多回路气动伺服弹性系统鲁棒稳定性分析方法研究
|
摘要
气动伺服弹性(ASE)涉及了空气动力、惯性力、结构力、敏感元件、执行机构以及飞行控制系统之间的相互作用，它们之间的相互作用可能会造成整个飞机系统的不稳定。因此，对飞机进行气动伺服弹性稳定性分析研究，已经作为现代飞机设计、试验及试飞过程中必不可少的一项重要工作。本文结合现代多回路系统的稳定性分析理论和现代信号处理工具，主要研究了直接由飞行试验数据分析多回路气动伺服弹性系统稳定性的方法，其中的研究成果已成功应用于某型飞机多回路气动伺服弹性系统的分析，并产生了显著的军事和经济效益。其主要内容如下：
1．设计并实现了采用扫频信号作为舵指令输入，确定飞机多回路气动伺服弹性系统稳定性的具体飞行试验方案，使得直接由飞行试验数据确定飞机气动伺服弹性稳定裕度成为可能；
2．为克服飞行试验数据中噪声对稳定性分析的影响，首先提出了一种针对扫频激励的小波时频域去噪的方法，在时频域实现了信噪分离，显著提高了飞行试验数据的信噪比；
3．在具体试验方案的基础上，提出了基于闭环系统回差矩阵最小奇异值理论的稳定性分析方法。该方法采用闭环系统回差矩阵的最小奇异值表示稳定程度。为便于工程描述，同时给出了最小奇异值与经典的幅值—相角裕度之间的对应关系；
4．为克服回差矩阵方法的保守性，又提出了基于结构奇异值μ理论的多回路气动伺服弹性系统稳定裕度的确定方法。同时分析了用μ方法得到的多回路鲁棒稳定裕度与经典的幅值—相角裕度之间的对应关系，给出了多回路系统的μ值与幅值—相角裕度的对应关系图；
5．设计并实现了飞机多回路气动伺服弹性系统稳定裕度的数据分析系统。该系统已通过实际飞行试验数据的测试，分析结果表明系统具有较强的可靠性和实用性。
最后将本文提出的飞行试验方法应用于某型飞机气动伺服弹性系统稳定性分析，结合飞行试验数据，比较了经典的稳定裕度分析方法(Bode图)、闭环系统回差矩阵最小奇异值稳定裕度分析法和鲁棒μ方法稳定裕度分析法的分析结果，并对分析结果进行了具体说明。结果表明：本文提出的方法可以给出飞机多回路气动伺服弹性系统稳定裕度的满意结果，同时上述方法也可以用于飞行控制系统稳定裕度的分析。因此，本文的研究成果对于高性能飞机的设计和试验鉴定具有重要意义。
Aeroservoelasticity (ASE) considers the interaction betweenaerodynamics,inertial,structural, actuation, sensing ,and control system.Theclosed-loop interaction of these elements may cause aircraft instabilities. Thus,aeroservoelastic stability analysis is an importance work for new aircraft designs andflight test. For this reason, some new methods based on advanced multi-loop systemstability analysis and advanced signal processing tools are presented to meet thedemand of new aircraft flight testing. The research results are applied to new aircraftASE stability analysis, and achieve great military and economy benefit. The mainresults of this thesis are described as follows:
1. A detailed scheme for ASE flight testing is designed firstly, which uses the sweepsignal as command to actuator. Finally, a flight test to evaluate the ASE stability isaccomplished.
2. A time-frequency filtering method based on Morlet wavelet is proposed to separatethe noise form flight data, which can reduce the effects of noise and provide a moreaccurate analysis result.
3. The return difference matrix (RDM) method is investigated, which evaluates thestability margin of aeroservoelastic system by determining the minimum singularvalue of the system return difference matrix. And the relationship between singularvalue and classical gain and phase margins are given for tesing engineer.
4. In order to overcome the conservativeness, a new method based on robustμanalysis is presented to evaluate the stability margin of multiloop aeroservoelasticsystem from flight test data. And the relationship betweenμand classical gainand phase margins is discussed in this paper, the evaluation diagram ofμand classical gain and phase margins for stability margins analysis is given.
5. An ASE data processing system is constructed and validated by real flight testing data, thefinal results show effectiveness and efficiency of the system.
Finally, the return difference matrix method and robustμmethod combined withtime-frequency filter are validated by real flight testing data, and the results arecompared with classical stability margin analysis method for single input single output(SISO) system, a detailed discussion is given.
The results illustrate that these method presented in this paper can be used toobtain satisfied stability margin during flight for multiloop aeroservoelastic system.Also, These methods can used to analyse stability margins of MIMO control system.Thus these methods for system stability margin analysis play important role in moderncombat aircrafts design and test.
1．设计并实现了采用扫频信号作为舵指令输入，确定飞机多回路气动伺服弹性系统稳定性的具体飞行试验方案，使得直接由飞行试验数据确定飞机气动伺服弹性稳定裕度成为可能；
2．为克服飞行试验数据中噪声对稳定性分析的影响，首先提出了一种针对扫频激励的小波时频域去噪的方法，在时频域实现了信噪分离，显著提高了飞行试验数据的信噪比；
3．在具体试验方案的基础上，提出了基于闭环系统回差矩阵最小奇异值理论的稳定性分析方法。该方法采用闭环系统回差矩阵的最小奇异值表示稳定程度。为便于工程描述，同时给出了最小奇异值与经典的幅值—相角裕度之间的对应关系；
4．为克服回差矩阵方法的保守性，又提出了基于结构奇异值μ理论的多回路气动伺服弹性系统稳定裕度的确定方法。同时分析了用μ方法得到的多回路鲁棒稳定裕度与经典的幅值—相角裕度之间的对应关系，给出了多回路系统的μ值与幅值—相角裕度的对应关系图；
5．设计并实现了飞机多回路气动伺服弹性系统稳定裕度的数据分析系统。该系统已通过实际飞行试验数据的测试，分析结果表明系统具有较强的可靠性和实用性。
最后将本文提出的飞行试验方法应用于某型飞机气动伺服弹性系统稳定性分析，结合飞行试验数据，比较了经典的稳定裕度分析方法(Bode图)、闭环系统回差矩阵最小奇异值稳定裕度分析法和鲁棒μ方法稳定裕度分析法的分析结果，并对分析结果进行了具体说明。结果表明：本文提出的方法可以给出飞机多回路气动伺服弹性系统稳定裕度的满意结果，同时上述方法也可以用于飞行控制系统稳定裕度的分析。因此，本文的研究成果对于高性能飞机的设计和试验鉴定具有重要意义。
Aeroservoelasticity (ASE) considers the interaction betweenaerodynamics,inertial,structural, actuation, sensing ,and control system.Theclosed-loop interaction of these elements may cause aircraft instabilities. Thus,aeroservoelastic stability analysis is an importance work for new aircraft designs andflight test. For this reason, some new methods based on advanced multi-loop systemstability analysis and advanced signal processing tools are presented to meet thedemand of new aircraft flight testing. The research results are applied to new aircraftASE stability analysis, and achieve great military and economy benefit. The mainresults of this thesis are described as follows:
1. A detailed scheme for ASE flight testing is designed firstly, which uses the sweepsignal as command to actuator. Finally, a flight test to evaluate the ASE stability isaccomplished.
2. A time-frequency filtering method based on Morlet wavelet is proposed to separatethe noise form flight data, which can reduce the effects of noise and provide a moreaccurate analysis result.
3. The return difference matrix (RDM) method is investigated, which evaluates thestability margin of aeroservoelastic system by determining the minimum singularvalue of the system return difference matrix. And the relationship between singularvalue and classical gain and phase margins are given for tesing engineer.
4. In order to overcome the conservativeness, a new method based on robustμanalysis is presented to evaluate the stability margin of multiloop aeroservoelasticsystem from flight test data. And the relationship betweenμand classical gainand phase margins is discussed in this paper, the evaluation diagram ofμand classical gain and phase margins for stability margins analysis is given.
5. An ASE data processing system is constructed and validated by real flight testing data, thefinal results show effectiveness and efficiency of the system.
Finally, the return difference matrix method and robustμmethod combined withtime-frequency filter are validated by real flight testing data, and the results arecompared with classical stability margin analysis method for single input single output(SISO) system, a detailed discussion is given.
The results illustrate that these method presented in this paper can be used toobtain satisfied stability margin during flight for multiloop aeroservoelastic system.Also, These methods can used to analyse stability margins of MIMO control system.Thus these methods for system stability margin analysis play important role in moderncombat aircrafts design and test.
引文
[1] Noll T E. Aeroservoelasticity. AIAA90-1073-CE
[2] Zames G. Functional Analysis Applied to Nonlinear Feedback Systems. IEEE Transactions on Circuits and Systems, CT-10: 392～404,1963.
[3] J.C. Doyle, Robustness of Multiloop Linear Feedback Systems, Proc. Of 1978 IEEE Conf. on Decision and Control, 8-10:12～18, San Diego, CA, January, 1979.
[4] J.C. Doyle and G. Stein, Multivariable feedback design: Concepts for a classical/modern synthesis," IEEE Transactions on Automatic Control, AC-26:4～16, Feb. 1981.
[5] Mukhopadhyay V, Application of matrix singular value properties for evaluating gain and phase margin of multiloop systems, AIAA, Guidance, Navigation and control conference SanDiego, California, 1420～428, 1982.
[6] Postlethwaite I, Edmunds J, MacFarlane A. Principal Gains and Principal Phases in the Analysis of Linear Multivariable Feedback Systems. IEEE Transactions on Automatic Control, 26(1):32～46,1981.
[7] J.C. Doyle, J. E. Wall and G. Stein, Performance and Robustness Analysis for Structured Uncertainty, Proc. IEEE Conf. on Decision and Control, 629-636, Orlando, FL, December 1982.
[8] J.C. Doyle, Analysis of Feedback Systems with Structured Uncertainties, IEE Proc., 129 Pt. D), 6:242～250, November 1982.
[9] M.J.Brenner, Aeroservoelastic Modeling and Validation of a Thrust-Vectoring F/A-18 Aircraft, NASA TP-3647,September 1996.
[10] R.Lind and M.Brenner, Robust Flutter Margins of an F/A-18 Aircraft from Aeroelastic Flight Data AIAA Joutrnal of Guidance, Control and Dynamics, 20(3):597-604, May-June 1997.
[11] R.Lind and M.Brenner ,Worst Case Flutter Margins From F/A-18 Aircraft Aeroelastic Data, AIAA Structures,Structural Dynamics and Materials Conference ,Kissimmee FL,AIAA-97-1266,April 1997.
[12] R.Lind and M.Brenner. Analyzing Aeroservolastic stability margins using μ merthod, AIAA-98-1895, 1672～1681,1998.
[13] R.Lind and M.Brenner., Robust Flutter Margin Anlysis That Incorporates Flight Data, NA SA/TP-1998-206543.
[14] R.Lind and M.Brenner., Robust Aeroservoelastic Stability Analysis: Flight Test Applications, Springer-Verlag London Limited, 1999.
[15] M.Brenner and R.Lind.,Wavelet-Processed Flight Data for Robust Aeroservoelastic Stability Margins, Journal Of Guidance.Control,and Dynamics, 21(6), November-December 1998
[16] M. Brenner and R. Lind, Wavelet Processing for Aeroservoelastic Stability Analysis, NASA Tech-Briefs, 22(6): 81～82, June 1998.
[17] Brenner M. Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data. NASA TM 4793, 1997.
[18] Nissim, E., and Gilyard, G., Method of Experimental Determination of Flutter Speed by Parameter Identication, NASA TP-2923, June 1989.6.
[19] M Brenner, R Lind, Wavelet Filtering To Reduce Conservatism In Aeroservoelastic Robust Stability Margins, AIAA-98-1896, 1682～1693, 1998.
[20] Ly, Uy-Loi, Robustness Analysis of a Multiloop Flight Control System AIAA Paper No. 83-2189, Aug. 1983.12.
[21] John J.Burken Flight-Determined Stability Analysis of Multiple-Input-Multiple-Output Control Systems NASA Technical Memorandum 4416.
[22] Tsao,T.T.,Lee,F.C., Relationship between Robustness μ-analysis and Classical Stability Margins, Aerospance Conference 1998 proceedings, IEEE. 4:481～486 March 1998,
[23] 周克敏，Doyle J C，Glover K著．鲁棒与最优控制，国防工业出版社，2002．
[24] 管德，飞机气动弹性力学手册．航空工业出版社．
[25] 吴斌，多变量飞控系统的稳定裕度分析[J]．航空学报，1998，19(6)：657～66．
[26] 孙卫、邹丛青，耦合的气动弹性系统鲁棒稳定裕度估算．北京航空航天大学学报．
[27] 陈桂彬、邹丛青、杨超，气动弹性设计基础 北京航空航天大学出版社2004．10．
[28] 陈桂彬，邹丛青，气动伺服弹性综合的应用，北京航空航天大学学报，22(3)：279-283Jun-1996．
[29] R. Lind, R.J. Prazenica, M.J. Brenner and D.H. Baldelli, Identifying Parameter-Dependent Volterra Kernels to Predict Aeroelastic Instabilities, AIAA Journal, 43(12):2496～2502 December 2005.
[30] Robert Clarke, Michael J. Allen, and Rvan P. Dibley, Fright Test of the F/A-18 Active Aeroelastic Wing Airplane,NASA/TM-2005-213664, August 2005.
[31] R. Lind, D. Voracek, R. Truax. T. Doyle, S. Potter, and M. Brenner, A Flight Test to Demonstrate Flutter and Evaluate the Flutterometer, The Aeronautical Journal, 107(1076),:577～588, October 2003.
[32] R. Albertani, P. Hubner, P. lfju, R. Lind and J. Jackowski, Wind Tunnel Testing of Micro Air Vehicles at Low Reynolds Numbers, Journal of Aerospace, 113(1):1474～14862005.
[33] de Gaston.R.R.,and Safonov, M., Exact calculation of the multiloop stability margin,IEEE trans on AC, 33(2), 1988.
[34] D.H. Baldelli, R. Lind and M. Brenner, Robust Aeroelastic Match-Point Solutions using Describing Function Method,Journl of Aircraft, 42(6) :1597-1605, November-December 2005
[35] D,H. Baldelli, R. Lind and M. Brenner, Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification,Journal of Guidance, Control and Dynamics, 28(5) :1056～1064.September-October 2005.
[36] R. Lind and J.P. Mortagua, Reducing Conservatism in Flutterometer Predictions using Volterra Modeling with Modal Parameter Estimation, Journal of Aircraft, 42(4) :998～1004,July-August 2005.
[37] R. Lind, R.J. Prazenica and M.J. Brenner, Estimating Nonlinearity using Volterra Kernels in Feedback with Linear Models, Nonlinear Dynamics, 39(1): 3-23,January 2005.
[38] D.H. Baldelli, R. Lind and M. Brenner, Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification,Journal of Guidance, Control and Dynamics, 28(5): 1056～1064.September-October 2005.
[39] R. Lind, Flight Test Evaluation of Flutter Prediction Methods , Journal of Aircraft, 40(5), 964～970.September-October 2003.
[40] R.J. Prazenica, R. Lind, and A.J. Kurdila, Uncertainty Estimation from Volterra Kernels for Robust Flutter Analysis, Journal of Guidance, Control, and Dynamics,26(2):331-339,March-April 2003.
[41] J.D. Johnson, J. Lu, A.E Dhawan, and R. Lind, Real-Time Identification of Flutter Boundaries using the Discrete Wavelet Transform, Journal of Guidance, Control, and Dynamics, 25(2):334-339,March-April 2002.
[42] R. Lind and J.P.Mortagua, Reducing Conservatism in Flutterometer Predictions using Volterra Modeling with Modal Parameter Estimation, Journal of Aircraft, 42(4):998-1004.July-August 2005.
[43] Peggy S. Williams-Hayes,Flight Test Implementation of a Second Generation Intelligent Flight Control System,NASA/TM-2005-213669,November 2005.
[44] Daubechies I. Ten, Lectures on Wavelets, Philadelphia, Society for Industrial and Applied Mathematics, 1992.
[45] Donoho D L. De-noising by Soft-Thresholding [J]. IEEE Transaction on Information Theory, 41 (3):613～627,1995.
[46] Donoho D L, Johnstone I M, A daption via Wavelet Shrinkage [J]. Biometrika, 81:425～455, 1994.
[47] 吉明、姚绪梁，鲁棒控制系统哈尔滨工程大学出版社2002．10。
[48] 梅生伟、申铁龙、刘康志，现代鲁棒控制理论与应用清华大学出版社2009．9。
[49] 蒋毅恒，现代鲁棒控制及其数学基础，华北电力大学学报，27(4)：93-98，2000．10。
[50] 吴斌，钟瑞麟，程鹏，多变量飞控系统稳定裕度与品质关系的研究，航空学报， 20(4)：313～315,Jul-1999。
[51] 蔡金狮，飞行器系统辨识学，国防工业出版社，2003。
[52] 肖业伦，航空航天器运动的建模—飞行动力学的理论基础，北京航空航天大学出版社2003。
[53] 田福礼，试飞确定电传飞控系统稳定裕度，飞行力学，17(2)，2000。
[54] 史忠科，频率域鲁棒性分析方法及其在飞控中的应用，飞行力学，15(1)，37～43，Mar-1997。
[55] 史忠科．非线性系统鲁棒稳定性条件及其在飞行控制中的应用．西北工业大学学报，21(4)：410～413．2003。
[56] 郑大钟编著．线性系统理论．清华大学出版社，1990。
[57] J C多伊尔等著．幕春棣译，反馈控制理论．清华大学出版社，1996。
[58] Becus, G. A., Automated Search for the Most Critical Flutter Configuration in Models with Uncertainty, Mathematical and Computer Modelling, 14, 77-982,1990.
[59] Becus, Georges A. and Corey Rekow, Robust Control Theory Methods in Flutter Analysis, International Forum on Aeroelasticity and Structural Dynamics ,91-06, 464～468.June 1991.
[60] Becus, Georges A., Stability Robustness of Aeroelastic Systems: A Perturbation Approach, International Forum on Aeroelasticity and Structural Dynamics, 1,425～432,June 1997.
[61] Balas, Gary J., et al, μ-Analysis and Synthesis Toolbox, Musyn Inc. and The MathWorks Inc.,Minneapolis, MN and Natiek, MA, 1995.
[62] Kehoe, M.W., A Historical Overview of Flight Flutter Testing, NASA-TM-4720, October 1995.
[63] Robert Clarke, John J. Burken. X-29 Flight Control System:Lessons Learned, NASA Technical Memorandum 4598.June 1974.
[64] Paduano, James D. and David R. Downing, Application of a Sensitivity Analysis Technique to High-Order Digital Flight Control Systems, NASA CR-179429, 1987.
[65] TANG Wei,SHI Zhong-ke,LI Hong-chao Wavelet denoising for chirp-like signal in time-frequency domain and application to aircraft flight flutter testing, IEEE conference on ICMLC,GuangZhou. 6, 3265～3270. Aug,2005.
[66] R Lind and M Brenner, Flutterometer: An On-Line Tool to Predict Robust Flutter Margins, Journal of Aircraft. 37(6):1105-1112. November-December 2000.
[67] Richard J. Prazenica, Rick Lind, and Andrew J. Kurdila, Uncertainty Estimation from Volterra Kernels for Robust Flutter Analysis, Journal Of Guidance,Control,and Dynamics, 26(2): 331～339,March-April 2003.
[68] M.Brenner, Aeroservoelastic Uncertainty Model Identification From Flight Data, NASA/TM-2001-210397.
[69] R.Lind, M.Brenner. Sidney M. haley.Estimation of modal Parameters using a Wavelet-Based Approach．NASA／TM-97-206300．
[70] 黄琳，稳定性与鲁棒性的理论基础，科学出版社。
[71] 冯纯伯，田玉平，忻欣著．鲁棒控制系统设计．东南大学出版社，1995。
[72] 阙志宏，线性系统理论，西北工业大学出版社，1995。
[73] 王尚文 余旭东 赵育善，飞行器结构动力学西北工业大学出版社1998。
[74] 谢绪凯著．现代控制理论基础．辽宁人民出版社，1980。
[75] 罗伯特．D．斯特拉姆 唐纳德．E．柯克，现代线性系统一使用MATLAB西安交通大学出版社。
[76] 高黛陵，吴麒，多变量频率域控制理论，清华大学出版社，1998年第一版。
[77] 郑建华，杨涤，鲁棒控制理论在倾斜转弯导弹中的应用，国防工业出版社，2001。
[78] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032～1037,1993,.
[79] Kevin A.Wise, Missile Autopilot Robustness Using the Real Multiloop Stability Margin, Journal of Guidance,Control and Dynamics, 16(2):354～362,1993.
[80] 苏为洲，秦丽江，具有参数摄动的多变量系统的鲁棒稳定性，自动化学报，17(5)：537～544，Sep-91．
[81] 张明廉主编．飞行控制系统．航空工业出版社，1994。
[82] 居余马等编著．线性代数．清华大学出版社，2002。
[83] J. C. Doyle. Robust and Optimal Control. Proceedings of the 35th IEEE Decision and Control,2 (11-13) :1595～1598,1996.
[84] 黄琳，王龙，于年才．系统鲁棒性的若干问题—背景、现状与挑战．控制理论与应用，1991，8(1)：1～29。
[85] 薛定宇，反馈控制系统设计与分析MATLAB语言应用，清华大学出版社，2000。
[86] 王伟，马颖学，多变量系统鲁棒稳定性分析，西北工业大学出版社。
[87] 祝小平，陈士橹，严恒元，弹性飞行器时域稳定鲁棒性分析，西北工业大学出版社。
[88] Wei-Min Lu, kemin zhou, J.C. Doyle, Stabilization of Uncertain Linear Systems:An LFT Approach, IEEE Transaction on Automatic Control, 41(1), 1996.
[89] Wei-Min Lu, John C. Doyle, control of nonlinear systems: a convex characterization, IEEE Transaction on Automatic Control, 40(9), 1995.
[90] M.dahleh, J.C.Doyle, Overview of Robust Stability and Performance Methods of Systems with Structured Mixed Perturbations, 31TH Conference On Decision & Control, 1992.
[91] Wei-Min Lu, kemin zhou, J. C. Doyle, Stabilization of LFT systems, 30TH Conference On Decision & Control, 1991.
[92] P.M. Young, J C. Doyle, computation of μ with Real and complex uncertainties, 29TH Conference On Decision & Control, 1990.
[93] J.C. Doyle, Structured Uncertaint in Control System Design, Proc. Of 24th conf. On Decision and Control, 260～265,1985.
[94] Michael G S,Alan J L,Gary L H, FeedBack Properties of Multivariable Systems:The role and use of the return difference matrix. IEEE Transaction on Automatic Control Ac 26(1):47～65,1981.
[95] Nainn-Ping Ke, An Algorithm of Symbolic Computation for Stability Margin, Proceedings of the American Control Conference. 2304～2308,Jun-98.
[96] H.Michael Mahon & Oscar D.Crisalle & Haniph Latchman and Kuo H, Yen, A New Method for Computing Robustness Margins for Real Parametric Uncertainties, Proceedings of the American Control Conference. 2301～2303,Jun-98.
[97] C.Gong and S.Thompson, Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control, 39(3): 548～550, Mar-94.
[98] Yong-Yan Cao and You-Yian Sun, A Counterexample of Comments on Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control,42(11): 1601～1601,Nov-97.
[99] Juing-Huei Su, Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control, 39(12): 2523～2524, Dec-1994.
[100] G. Ferreres, J.M. Biannic. Reliable Compution of the Robustness Margin for a Flexible Transport Aircraft. AIAA-2000-4365, 1212～1221, 2000.
[101] Jeffrey Jay Harris and G.Thomas Black, F-22 Control Law Development and Flying Qualities, AIAA-96-3379-CP, 155～163.1996.
[102] Dwight L.Balough, Determination of X-36 Stability Margins Using Real-Time Frequency Response Techniques, AIAA-98-4154, 105～115,1998.
[103] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032～1037, 1993.
[104] Kevin A.Wise. Missile Autopilot Robustness Using the Real Multiloop Stability Margin, Journal Of Guidance.Control.and Dynamics, 16(2): 354-362,1993.
[105] R. Lind and M. Brenner. Flutterometer: An On-Line Tool to Predict Robust Flutter Margins, Journal of Aircraft, 37(6):1105～1112, November-December 2000.
[106] John T. Bosworth and John J. Burken, Tailored Excitation for Multivariable Stability-Margin Measurement applied to the X-31A Nonlinear Simulation, NASA Technical Memorandum 113085, 1997.
[107] Jeffrey D. Johnson, Jun Lu, Atam P. Dhawan, Real-time Identification of Flutter Boundaries Using the Discrete Wavelet Transform, Journal Of Guidance,Control,and Dynamics, 25(2):334～339,2002.
[108] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032~1037,1993.
[109] Kevin A. Wise, Comparison of Six Robustness Tests Evaluating Missile Autopilot Robustness to Uncertain Aerodynamics, Journal Of Guidance,Control,and Dynamics, 5(4):861-869,1992.
[110] John T. Bosworth, Johnny C. West, Real-Time Open-Loop Frequency Response Analysis of Flight Test Data.
[111] Jong-Yeob Shin & Gary J.Balas and Andrew K.Packard, Worst Case Analysis of the Flight Control System X-38 Crew Return Vehicle,AIAA-99-4052, 552～562,1999.
[112] Anthony S.Pototzky, et al, Development and Testing of Methodology for Evaluating the Performance Of Multi-Input/Multi-Output Digital Control Systems, AIAA-90-3501-CP,1673-1682,1990.
[113] Anthony S.Pototzky, et al, On-line Performance Evaluation of Multiloop Digital Control Systems, Journal Of Guidance,Control,and Dynamics, 15(4):, 878～884,1992.
[114] John T. Bosworth and John J. Burken, Tailored Excitation for Multivariable Stability-Margin Measurement Applied to The X-31A Nonlinear Simulation, NASA Technical Memorandum 113085, 1997.
[115] V Frank R.Chavez & David K.Schmidt, Uncertainty modeling for Multivariable-Control Robustness Analysis of Elastic High-Speed Vehicles, Journal Of Guidance,Control,and Dynamics,22(1): 87～95, 1999.
[116] M. Abdulrahim, H. Garcia and R. Lind, Flight Characteristics of Shaping the Membrane Wing of a Micro Air Vehicle, Journal of Aircraft,41(1): 131～137, January-February 2005.
[2] Zames G. Functional Analysis Applied to Nonlinear Feedback Systems. IEEE Transactions on Circuits and Systems, CT-10: 392～404,1963.
[3] J.C. Doyle, Robustness of Multiloop Linear Feedback Systems, Proc. Of 1978 IEEE Conf. on Decision and Control, 8-10:12～18, San Diego, CA, January, 1979.
[4] J.C. Doyle and G. Stein, Multivariable feedback design: Concepts for a classical/modern synthesis," IEEE Transactions on Automatic Control, AC-26:4～16, Feb. 1981.
[5] Mukhopadhyay V, Application of matrix singular value properties for evaluating gain and phase margin of multiloop systems, AIAA, Guidance, Navigation and control conference SanDiego, California, 1420～428, 1982.
[6] Postlethwaite I, Edmunds J, MacFarlane A. Principal Gains and Principal Phases in the Analysis of Linear Multivariable Feedback Systems. IEEE Transactions on Automatic Control, 26(1):32～46,1981.
[7] J.C. Doyle, J. E. Wall and G. Stein, Performance and Robustness Analysis for Structured Uncertainty, Proc. IEEE Conf. on Decision and Control, 629-636, Orlando, FL, December 1982.
[8] J.C. Doyle, Analysis of Feedback Systems with Structured Uncertainties, IEE Proc., 129 Pt. D), 6:242～250, November 1982.
[9] M.J.Brenner, Aeroservoelastic Modeling and Validation of a Thrust-Vectoring F/A-18 Aircraft, NASA TP-3647,September 1996.
[10] R.Lind and M.Brenner, Robust Flutter Margins of an F/A-18 Aircraft from Aeroelastic Flight Data AIAA Joutrnal of Guidance, Control and Dynamics, 20(3):597-604, May-June 1997.
[11] R.Lind and M.Brenner ,Worst Case Flutter Margins From F/A-18 Aircraft Aeroelastic Data, AIAA Structures,Structural Dynamics and Materials Conference ,Kissimmee FL,AIAA-97-1266,April 1997.
[12] R.Lind and M.Brenner. Analyzing Aeroservolastic stability margins using μ merthod, AIAA-98-1895, 1672～1681,1998.
[13] R.Lind and M.Brenner., Robust Flutter Margin Anlysis That Incorporates Flight Data, NA SA/TP-1998-206543.
[14] R.Lind and M.Brenner., Robust Aeroservoelastic Stability Analysis: Flight Test Applications, Springer-Verlag London Limited, 1999.
[15] M.Brenner and R.Lind.,Wavelet-Processed Flight Data for Robust Aeroservoelastic Stability Margins, Journal Of Guidance.Control,and Dynamics, 21(6), November-December 1998
[16] M. Brenner and R. Lind, Wavelet Processing for Aeroservoelastic Stability Analysis, NASA Tech-Briefs, 22(6): 81～82, June 1998.
[17] Brenner M. Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data. NASA TM 4793, 1997.
[18] Nissim, E., and Gilyard, G., Method of Experimental Determination of Flutter Speed by Parameter Identication, NASA TP-2923, June 1989.6.
[19] M Brenner, R Lind, Wavelet Filtering To Reduce Conservatism In Aeroservoelastic Robust Stability Margins, AIAA-98-1896, 1682～1693, 1998.
[20] Ly, Uy-Loi, Robustness Analysis of a Multiloop Flight Control System AIAA Paper No. 83-2189, Aug. 1983.12.
[21] John J.Burken Flight-Determined Stability Analysis of Multiple-Input-Multiple-Output Control Systems NASA Technical Memorandum 4416.
[22] Tsao,T.T.,Lee,F.C., Relationship between Robustness μ-analysis and Classical Stability Margins, Aerospance Conference 1998 proceedings, IEEE. 4:481～486 March 1998,
[23] 周克敏，Doyle J C，Glover K著．鲁棒与最优控制，国防工业出版社，2002．
[24] 管德，飞机气动弹性力学手册．航空工业出版社．
[25] 吴斌，多变量飞控系统的稳定裕度分析[J]．航空学报，1998，19(6)：657～66．
[26] 孙卫、邹丛青，耦合的气动弹性系统鲁棒稳定裕度估算．北京航空航天大学学报．
[27] 陈桂彬、邹丛青、杨超，气动弹性设计基础 北京航空航天大学出版社2004．10．
[28] 陈桂彬，邹丛青，气动伺服弹性综合的应用，北京航空航天大学学报，22(3)：279-283Jun-1996．
[29] R. Lind, R.J. Prazenica, M.J. Brenner and D.H. Baldelli, Identifying Parameter-Dependent Volterra Kernels to Predict Aeroelastic Instabilities, AIAA Journal, 43(12):2496～2502 December 2005.
[30] Robert Clarke, Michael J. Allen, and Rvan P. Dibley, Fright Test of the F/A-18 Active Aeroelastic Wing Airplane,NASA/TM-2005-213664, August 2005.
[31] R. Lind, D. Voracek, R. Truax. T. Doyle, S. Potter, and M. Brenner, A Flight Test to Demonstrate Flutter and Evaluate the Flutterometer, The Aeronautical Journal, 107(1076),:577～588, October 2003.
[32] R. Albertani, P. Hubner, P. lfju, R. Lind and J. Jackowski, Wind Tunnel Testing of Micro Air Vehicles at Low Reynolds Numbers, Journal of Aerospace, 113(1):1474～14862005.
[33] de Gaston.R.R.,and Safonov, M., Exact calculation of the multiloop stability margin,IEEE trans on AC, 33(2), 1988.
[34] D.H. Baldelli, R. Lind and M. Brenner, Robust Aeroelastic Match-Point Solutions using Describing Function Method,Journl of Aircraft, 42(6) :1597-1605, November-December 2005
[35] D,H. Baldelli, R. Lind and M. Brenner, Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification,Journal of Guidance, Control and Dynamics, 28(5) :1056～1064.September-October 2005.
[36] R. Lind and J.P. Mortagua, Reducing Conservatism in Flutterometer Predictions using Volterra Modeling with Modal Parameter Estimation, Journal of Aircraft, 42(4) :998～1004,July-August 2005.
[37] R. Lind, R.J. Prazenica and M.J. Brenner, Estimating Nonlinearity using Volterra Kernels in Feedback with Linear Models, Nonlinear Dynamics, 39(1): 3-23,January 2005.
[38] D.H. Baldelli, R. Lind and M. Brenner, Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification,Journal of Guidance, Control and Dynamics, 28(5): 1056～1064.September-October 2005.
[39] R. Lind, Flight Test Evaluation of Flutter Prediction Methods , Journal of Aircraft, 40(5), 964～970.September-October 2003.
[40] R.J. Prazenica, R. Lind, and A.J. Kurdila, Uncertainty Estimation from Volterra Kernels for Robust Flutter Analysis, Journal of Guidance, Control, and Dynamics,26(2):331-339,March-April 2003.
[41] J.D. Johnson, J. Lu, A.E Dhawan, and R. Lind, Real-Time Identification of Flutter Boundaries using the Discrete Wavelet Transform, Journal of Guidance, Control, and Dynamics, 25(2):334-339,March-April 2002.
[42] R. Lind and J.P.Mortagua, Reducing Conservatism in Flutterometer Predictions using Volterra Modeling with Modal Parameter Estimation, Journal of Aircraft, 42(4):998-1004.July-August 2005.
[43] Peggy S. Williams-Hayes,Flight Test Implementation of a Second Generation Intelligent Flight Control System,NASA/TM-2005-213669,November 2005.
[44] Daubechies I. Ten, Lectures on Wavelets, Philadelphia, Society for Industrial and Applied Mathematics, 1992.
[45] Donoho D L. De-noising by Soft-Thresholding [J]. IEEE Transaction on Information Theory, 41 (3):613～627,1995.
[46] Donoho D L, Johnstone I M, A daption via Wavelet Shrinkage [J]. Biometrika, 81:425～455, 1994.
[47] 吉明、姚绪梁，鲁棒控制系统哈尔滨工程大学出版社2002．10。
[48] 梅生伟、申铁龙、刘康志，现代鲁棒控制理论与应用清华大学出版社2009．9。
[49] 蒋毅恒，现代鲁棒控制及其数学基础，华北电力大学学报，27(4)：93-98，2000．10。
[50] 吴斌，钟瑞麟，程鹏，多变量飞控系统稳定裕度与品质关系的研究，航空学报， 20(4)：313～315,Jul-1999。
[51] 蔡金狮，飞行器系统辨识学，国防工业出版社，2003。
[52] 肖业伦，航空航天器运动的建模—飞行动力学的理论基础，北京航空航天大学出版社2003。
[53] 田福礼，试飞确定电传飞控系统稳定裕度，飞行力学，17(2)，2000。
[54] 史忠科，频率域鲁棒性分析方法及其在飞控中的应用，飞行力学，15(1)，37～43，Mar-1997。
[55] 史忠科．非线性系统鲁棒稳定性条件及其在飞行控制中的应用．西北工业大学学报，21(4)：410～413．2003。
[56] 郑大钟编著．线性系统理论．清华大学出版社，1990。
[57] J C多伊尔等著．幕春棣译，反馈控制理论．清华大学出版社，1996。
[58] Becus, G. A., Automated Search for the Most Critical Flutter Configuration in Models with Uncertainty, Mathematical and Computer Modelling, 14, 77-982,1990.
[59] Becus, Georges A. and Corey Rekow, Robust Control Theory Methods in Flutter Analysis, International Forum on Aeroelasticity and Structural Dynamics ,91-06, 464～468.June 1991.
[60] Becus, Georges A., Stability Robustness of Aeroelastic Systems: A Perturbation Approach, International Forum on Aeroelasticity and Structural Dynamics, 1,425～432,June 1997.
[61] Balas, Gary J., et al, μ-Analysis and Synthesis Toolbox, Musyn Inc. and The MathWorks Inc.,Minneapolis, MN and Natiek, MA, 1995.
[62] Kehoe, M.W., A Historical Overview of Flight Flutter Testing, NASA-TM-4720, October 1995.
[63] Robert Clarke, John J. Burken. X-29 Flight Control System:Lessons Learned, NASA Technical Memorandum 4598.June 1974.
[64] Paduano, James D. and David R. Downing, Application of a Sensitivity Analysis Technique to High-Order Digital Flight Control Systems, NASA CR-179429, 1987.
[65] TANG Wei,SHI Zhong-ke,LI Hong-chao Wavelet denoising for chirp-like signal in time-frequency domain and application to aircraft flight flutter testing, IEEE conference on ICMLC,GuangZhou. 6, 3265～3270. Aug,2005.
[66] R Lind and M Brenner, Flutterometer: An On-Line Tool to Predict Robust Flutter Margins, Journal of Aircraft. 37(6):1105-1112. November-December 2000.
[67] Richard J. Prazenica, Rick Lind, and Andrew J. Kurdila, Uncertainty Estimation from Volterra Kernels for Robust Flutter Analysis, Journal Of Guidance,Control,and Dynamics, 26(2): 331～339,March-April 2003.
[68] M.Brenner, Aeroservoelastic Uncertainty Model Identification From Flight Data, NASA/TM-2001-210397.
[69] R.Lind, M.Brenner. Sidney M. haley.Estimation of modal Parameters using a Wavelet-Based Approach．NASA／TM-97-206300．
[70] 黄琳，稳定性与鲁棒性的理论基础，科学出版社。
[71] 冯纯伯，田玉平，忻欣著．鲁棒控制系统设计．东南大学出版社，1995。
[72] 阙志宏，线性系统理论，西北工业大学出版社，1995。
[73] 王尚文 余旭东 赵育善，飞行器结构动力学西北工业大学出版社1998。
[74] 谢绪凯著．现代控制理论基础．辽宁人民出版社，1980。
[75] 罗伯特．D．斯特拉姆 唐纳德．E．柯克，现代线性系统一使用MATLAB西安交通大学出版社。
[76] 高黛陵，吴麒，多变量频率域控制理论，清华大学出版社，1998年第一版。
[77] 郑建华，杨涤，鲁棒控制理论在倾斜转弯导弹中的应用，国防工业出版社，2001。
[78] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032～1037,1993,.
[79] Kevin A.Wise, Missile Autopilot Robustness Using the Real Multiloop Stability Margin, Journal of Guidance,Control and Dynamics, 16(2):354～362,1993.
[80] 苏为洲，秦丽江，具有参数摄动的多变量系统的鲁棒稳定性，自动化学报，17(5)：537～544，Sep-91．
[81] 张明廉主编．飞行控制系统．航空工业出版社，1994。
[82] 居余马等编著．线性代数．清华大学出版社，2002。
[83] J. C. Doyle. Robust and Optimal Control. Proceedings of the 35th IEEE Decision and Control,2 (11-13) :1595～1598,1996.
[84] 黄琳，王龙，于年才．系统鲁棒性的若干问题—背景、现状与挑战．控制理论与应用，1991，8(1)：1～29。
[85] 薛定宇，反馈控制系统设计与分析MATLAB语言应用，清华大学出版社，2000。
[86] 王伟，马颖学，多变量系统鲁棒稳定性分析，西北工业大学出版社。
[87] 祝小平，陈士橹，严恒元，弹性飞行器时域稳定鲁棒性分析，西北工业大学出版社。
[88] Wei-Min Lu, kemin zhou, J.C. Doyle, Stabilization of Uncertain Linear Systems:An LFT Approach, IEEE Transaction on Automatic Control, 41(1), 1996.
[89] Wei-Min Lu, John C. Doyle, control of nonlinear systems: a convex characterization, IEEE Transaction on Automatic Control, 40(9), 1995.
[90] M.dahleh, J.C.Doyle, Overview of Robust Stability and Performance Methods of Systems with Structured Mixed Perturbations, 31TH Conference On Decision & Control, 1992.
[91] Wei-Min Lu, kemin zhou, J. C. Doyle, Stabilization of LFT systems, 30TH Conference On Decision & Control, 1991.
[92] P.M. Young, J C. Doyle, computation of μ with Real and complex uncertainties, 29TH Conference On Decision & Control, 1990.
[93] J.C. Doyle, Structured Uncertaint in Control System Design, Proc. Of 24th conf. On Decision and Control, 260～265,1985.
[94] Michael G S,Alan J L,Gary L H, FeedBack Properties of Multivariable Systems:The role and use of the return difference matrix. IEEE Transaction on Automatic Control Ac 26(1):47～65,1981.
[95] Nainn-Ping Ke, An Algorithm of Symbolic Computation for Stability Margin, Proceedings of the American Control Conference. 2304～2308,Jun-98.
[96] H.Michael Mahon & Oscar D.Crisalle & Haniph Latchman and Kuo H, Yen, A New Method for Computing Robustness Margins for Real Parametric Uncertainties, Proceedings of the American Control Conference. 2301～2303,Jun-98.
[97] C.Gong and S.Thompson, Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control, 39(3): 548～550, Mar-94.
[98] Yong-Yan Cao and You-Yian Sun, A Counterexample of Comments on Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control,42(11): 1601～1601,Nov-97.
[99] Juing-Huei Su, Stability Margin Evaluation for Uncertain Linear Systems, IEEE Transaction on Automatic Control, 39(12): 2523～2524, Dec-1994.
[100] G. Ferreres, J.M. Biannic. Reliable Compution of the Robustness Margin for a Flexible Transport Aircraft. AIAA-2000-4365, 1212～1221, 2000.
[101] Jeffrey Jay Harris and G.Thomas Black, F-22 Control Law Development and Flying Qualities, AIAA-96-3379-CP, 155～163.1996.
[102] Dwight L.Balough, Determination of X-36 Stability Margins Using Real-Time Frequency Response Techniques, AIAA-98-4154, 105～115,1998.
[103] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032～1037, 1993.
[104] Kevin A.Wise. Missile Autopilot Robustness Using the Real Multiloop Stability Margin, Journal Of Guidance.Control.and Dynamics, 16(2): 354-362,1993.
[105] R. Lind and M. Brenner. Flutterometer: An On-Line Tool to Predict Robust Flutter Margins, Journal of Aircraft, 37(6):1105～1112, November-December 2000.
[106] John T. Bosworth and John J. Burken, Tailored Excitation for Multivariable Stability-Margin Measurement applied to the X-31A Nonlinear Simulation, NASA Technical Memorandum 113085, 1997.
[107] Jeffrey D. Johnson, Jun Lu, Atam P. Dhawan, Real-time Identification of Flutter Boundaries Using the Discrete Wavelet Transform, Journal Of Guidance,Control,and Dynamics, 25(2):334～339,2002.
[108] Rama K.Yedavalli, Flight Control Application of New Stability Robustness Bounds for Linear Uncertain Systems, Journal Of Guidance,Control,and Dynamics, 16(6): 1032~1037,1993.
[109] Kevin A. Wise, Comparison of Six Robustness Tests Evaluating Missile Autopilot Robustness to Uncertain Aerodynamics, Journal Of Guidance,Control,and Dynamics, 5(4):861-869,1992.
[110] John T. Bosworth, Johnny C. West, Real-Time Open-Loop Frequency Response Analysis of Flight Test Data.
[111] Jong-Yeob Shin & Gary J.Balas and Andrew K.Packard, Worst Case Analysis of the Flight Control System X-38 Crew Return Vehicle,AIAA-99-4052, 552～562,1999.
[112] Anthony S.Pototzky, et al, Development and Testing of Methodology for Evaluating the Performance Of Multi-Input/Multi-Output Digital Control Systems, AIAA-90-3501-CP,1673-1682,1990.
[113] Anthony S.Pototzky, et al, On-line Performance Evaluation of Multiloop Digital Control Systems, Journal Of Guidance,Control,and Dynamics, 15(4):, 878～884,1992.
[114] John T. Bosworth and John J. Burken, Tailored Excitation for Multivariable Stability-Margin Measurement Applied to The X-31A Nonlinear Simulation, NASA Technical Memorandum 113085, 1997.
[115] V Frank R.Chavez & David K.Schmidt, Uncertainty modeling for Multivariable-Control Robustness Analysis of Elastic High-Speed Vehicles, Journal Of Guidance,Control,and Dynamics,22(1): 87～95, 1999.
[116] M. Abdulrahim, H. Garcia and R. Lind, Flight Characteristics of Shaping the Membrane Wing of a Micro Air Vehicle, Journal of Aircraft,41(1): 131～137, January-February 2005.