, Page(s):1994 - 2004.
[12] Canuto E, Donati F, Bertinetto F. Active distance stabilization of large bodies with pico-meter repeatability. Control Applications, 1999. Proceedings of the 1999 IEEE International Conference on Volume 2, 22-27 Aug. 1999, Page(s):1704 - 1709 vol. 2.
[13] Ratan K.S., Felix V. Feed forward Control of Flexible Manipulators. Proc. Of the 1992 IEEE Int. Conf. on Robotics and Automation, Nice, France, 1992:788-793P.
[14] Magee D. P., Book W.J. Implementing Modified Command Filtering to Eliminat Multiple Modes of Vibration. Proc. of the 1986 AIAA AerospaceSciences Meeting, Reno, NV.1986.
[15] Luo Fei. A Method to Reduce Vibration in Pegand Hole Task: Force Control Compensated by Position. Proc. Of the 31st SICE Annual Conf. Int. Session, Kumamo to, Japan.1992:1107-1110.
[16] Thomas Bailey, Hubbard JE. Distributed piezoelectric polymer active vibration control of a cantilever beam. Journal of Guidance, Control and Dynamics.1985, 8(5): 605-611.
[17] Hanagud S., Obal M.W. and Meyyappa M. Electronic damping techniques and active vibration control. American Institute of Aeronautics and Astronautics.1985, 8(5): 443-453.
[18] Crawley E. F. and. DE Luis J. Use of piezoelectric actuators as elements of intelligent structures.American Institute of Aeronautics and Astronautics. 1987,10(5): 1373-1385.
[19] Im S. and Atluri S.N.Effects of a piezo-actuator on a finitely deformed beam subjected to general loading. American Institute of Aeronautics and Astronautics.1989, 27(5): 1801-1807.
[20] Chandra R. and Chopra I.Structural modeling of composite beams with induced-strain actuator. American Institute of Aeronautics and Astronautics. 1993,31(5):1692-1701.
[21] Gerhold C.H. and Rocha R.Active control of flexural vibrations in beams. Journal of Aerospace Engineering.1989,2: 141-154.
[22] Lee C.K. Theory of laminated piezoelectric plates for the design of distributed sensors/actuator. Part I: Governing equations and reciprocal relationships. Journal of Acoustical Society of American.1990,87:1144-1158.
[23] Crawley E.F. and Lazarus K. B.Induced strain actuation of isotropic and anisotropic plates. American Institute of Aeronautics and Astronautics. 1991, 29(6): 944-951.
[24] Pai P. F., Nayfeh A.H., Oh K.A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors. International Journal of Solids and Structures. 1993,30:1603-1630.
[25] Tzou H. S. and Cadre M. Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls. Journal of Sound and Vibration.1989,132: 433-450.
[26]司洪伟,李东旭.小波理论在人型空间智能结构振动控制中的应用.国防利技大学学报. 2003 , 25(3):14-18.
[27]孙东昌,王大钧.梁振动控制的分布压电单元法.北京大学学报.1996, 32(5):585-592.
[28] James R.Wiegand, John J. Helferty. Distributed fuzzy control of a flexible structures, smart structures and materials.1994.SPIE proceedings:488-499。
[29]乔溪荣.模糊神经网络控制器及其在航大姿态控制系统中的应用研究.航大控制. 1998:13-18.
[30]王存堂,唐建中.柔性结构模糊主动振动控制研究.振动工程学报. 1998,11 (3): 266- 272.
[31]张宪民,崔继彬.弹性连杆机构振动的模糊主动控制研究.机械工程学报. 2002, 13(11) :952- 955.
[32] Kelly Cohen, Tanchum Weller, Joseph Levitas etl.An adaptive fuzzy control algorithm for model-independ active vibration damping of flexible beam-like structures. J.Of intelligent Material System and Structures.1996, 7 :168-175.
[33]王宗利,林启荣,刘正兴.压电智能梁振动控制的优化设计.力学季刊. 2002, 21(4): 454-461.
[34]任建亭,闫云聚,姜洁胜.分布参数压电层合梁的振动主动控制.机械强度. 2000, 22(4) :303-306.
[35]唐凤,黄尚廉.机敏柔性梁的振动主动控制计算力学学报. 2002,17 (4):441-446.
[36] Hidekazu NISHIMURA.,Akihito KOJIMA. Active Vibration Isolation Control for a Multi-Degree-of-Freedom Structure with Uncertain Base Dynamics. JSME Internationa1 Journa1 Series C2 Vol.41,NO.1.1998.
[37]刘华.基于神经网络的振动智能控制理论、方法及实验研究.天津大学博士论文. 1995.
[38]张阿舟,姚起杭等编著.振动控制工程.北京:航空工业出版社,1989.
[39] James T P et al. Compt of structural control.J. of structure Div.1972, No.s17.
[40] Haiping Du, Boffa, J, Nong Zhang. Active seismic response control of tall buildings based on reduced order model. American Control Conference, 2006 14-16 June 2006, Page(s):6 pp.
[41] Agrawal A.K., He W.L. Control of seismically excited cable-stayed bridge using a resetting semi-active stiffness damper. American Control Conference, 2001. Proceedings of the 2001 Volume 2, 25-27 June 2001, Page(s):1103 - 1108 vol.2.
[42] Luckel J., Hestermeyer T., Liu-Henke X. Generalization of the cascade principle in view of a structured form of mechanical systems. AdvancedIntelligent Mechatronics, 2001. Proceedings. 2001 IEEE/ASME International Conference on Volume 1, 8-12 July 2001, Page(s):123 - 128 vol.1.
[43] Vilnay O. Active control of machinery foundation. ASCE. J. Eng. Mech. Div. 1984: 110: EM2.
[44] Nagashio T, Kida T. Robust control of flexible mechanical system by utilizing symmetry and its application to large space structures. Volume 1, 2-4 Sept. 2004, Page(s):418 - 423 Vol.1Control Applications, 2004. Proceedings of the 2004 IEEE International Conference on.
[45] Gourishankar V, Ramar K.Pole assignment with minimum eigenvalue sensitivity to plant parameter variations.Int. J. Control.1976, 23 (4): 493-504.
[46] Balas M J. Feedback control of flexible system. IEEE Transactions on Automatic Control. 1978, 23 (4): 673-679.
[47]吴淇泰.结构的主动控制.力学进展. 1987, 17 (4): 502-508.
[48] Morgan D R. An adaptive modal-based active control system. Acoust. Soc. Am.1991, 89(1): 241- 258.
[49] An-Chen Lee. Collocated sensor/actuator positioning and feedback design in the control of flexible structure system. Tran of ASME.1994, 116: 146-154.
[50] Balas M J. Active control of flexible system. Optimization theory and application.1979, 25 (3): 415-436.
[51] Meirovitch L, Baruh H, Oz H A. Comparison of control techniques for large flexible systems. Guidance Control. Dyn.6, 1983:302-310.
[52] Baz A, Poh S. Modified independent modal space control method for active control of flexible systems. NASA Technical, Report. Contract No 30429-d (Feb,1987)
[53] Mace B R. Active control of flexible vibrations. Sound Vib. 1987, 114:253-270.
[54]刘济深,赵会诚.结构振动模态局部化评述.振动与冲击.1995,14 (4):1-4。
[55] Kharitonov V L. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Uravnenija, 1978, 14 :2086-2088.
[56] Zames, G. Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans. Auto. Contr.1981,26 (2):301-320.
[57] Doyle J C.Analysis of control systems with structured uncertainty. IEE Proc. Part D. 1982, 129: 242 -250.
[58] Doyle J C, Glover K, Khargonekar P P, Francis B A.State-space solution tostandard H2 and H∞control problem. IEEE Trans. Auto. Contr. 1989,34 (8):831-847.
[59] Ball J A, Cohen N. The sensitivity minimization in an H∞norm: parameterization of all optimal solutions. Int. J. Contr. 1987,46:785-816.
[60] Kimura H, Lu Y, Kawatani R J. Robust H∞control for parameter uncertain system with time-varying delayed states: output feedback case. Proc. ACC'97, Albuquerque, New Mexico, USA.1991: 3679-3683.
[61] Limebeer D J N, Halikias G D. A controller degree bound for H∞optimal problem of the second kind. SIAM J. Contr. Optimiz. 1987, 32 :646-667.
[62] Khargonekar P P, Petersen I R, Rotea M A. H∞optimal control with state feedback. IEEE Trans. Auto. Contr.1988,33 :786-788.
[63] Gover K, Doyle J C. State-space formulae for all stabilizing controllers that satisfy an H∞norm bound and relations to risk sensitivity. Sys. & Contr. Let. 1988, 11(1):167-172.
[64] Bernstein D S, Haddad W M. LQG control with an H∞performance bound: a Riccati equation approach. IEEE Trans. Auto. Contr.1989, 34 :203-305.
[65] Scherer C, Gahinet P, Chilali M. Multi objective output-feedback control via LMI optimization. IEEE Trans. Auto. Contr. 1997,42 (7):898-911.
[66]陶永华,尹怡欣,葛芦生.新型PID控制及其应用.机械工业出版社.1999.
[67] Baz A., Poh S. Performance of an Active Control System with Piezoelectric Actuator.Journal of Sound and Vibration.1988, 126(2):327-343.
[68]刘富强.柔性智能桁架结构振动主动控制及相关问题研究. [博士学位论文],南京航空航天大学.1999.
[69]朱桂东,郑钢铁,邵成勋.框架结构模态分析的行波方法.宇航学报.1999,20(3):1-6.
[70] Von Flotow A.H. Traveling Wave Control for Large Spacecraft Structures. Journal of Guidance.1986, 9:462-468.
[71]舒歌群,郝志勇.结构振动控制中的弹性波主动控制技术.振动冲击. 2000,19(2):28-31.
[72] Balas, M.J. Guidance Control.1,93:1979,Ibid.,2,252.
[73] Goh,C.J. and Caughey,T.K. On the Stability Problem Caused by Finite Actuator Dynamics in the Control of Large Space Structures. International Journal of Control.Vol.41,No.3,1985,pp.787—802.
[74] Song G, Schmidt SP, Agrawal BN. Active vibration suppression of a flexible structure using smart material and modular control patch. Proceedings of theInstitution of Mechanical Engineers. 2000,214G: 217—229.
[75] Vineet Sethi,Gangbing Song and Pizhong Qiao. System identification and active vibration control of a composite I-beam using smart materials. Struct.Control Health Monit.2006,13:868—884.
[76]钱振东,沈建华,黄卫等.采用压电陶瓷元件进行智能板振动控制.振动、测试与诊断. 2000,20(3):196-201.
[77]丁文镜.振动主动控制当前的主要研究课题.力学进展. 1994,24(2): 173-180.
[78]王大钧,孙东昌.压电智能结构的一种模态控制新方法.振动工程学报. 1999,Vol.12 No.3.
[79]唐永杰.结构振动控制中压电阻尼技术的研究.压电与声光. 1996, Vol.18 No.1,p p.28-31.
[80] Hagedorn P.On a new concept of active vibration damping of elastic structures Waterloo. Canada, 1985:261-277.
[81] Scheuren J.Active control of bending waves in beams. Proceedings of Inter-Noise 85.1985:591- 595.
[82] Von Flotow A H. Traveling wave control for large spacecraft structures. Guidance Control Dyn. 9. 1986: 462-468.
[2]戴德沛.阻尼技术的工程应用.北京:清华大学出版社,1991,10.
[3]顾仲权,马扣根,陈卫东等.振动主动控制.北京:国防工业出版社,1997.
[4]毛剑琴,卜庆忠,张杰,等.结构振动控制的新进展.控制理论与应用. 2001,18(5):647-652.
[5] Balas M. J. Direct Velocity Feedback control of Large Space Structures. Journal Guidance, control, and Dynamics. 1979, 2(3):252-253.
[6] Fanson J.L., Caughey T. K. Positive Position Feedback Control for Large Space Structures. AIAA Journal. 1990, 28(4):717-724.
[7]左振雷.柴油机双层隔振台架测试及振动有源控制仿真.哈尔滨工程大学硕士论文. 2000.
[8]黄金娥.基于神经网络的振动主动控制技术的研究.哈尔滨工程大学硕士论文. 2001.
[9] Blanco A., Beltran F., Silva G. On-Line Algebraic Identification of Eccentricity in Active Vibration Control of Rotor-Bearing Systems. Electrical and Electronics Engineering, 2007. ICEEE 2007. 4th International Conference on 5-7 Sept. 2007, Page(s):253– 256.
[10] Piroddi L., Leva A., Casaro F., Modelling and active vibration control of a turbomolecular vacuum pump. Control Applications, 2006 IEEE International Conference on Oct. 2006, Page(s):1103 - 1108.
[11] Yu-Chen Lin, Chun-Liang Lin, Chih-Chieh Yang. Robust Active Vibration Control for Rail Vehicle Pantograph. Vehicular Technology, IEEE Transactions on Volume 56, Issue 4, Part 2, July 2007, Page(s):1994 - 2004.
[12] Canuto E, Donati F, Bertinetto F. Active distance stabilization of large bodies with pico-meter repeatability. Control Applications, 1999. Proceedings of the 1999 IEEE International Conference on Volume 2, 22-27 Aug. 1999, Page(s):1704 - 1709 vol. 2.
[13] Ratan K.S., Felix V. Feed forward Control of Flexible Manipulators. Proc. Of the 1992 IEEE Int. Conf. on Robotics and Automation, Nice, France, 1992:788-793P.
[14] Magee D. P., Book W.J. Implementing Modified Command Filtering to Eliminat Multiple Modes of Vibration. Proc. of the 1986 AIAA AerospaceSciences Meeting, Reno, NV.1986.
[15] Luo Fei. A Method to Reduce Vibration in Pegand Hole Task: Force Control Compensated by Position. Proc. Of the 31st SICE Annual Conf. Int. Session, Kumamo to, Japan.1992:1107-1110.
[16] Thomas Bailey, Hubbard JE. Distributed piezoelectric polymer active vibration control of a cantilever beam. Journal of Guidance, Control and Dynamics.1985, 8(5): 605-611.
[17] Hanagud S., Obal M.W. and Meyyappa M. Electronic damping techniques and active vibration control. American Institute of Aeronautics and Astronautics.1985, 8(5): 443-453.
[18] Crawley E. F. and. DE Luis J. Use of piezoelectric actuators as elements of intelligent structures.American Institute of Aeronautics and Astronautics. 1987,10(5): 1373-1385.
[19] Im S. and Atluri S.N.Effects of a piezo-actuator on a finitely deformed beam subjected to general loading. American Institute of Aeronautics and Astronautics.1989, 27(5): 1801-1807.
[20] Chandra R. and Chopra I.Structural modeling of composite beams with induced-strain actuator. American Institute of Aeronautics and Astronautics. 1993,31(5):1692-1701.
[21] Gerhold C.H. and Rocha R.Active control of flexural vibrations in beams. Journal of Aerospace Engineering.1989,2: 141-154.
[22] Lee C.K. Theory of laminated piezoelectric plates for the design of distributed sensors/actuator. Part I: Governing equations and reciprocal relationships. Journal of Acoustical Society of American.1990,87:1144-1158.
[23] Crawley E.F. and Lazarus K. B.Induced strain actuation of isotropic and anisotropic plates. American Institute of Aeronautics and Astronautics. 1991, 29(6): 944-951.
[24] Pai P. F., Nayfeh A.H., Oh K.A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors. International Journal of Solids and Structures. 1993,30:1603-1630.
[25] Tzou H. S. and Cadre M. Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls. Journal of Sound and Vibration.1989,132: 433-450.
[26]司洪伟,李东旭.小波理论在人型空间智能结构振动控制中的应用.国防利技大学学报. 2003 , 25(3):14-18.
[27]孙东昌,王大钧.梁振动控制的分布压电单元法.北京大学学报.1996, 32(5):585-592.
[28] James R.Wiegand, John J. Helferty. Distributed fuzzy control of a flexible structures, smart structures and materials.1994.SPIE proceedings:488-499。
[29]乔溪荣.模糊神经网络控制器及其在航大姿态控制系统中的应用研究.航大控制. 1998:13-18.
[30]王存堂,唐建中.柔性结构模糊主动振动控制研究.振动工程学报. 1998,11 (3): 266- 272.
[31]张宪民,崔继彬.弹性连杆机构振动的模糊主动控制研究.机械工程学报. 2002, 13(11) :952- 955.
[32] Kelly Cohen, Tanchum Weller, Joseph Levitas etl.An adaptive fuzzy control algorithm for model-independ active vibration damping of flexible beam-like structures. J.Of intelligent Material System and Structures.1996, 7 :168-175.
[33]王宗利,林启荣,刘正兴.压电智能梁振动控制的优化设计.力学季刊. 2002, 21(4): 454-461.
[34]任建亭,闫云聚,姜洁胜.分布参数压电层合梁的振动主动控制.机械强度. 2000, 22(4) :303-306.
[35]唐凤,黄尚廉.机敏柔性梁的振动主动控制计算力学学报. 2002,17 (4):441-446.
[36] Hidekazu NISHIMURA.,Akihito KOJIMA. Active Vibration Isolation Control for a Multi-Degree-of-Freedom Structure with Uncertain Base Dynamics. JSME Internationa1 Journa1 Series C2 Vol.41,NO.1.1998.
[37]刘华.基于神经网络的振动智能控制理论、方法及实验研究.天津大学博士论文. 1995.
[38]张阿舟,姚起杭等编著.振动控制工程.北京:航空工业出版社,1989.
[39] James T P et al. Compt of structural control.J. of structure Div.1972, No.s17.
[40] Haiping Du, Boffa, J, Nong Zhang. Active seismic response control of tall buildings based on reduced order model. American Control Conference, 2006 14-16 June 2006, Page(s):6 pp.
[41] Agrawal A.K., He W.L. Control of seismically excited cable-stayed bridge using a resetting semi-active stiffness damper. American Control Conference, 2001. Proceedings of the 2001 Volume 2, 25-27 June 2001, Page(s):1103 - 1108 vol.2.
[42] Luckel J., Hestermeyer T., Liu-Henke X. Generalization of the cascade principle in view of a structured form of mechanical systems. AdvancedIntelligent Mechatronics, 2001. Proceedings. 2001 IEEE/ASME International Conference on Volume 1, 8-12 July 2001, Page(s):123 - 128 vol.1.
[43] Vilnay O. Active control of machinery foundation. ASCE. J. Eng. Mech. Div. 1984: 110: EM2.
[44] Nagashio T, Kida T. Robust control of flexible mechanical system by utilizing symmetry and its application to large space structures. Volume 1, 2-4 Sept. 2004, Page(s):418 - 423 Vol.1Control Applications, 2004. Proceedings of the 2004 IEEE International Conference on.
[45] Gourishankar V, Ramar K.Pole assignment with minimum eigenvalue sensitivity to plant parameter variations.Int. J. Control.1976, 23 (4): 493-504.
[46] Balas M J. Feedback control of flexible system. IEEE Transactions on Automatic Control. 1978, 23 (4): 673-679.
[47]吴淇泰.结构的主动控制.力学进展. 1987, 17 (4): 502-508.
[48] Morgan D R. An adaptive modal-based active control system. Acoust. Soc. Am.1991, 89(1): 241- 258.
[49] An-Chen Lee. Collocated sensor/actuator positioning and feedback design in the control of flexible structure system. Tran of ASME.1994, 116: 146-154.
[50] Balas M J. Active control of flexible system. Optimization theory and application.1979, 25 (3): 415-436.
[51] Meirovitch L, Baruh H, Oz H A. Comparison of control techniques for large flexible systems. Guidance Control. Dyn.6, 1983:302-310.
[52] Baz A, Poh S. Modified independent modal space control method for active control of flexible systems. NASA Technical, Report. Contract No 30429-d (Feb,1987)
[53] Mace B R. Active control of flexible vibrations. Sound Vib. 1987, 114:253-270.
[54]刘济深,赵会诚.结构振动模态局部化评述.振动与冲击.1995,14 (4):1-4。
[55] Kharitonov V L. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Uravnenija, 1978, 14 :2086-2088.
[56] Zames, G. Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans. Auto. Contr.1981,26 (2):301-320.
[57] Doyle J C.Analysis of control systems with structured uncertainty. IEE Proc. Part D. 1982, 129: 242 -250.
[58] Doyle J C, Glover K, Khargonekar P P, Francis B A.State-space solution tostandard H2 and H∞control problem. IEEE Trans. Auto. Contr. 1989,34 (8):831-847.
[59] Ball J A, Cohen N. The sensitivity minimization in an H∞norm: parameterization of all optimal solutions. Int. J. Contr. 1987,46:785-816.
[60] Kimura H, Lu Y, Kawatani R J. Robust H∞control for parameter uncertain system with time-varying delayed states: output feedback case. Proc. ACC'97, Albuquerque, New Mexico, USA.1991: 3679-3683.
[61] Limebeer D J N, Halikias G D. A controller degree bound for H∞optimal problem of the second kind. SIAM J. Contr. Optimiz. 1987, 32 :646-667.
[62] Khargonekar P P, Petersen I R, Rotea M A. H∞optimal control with state feedback. IEEE Trans. Auto. Contr.1988,33 :786-788.
[63] Gover K, Doyle J C. State-space formulae for all stabilizing controllers that satisfy an H∞norm bound and relations to risk sensitivity. Sys. & Contr. Let. 1988, 11(1):167-172.
[64] Bernstein D S, Haddad W M. LQG control with an H∞performance bound: a Riccati equation approach. IEEE Trans. Auto. Contr.1989, 34 :203-305.
[65] Scherer C, Gahinet P, Chilali M. Multi objective output-feedback control via LMI optimization. IEEE Trans. Auto. Contr. 1997,42 (7):898-911.
[66]陶永华,尹怡欣,葛芦生.新型PID控制及其应用.机械工业出版社.1999.
[67] Baz A., Poh S. Performance of an Active Control System with Piezoelectric Actuator.Journal of Sound and Vibration.1988, 126(2):327-343.
[68]刘富强.柔性智能桁架结构振动主动控制及相关问题研究. [博士学位论文],南京航空航天大学.1999.
[69]朱桂东,郑钢铁,邵成勋.框架结构模态分析的行波方法.宇航学报.1999,20(3):1-6.
[70] Von Flotow A.H. Traveling Wave Control for Large Spacecraft Structures. Journal of Guidance.1986, 9:462-468.
[71]舒歌群,郝志勇.结构振动控制中的弹性波主动控制技术.振动冲击. 2000,19(2):28-31.
[72] Balas, M.J. Guidance Control.1,93:1979,Ibid.,2,252.
[73] Goh,C.J. and Caughey,T.K. On the Stability Problem Caused by Finite Actuator Dynamics in the Control of Large Space Structures. International Journal of Control.Vol.41,No.3,1985,pp.787—802.
[74] Song G, Schmidt SP, Agrawal BN. Active vibration suppression of a flexible structure using smart material and modular control patch. Proceedings of theInstitution of Mechanical Engineers. 2000,214G: 217—229.
[75] Vineet Sethi,Gangbing Song and Pizhong Qiao. System identification and active vibration control of a composite I-beam using smart materials. Struct.Control Health Monit.2006,13:868—884.
[76]钱振东,沈建华,黄卫等.采用压电陶瓷元件进行智能板振动控制.振动、测试与诊断. 2000,20(3):196-201.
[77]丁文镜.振动主动控制当前的主要研究课题.力学进展. 1994,24(2): 173-180.
[78]王大钧,孙东昌.压电智能结构的一种模态控制新方法.振动工程学报. 1999,Vol.12 No.3.
[79]唐永杰.结构振动控制中压电阻尼技术的研究.压电与声光. 1996, Vol.18 No.1,p p.28-31.
[80] Hagedorn P.On a new concept of active vibration damping of elastic structures Waterloo. Canada, 1985:261-277.
[81] Scheuren J.Active control of bending waves in beams. Proceedings of Inter-Noise 85.1985:591- 595.
[82] Von Flotow A H. Traveling wave control for large spacecraft structures. Guidance Control Dyn. 9. 1986: 462-468.