振动系统的特征结构配置问题
|
摘要
本文运用代数特征值反问题的理论与方法,研究了一阶线性系统、无阻尼结构系统与阻尼结构系统的特征结构配置问题,全文主要包括以下内容。
研究了一阶线性系统指定区域的特征结构配置问题。本文根据孙继广给出的系统鲁棒性的度量,把问题转化为一个无约束的优化问题,分析了问题的性质,给出了目标函数梯度向量的计算公式,提出了求解此问题的一个新算法,该方法计算公式简单,大大提高了计算效率。数值算例表明,这一算法具有良好的数值性态。
研究了无阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,分析了问题有解的条件,给出了解的表达式,并根据矩阵扰动理论给出了无阻尼结构系统鲁棒性的度量,由此提出了求解此问题的数值方法;研究了无阻尼结构系统保持对称性的特征结构配置问题,给出了此问题有解的条件与解的表达式,并考虑了在控制矩阵不给定的情况下,如何根据给定的特征结构求控制矩阵与反馈矩阵的方法;研究了无阻尼结构系统部分特征结构配置问题,即只改变系统的一部分特征值与相应的特征向量,而保持其余的特征结构不变,给出了此问题有解的条件与解的表达式,并给出了系统的鲁棒性度量,提出了求解此问题的两个算法:正交化向量方法与正交基方法;为了保持系统的对称性,利用输出反馈,给出了保持对称性的部分特征结构配置问题的一个特解;研究了一类结构动力模型修正问题,利用振动测量数据修正质量矩阵,使得修正后的动力学分析结果与相应的试验结果相一致。
研究了阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,利用阻尼结构系统鲁棒性的度量,提出了求解此问题的两个数值解法,新方法具有较好的数值稳定性。对于阻尼结构系统部分特征结构配置问题,利用矩阵扰动理论与特征值的灵敏度分析,给出了在测量的特征结构不完备时,如何选择要配置的若干个特征值与特征向量,并设计了一个数值算法来有效地求解此问题。对一般的特征结构配置问题,研究了对任意给定的特征值与特征向量,在控制矩阵不给定的情况下,如何设计控制矩阵与反馈矩阵的问题,提出了同时确定控制矩阵与反馈矩阵的方法。
According to the theory and methods of the algebraic inverse eigenvalue problems, in this dissertation, we study the eigenstructure assignment problems on linear systems, undamped structural systems and damped structural systems. The main contribution is as follows.
The robust eigenstructure assignment problem of linear system in a specified region is studied. The problem is formulated as an optimization problem. According to a Sun’s measure of robustness, we analyze the properties of this problem, and suggest the formula of the gradient vector of the objective function. Then a new algorithm for solving this problem is presented. Numerical examples show that the problem of robust pole assignment in a specified region can be solved effectively.
The eigenstructure assignment problems of undamped structural systems are considered. For the case that all the poles are prescribed, we give the conditions and the expressions of the solutions, and give a new measure of robustness according to the theory of matrix perturbation. Thus, we propose a numerical method for solving this problem. we study the preserve symmetric eigenstructure assignment problem, and give the conditions and the expressions of the solutions. We study the partial eigenstructure assignment problem of undamped structural systems, that is a few eigenvalues and eigenvectors of system are undesirable, and the rest of the eigenstructure invariant, and we give the conditions and the expressions of the solutions. According to a new measure of robustness, we give an algorithm for solving this problem. Moreover, in order to preserve the symmetry of the system, we consider the partial eigenstructure assignment problem using output feedback, and give a special solution of this problem. Lastly, we consider a structural dynamics model updating problem.
The eigenstructure assignment problems of damping structural systems are investigated. For the case that all the poles are prescribed, we give two algorithms for solving this problem. The procedure of this method is easy to realize, and have a good numerical stability. For the partial eigenstructure assignment problems of damping structural systems, according to the perturbation theory of matrices, we give a method for choosing the assigned eigenstructure, and propose an algorithm for solving this problem. For general eigenstructure assignment problem, in the case of the assigned eigenvectors are given arbitrarily, we give a method for getting the control matrix and the feedback matrices in the condition of the control matrix is unknown.
研究了一阶线性系统指定区域的特征结构配置问题。本文根据孙继广给出的系统鲁棒性的度量,把问题转化为一个无约束的优化问题,分析了问题的性质,给出了目标函数梯度向量的计算公式,提出了求解此问题的一个新算法,该方法计算公式简单,大大提高了计算效率。数值算例表明,这一算法具有良好的数值性态。
研究了无阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,分析了问题有解的条件,给出了解的表达式,并根据矩阵扰动理论给出了无阻尼结构系统鲁棒性的度量,由此提出了求解此问题的数值方法;研究了无阻尼结构系统保持对称性的特征结构配置问题,给出了此问题有解的条件与解的表达式,并考虑了在控制矩阵不给定的情况下,如何根据给定的特征结构求控制矩阵与反馈矩阵的方法;研究了无阻尼结构系统部分特征结构配置问题,即只改变系统的一部分特征值与相应的特征向量,而保持其余的特征结构不变,给出了此问题有解的条件与解的表达式,并给出了系统的鲁棒性度量,提出了求解此问题的两个算法:正交化向量方法与正交基方法;为了保持系统的对称性,利用输出反馈,给出了保持对称性的部分特征结构配置问题的一个特解;研究了一类结构动力模型修正问题,利用振动测量数据修正质量矩阵,使得修正后的动力学分析结果与相应的试验结果相一致。
研究了阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,利用阻尼结构系统鲁棒性的度量,提出了求解此问题的两个数值解法,新方法具有较好的数值稳定性。对于阻尼结构系统部分特征结构配置问题,利用矩阵扰动理论与特征值的灵敏度分析,给出了在测量的特征结构不完备时,如何选择要配置的若干个特征值与特征向量,并设计了一个数值算法来有效地求解此问题。对一般的特征结构配置问题,研究了对任意给定的特征值与特征向量,在控制矩阵不给定的情况下,如何设计控制矩阵与反馈矩阵的问题,提出了同时确定控制矩阵与反馈矩阵的方法。
According to the theory and methods of the algebraic inverse eigenvalue problems, in this dissertation, we study the eigenstructure assignment problems on linear systems, undamped structural systems and damped structural systems. The main contribution is as follows.
The robust eigenstructure assignment problem of linear system in a specified region is studied. The problem is formulated as an optimization problem. According to a Sun’s measure of robustness, we analyze the properties of this problem, and suggest the formula of the gradient vector of the objective function. Then a new algorithm for solving this problem is presented. Numerical examples show that the problem of robust pole assignment in a specified region can be solved effectively.
The eigenstructure assignment problems of undamped structural systems are considered. For the case that all the poles are prescribed, we give the conditions and the expressions of the solutions, and give a new measure of robustness according to the theory of matrix perturbation. Thus, we propose a numerical method for solving this problem. we study the preserve symmetric eigenstructure assignment problem, and give the conditions and the expressions of the solutions. We study the partial eigenstructure assignment problem of undamped structural systems, that is a few eigenvalues and eigenvectors of system are undesirable, and the rest of the eigenstructure invariant, and we give the conditions and the expressions of the solutions. According to a new measure of robustness, we give an algorithm for solving this problem. Moreover, in order to preserve the symmetry of the system, we consider the partial eigenstructure assignment problem using output feedback, and give a special solution of this problem. Lastly, we consider a structural dynamics model updating problem.
The eigenstructure assignment problems of damping structural systems are investigated. For the case that all the poles are prescribed, we give two algorithms for solving this problem. The procedure of this method is easy to realize, and have a good numerical stability. For the partial eigenstructure assignment problems of damping structural systems, according to the perturbation theory of matrices, we give a method for choosing the assigned eigenstructure, and propose an algorithm for solving this problem. For general eigenstructure assignment problem, in the case of the assigned eigenvectors are given arbitrarily, we give a method for getting the control matrix and the feedback matrices in the condition of the control matrix is unknown.
引文
[1] Gladwell G M L, Inverse problem in vibration, Second Edition, Kluwer Academic Publishers, Dordrecht, 2004
[2]周树荃,戴华,代数特征值反问题,郑州:河南科学技术出版社,1991
[3]傅志方,振动模态分析与参数识别,北京:机械工业出版社,2003
[4]荣见华,郑健龙,徐飞鸿,结构动力修改及优化设计,北京:人民交通出版社,2002
[5]欧进萍,结构振动控制:主动、半主动和智能控制,北京:科学出版社,2003
[6] Yao J T P, Concept of structure control, ASCE Journal of Structure Division,1972,98(ST7): 1567-1574
[7]张春巍,欧进萍,结构振动控制Benchmark研究发展综述,现代土木工程理论与实践,南京:河海大学出版社,2003
[8] Wonham W M, On pole assignment in multi-input controllable linear systems, IEEE Transactions on Automatic Control, 1967, 12: 660-665
[9] Wonham W M, Linear Multivariable Control: A Geometric Approach, 2nd ed, New York, Springer-Verlag, 1979
[10] Kailath T, Linear Systems, Prentice-Hall, 1980
[11] Miminis G S, Paige C C, A direct algorithm for pole assignment of time-invariant multi-input linear systems using state feedback, Automatica, 1988, 24: 343-356
[12] Miminis G S, Paige C C, An algorithm for pole assignment of time-invariant linear systems, Int J Control, 1982, 35: 341-354
[13] Miminis G S, Paige C C, A QR-like approach for the eigenvalue assignment problem, in Proceedings of the 2nd Hellenic Conference on Mathematics and Information, Athens, Greece, Sept, 1994
[14] Patel R V, Misra P, Numerical algorithm for eigenvalue assignment by state feedback, Proc IEEE, 1984, 72: 1755-1764
[15] Petkov P Hr, Chistov N D and Koustantinov M M, A computational algorithm for pole assignment of linear single-input systems, IEEE Transactions on Automatic Control, 1984, 29: 1045-1048
[16] Petkov P Hr, Koustantinov M M and Chistov N D, Computational algorithms for linear control systems: a brief survey, Int J Systems Sci, 1985, 16: 465-477
[17] Petkov P Hr, Chistov N D and Koustantinov M M, A computational algorithm for pole assignment of linear multi-input systems, IEEE Transactions on Automatic Control, 1986, 31: 1044-1047
[18] Varga A, A Schur method for pole assignment, IEEE Transactions on Automatic Control, 1981, 26: 517-519
[19] Chu E K, Pole assignment via the Schur form, Systems and Control Letters, 2007, 56: 303-314
[20] Kautsky J, Nichols N K and Van Dooren P, Robust pole assignment in linear state feedback, Int J Control, 1985, 41:1129-1155
[21] Tits A L, Yang Y, Globally convergent algorithm for robust pole assignment by state feedback, IEEE Transactions on Automatic Control, 1996, 41: 1432-1452
[22] Byers R, Nash S G, Approaches to robust pole assignment, Int J Control, 1989, 49:97-117
[23] Sun J G, On numerical methods for robust pole assignment in control system design, J Comp Math, 1987, 5(2):119-134
[24]孙继广,极点配置问题的注记,计算数学,1988,10:438-443
[25] Sun J G, Perturbation analysis of the pole assignment problem, SIAM J Matrix Anal Appl, 1996, 17: 313-331
[26] Varga A, Robust pole assignment via Sylvester equation based state feedback, Proceedings of the 2000 IEEE International Symposium on Computer-Aided Control System Design Anchorage, Alaska, USA, 2000 25-27
[27] Chu E K, A pole-assignment algorithm for linear state feedback, Systems and Control Letter, 1986, 7: 289-299
[28] Ramadan M, An algorithm for the multi-input complex eigenvalue assignment problem, Applied Mathematics and Computation, 2003, 140: 455-473
[29] Gourishankar V, Ramar K, Pole assignment with minimum eigenvalue sensitivity to plant parameter variation, Int J Control, 1976, 23: 493-504
[30] Juang J N, Lim K B and Junkins J L, Robust eigensystem assignment for flexible structure, Journal of Guidance, Control and Dynamics, 1989, 12: 381-387
[31] Andry A N, Jr Shapiro E Y and Chung J C, Eigenstructure assignment for linear systems, IEEE Trans on Aerospace and Electronic Systems, 1983,19: 711-729
[32] White B A, Eigenstructure assignment: a survey, Journal of Systems and Control Engineering, 1995, 209: 1-11
[33] Saad Y, Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Transactions on Automatic Control, 1988, 33: 290-297
[34] Datta B N, Saad Y, Arnoldi methods for large Sylvester-like observer matrix equations and an associated algorithm for partial spectrum assignment, Linear Algebra Appl, 1991, 154-156: 225-244
[35] Datta B N, Sarkissian D, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proc MTNS'2002, Notre Dame, Aug 2002
[36] Nichols N K, Robustness in partial pole placement, IEEE Transactions on Automatic Control, 1987,32: 728-732
[37] Misra P, Patel R V, Numerical algorithms for eigenvalue assignment by constant and dynamic output feedback, IEEE Transactions on Automatic Control, 1989,34: 579-588
[38]陈春晖,输出反馈极点配置问题的一个算法,计算数学,1988,2:138-145
[39] Chu E K, Nichols N K and Kausky J, Robust pole assignment for output feedback, Proc 4th IMA Conference on Control Theory, 1984
[40] Chu E K, Approximate pole assignment, Int J Control, 1993, 58: 471-484
[41]陈春晖,关于鲁棒的输出反馈极点配置问题的算法,计算数学,1988,1:59-67
[42] Sun J G, On numerical methods for robust pole assignment in control system design (Ⅱ), J Comp Math, 1987, 5(4): 352-363
[43] Juang Y T, Hong Z C and Wang Y T, Lyapunov approach to robust pole-assignment analysis, Int J Control, 1989, 921-927
[44]刘志东,极点配置在指定区域的一种鲁棒性分析方法,黑龙江自动化技术与应用,1994,13:1-3
[45] Syrmos V L, Lewis F L, Robust eigenvalue assignment for generalized systems, Automatica, 1992, 28: 1223-1228
[46] Kautsky J, Nichols N K, Algorithms for robust pole assignment in singular systems, Proceedings of the American Control Conference, 1986, 433-436
[47] Gobb R G, Liebst B S, Structural damage identification using assignment partial eigenstructure, AIAA Journal, 1997, 35: 152-158
[48] Elsner L, Sun J G, Perturbation theorems for the generalized eigenvalue problem, Linear Algebra Appl, 1982, 48: 341-357
[49] Higham D J, Higham L J, Structured backward error and condition of generalized eigenvalue problems, SIAM J Matrix Anal Appl, 1999, 20: 493-512
[50] Stewart G W, Perturbation Theory for the Generalized Eigenvalue Problem, New York Academic Press, 1978
[51] Stewart G W, On the sensitivity of the eigenvalue problem Ax =λBx, SIAM J Numer Anal, 1972, 9: 669-686
[52] Fletcher L R, Kausky J, Nichols N K, Eigenstructure assignment in descriptor system, IEEE Transactions on Automatic Control, 1986, 31: 1138-1141
[53] Fahmy M M, O’Reilly J, Parametric eigenstructure assignment for continuous-time descriptorsystems, Int J Control, 1989, 49: 129-143
[54] Duan G R, Solution to matrix equation AV + BW = EVFand eigenstructure assignment for descriptor systems, Automatica, 1992, 25: 639-643
[55] Duan G R, Patton R J, Eigenstructure assignment in descriptor system via state feedback—a new complete parametric approach, Int J Systems Science, 1998, 29: 167-178
[56] Duan G R, Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control, Int J control, 1998, 65: 663-694
[57] Fletcher, L R, Eigenstructure assignment by output feedback in descriptor systems, IEE Proc Part D: Control Theory and Applications, 1988, 135: 302-308
[58] Duan G R, Eigenstructure assignment in descriptor systems via output feedbak: a new complete parametric approach, Int J Control, 1997, 72: 345-364
[59] Duan G R, Patton R J, Robust pole assignment in descriptor systems via proportional plus partial derivative state feedback, Int J Control, 1999, 72: 1193-1203
[60] Vagar A, A numerical reliable approach to robust pole assignment for descriptor systems, Future Generation Computer Systems, 2003, 19: 1221-1230
[61] Balas M J, Trends in large space structure control theory: fondest hopes wildest dreams, IEEE Transactions on Automatic Control, 1982, 27: 522-535
[62] Bhaya A, Desoer C, On the design of large flexible space structures, IEEE Transactions on Automatic Control, 1985, 30: 1118-1120
[63] Joshi S M, Control of large flexible space structures, Lecture Notes in Control and Inform Sci, 1989, 131, Berlin, Springer-Verlag
[64] Meirovitch L, Baruh H and Oz H, A comparison of control techniques for large flexible systems, Journal of Guidance, Contorl and Dynamics, 1983, 6: 302-310
[65] Clough R W, Mojtahedi S, Earthquake response analysis condidering non-proportional damping, Earthquake Engrg Structural Dynam, 1976, 4: 489-496
[66] Smith H A, Singh R K and Sorensen D C, Formulation and solution of the non-linear damped eigenvalue problem for skeletal systems, Internat J Numer Methods Engrg, 1995, 38, 3071-3085
[67] Laub A J, Arnold W F, Controllability and observability criteria for multivariate linear second order models, IEEE Transactions on Automatic Control, 1984, 29: 163-165
[68] Inman D J, Kress A, Eigenstructure assignment via inverse eigenvalue methods, AIAA J Guidance, Control and Dynamics, 1995, 18: 625-627
[69] Duan G R, Liu G P, Complete parametric approach for eigenstructure assignment in a class of second-order linear systems , Automatica, 2002, 38 : 725-729
[70]王国胜,段广仁,二阶动力学系统输出反馈特征结构配置,系统工程与电子技术, 2004, 26 (8): 1080-1083
[71] Chu E K, Datta B N, Numerically robust pole assignment for second-order Systems, Int J Control, 1996, 64: 1113-1127
[72] Chu E K, Pole assignment for second-order systems, Mechanical Systems and Signal Processing, 2002, 16: 39-59
[73] Juang J, Maghami P G, Robust eigensystem assignment for second-order dynamics systems, Mechanics and Control of Large Flexible Structures, Progress in Astronautics and Aeronautics, 1990, 129(Washington DC:AIAA): 373-388
[74] Nichols N K, Kautsky J, Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case, SIAM J Matrix Anal and Appl, 2001, 23 : 77-102
[75] Tisseur F, Backward error and condition of polynomial eigenvalue problems, Lin Algebra Appl, 2000, 339: 309-361
[76] Langer H, Najman B and Veselic K, Perturbation of the eigenvalues of quadratic matrix polynomials, SIAM J Matrix Anal Appl, 1992, 13: 474-489
[77] Radjabalipour M, Salem A, On eigenvalues of quadratic matrix polynomials and their perturbations, SIAM J Matrix Anal Appl, 1996, 17: 563-569
[78] Gohberg I, Lancaster P, Rodman L, Matrix Polynomials, New York, Academic Press, 1982
[79] Chan H C, Lam J and Ho D W C, Robust eigenvalue assignment in second-order systems: A gradient flow approach, Optim Control Appl Methods, 1997, 18: 283-296
[80] Henrion D, Sebek M and Kucera V, Robust pole placement for second-order systems: an LMI approach, Kybernetika, 2005, 41 (1): 1-14
[81] Datta B N, Numerical Methods for Linear Control Systems Design and Analysis, Elsevier Academic Press, 2003
[82] Datta B N, Elhay S and Ram Y, Orthogonality and partial pole assignment for the symmetric definite quadratic pencil, Linear Algebra and its Applications, 1997, 257: 29-48
[83] Datta B N, Elhay S and Ram Y, An algorithm for the partial multi-input pole assignment of a second-order control system, Proc Conference on Decision and Control, 1996, 2025-2029
[84] Datta B N, Sarkissian D R, Theory and computations of some inverse eigenvalue problems for the quadratic pencil, Contemporary Mathematics Volume Structured Matrices in Operator Theory, Control, Signal and Image Processing, American Mathematical Society, 2001,280: 221-240
[85] Datta B N, Sarkissian D R, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proc. MTNS'2002 , Notre Dame, Aug 2002
[86] Datta B N, Elhay S and Ram Y M et al, Partial eigenstructure assignment for the quadratic pencil , J Sound and Vibration, 2000, 230: 101-110
[87] Lin W W, Wang J N, Partial pole assignment for the quadratic pencil by output feedback control with feedback designs, Numerical Linear Algebra with Applications, 2005, 12, 967-979
[88] Zimmerman D, Widengren M, Correcting finite element models using a symmetric eignenstructure assignment technique , AIAA Journal, 1990, 28(9): 1670-1676
[89] Carvalho J, Datta B N and Lin W W et al, Symmetric preserving eigenvalue embedding in finite element model updating of vibrating structures, J Sound and Vibration, 2006, 290(3-5): 839-864
[90] Guo Y C, Lin W W, Xu S F, A new model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment, AIAA Journal, 2005, 43 (12): 2593-2598
[91] Mottershead J E, Friswell M I, Model updating in structural dynamics: a survey, J Sound and Vibration, 1993, 167: 347-375
[92] Qian J, Xu S F, Robust partial eigenvalue assignment problem for the second-order system, J Sound and Vibration , 2005, 282: 937-948
[93]钱江,极点配置问题的数值解法,北京大学博士学位论文,2004
[94] Datta B N, Ram Y and Sarkissian D, Single-input partial pole-placement for gyroscopic operator pencil, Proc Mathematical Theory of Networks and Systems , 2000
[95] Datta B N, Ram Y and Sarkissian D, Multi-input partial pole-placement for undamped gyroscopic distributed parameter systems, Proc IEEE Conference on Decision and Control, 2000, 4661-4665
[96] Datta B N, Ram Y and Sarkissian D, Multi-input partial pole placement for distributed parameter gyroscopic systems, Proc IEEE International Conference on Decision and Control , Sidney, Dec 2000
[97] Datta B N, Sarkissian D, Feedback control in distributed parameter gyroscopic systems : a solution of the partial eigenvalue assignment problem, Mechanical Systems and Signal Processing , , 2001, 16: 3-17
[98] Lin W W, Wang J N, Partial pole assignment for the vibrating system with aerodynamic effect, Numerical Linear Algebra with Applications, 2004, 11: 41–58
[99] Datta B N, Lin W W and Wang J N, Robust partial pole assignment for the vibrating system with aerodynamic effect, IEEE Transactions on Automatic Control, 2006, 51(12): 1979-1984
[100] Xu S F, An Introduction to Inverse Algebraic Eigenvalue Problems, Peking University Press,Beijing, 1998
[101]黄红选,韩继业,数学规划,北京:清华大学出版社,2006
[102]孙继广,矩阵扰动分析,北京:科学出版社,2001
[103]马扣根,顾仲权,最优极点配置法在梁式结构振动主动控制中的应用,振动与冲击,1991,3: 63-66
[104]张德文,魏阜旋,模型修正与破损诊断,北京:科学出版社,1999
[105]戴华,矩阵论,北京:科学出版社,2001
[106]解惠青,特征值问题的灵敏度分析,南京航空航天大学博士学位论文,2003
[107]袁永新,结构动力模型修正中的若干问题研究,南京航空航天大学博士学位论文,2006
[108] Paige C C, Saunders M A, Towards a generalized singular value decomposition, SIAM J Numer Anal, 1981, 18: 398~405
[109] Golub G H, Van Loan C F, Matrix Computations, The Johns Hopkins University Press, Baltimore, 1996
[110] Aubin J P, Appliced Functional Analysis, John Wiley & Sons, Inc, 1979
[111] Luenberger D G, Introduction to linear and nonlinear programming, Addison-Wesley Publishing Company, Inc, 1973
[112] Horst P, Relations among on m set of measures, Psychometrika, 1961, 26: 129-149
[113]王国胜,动力学系统特征结构配置设计及其应用,哈尔滨工业大学博士学位论文,2004
[114] Albert A, Conditions for positive and nonnegative in terms of pseudoinverse, SIAM J Appl Math, 1969, 17: 434-440
[2]周树荃,戴华,代数特征值反问题,郑州:河南科学技术出版社,1991
[3]傅志方,振动模态分析与参数识别,北京:机械工业出版社,2003
[4]荣见华,郑健龙,徐飞鸿,结构动力修改及优化设计,北京:人民交通出版社,2002
[5]欧进萍,结构振动控制:主动、半主动和智能控制,北京:科学出版社,2003
[6] Yao J T P, Concept of structure control, ASCE Journal of Structure Division,1972,98(ST7): 1567-1574
[7]张春巍,欧进萍,结构振动控制Benchmark研究发展综述,现代土木工程理论与实践,南京:河海大学出版社,2003
[8] Wonham W M, On pole assignment in multi-input controllable linear systems, IEEE Transactions on Automatic Control, 1967, 12: 660-665
[9] Wonham W M, Linear Multivariable Control: A Geometric Approach, 2nd ed, New York, Springer-Verlag, 1979
[10] Kailath T, Linear Systems, Prentice-Hall, 1980
[11] Miminis G S, Paige C C, A direct algorithm for pole assignment of time-invariant multi-input linear systems using state feedback, Automatica, 1988, 24: 343-356
[12] Miminis G S, Paige C C, An algorithm for pole assignment of time-invariant linear systems, Int J Control, 1982, 35: 341-354
[13] Miminis G S, Paige C C, A QR-like approach for the eigenvalue assignment problem, in Proceedings of the 2nd Hellenic Conference on Mathematics and Information, Athens, Greece, Sept, 1994
[14] Patel R V, Misra P, Numerical algorithm for eigenvalue assignment by state feedback, Proc IEEE, 1984, 72: 1755-1764
[15] Petkov P Hr, Chistov N D and Koustantinov M M, A computational algorithm for pole assignment of linear single-input systems, IEEE Transactions on Automatic Control, 1984, 29: 1045-1048
[16] Petkov P Hr, Koustantinov M M and Chistov N D, Computational algorithms for linear control systems: a brief survey, Int J Systems Sci, 1985, 16: 465-477
[17] Petkov P Hr, Chistov N D and Koustantinov M M, A computational algorithm for pole assignment of linear multi-input systems, IEEE Transactions on Automatic Control, 1986, 31: 1044-1047
[18] Varga A, A Schur method for pole assignment, IEEE Transactions on Automatic Control, 1981, 26: 517-519
[19] Chu E K, Pole assignment via the Schur form, Systems and Control Letters, 2007, 56: 303-314
[20] Kautsky J, Nichols N K and Van Dooren P, Robust pole assignment in linear state feedback, Int J Control, 1985, 41:1129-1155
[21] Tits A L, Yang Y, Globally convergent algorithm for robust pole assignment by state feedback, IEEE Transactions on Automatic Control, 1996, 41: 1432-1452
[22] Byers R, Nash S G, Approaches to robust pole assignment, Int J Control, 1989, 49:97-117
[23] Sun J G, On numerical methods for robust pole assignment in control system design, J Comp Math, 1987, 5(2):119-134
[24]孙继广,极点配置问题的注记,计算数学,1988,10:438-443
[25] Sun J G, Perturbation analysis of the pole assignment problem, SIAM J Matrix Anal Appl, 1996, 17: 313-331
[26] Varga A, Robust pole assignment via Sylvester equation based state feedback, Proceedings of the 2000 IEEE International Symposium on Computer-Aided Control System Design Anchorage, Alaska, USA, 2000 25-27
[27] Chu E K, A pole-assignment algorithm for linear state feedback, Systems and Control Letter, 1986, 7: 289-299
[28] Ramadan M, An algorithm for the multi-input complex eigenvalue assignment problem, Applied Mathematics and Computation, 2003, 140: 455-473
[29] Gourishankar V, Ramar K, Pole assignment with minimum eigenvalue sensitivity to plant parameter variation, Int J Control, 1976, 23: 493-504
[30] Juang J N, Lim K B and Junkins J L, Robust eigensystem assignment for flexible structure, Journal of Guidance, Control and Dynamics, 1989, 12: 381-387
[31] Andry A N, Jr Shapiro E Y and Chung J C, Eigenstructure assignment for linear systems, IEEE Trans on Aerospace and Electronic Systems, 1983,19: 711-729
[32] White B A, Eigenstructure assignment: a survey, Journal of Systems and Control Engineering, 1995, 209: 1-11
[33] Saad Y, Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Transactions on Automatic Control, 1988, 33: 290-297
[34] Datta B N, Saad Y, Arnoldi methods for large Sylvester-like observer matrix equations and an associated algorithm for partial spectrum assignment, Linear Algebra Appl, 1991, 154-156: 225-244
[35] Datta B N, Sarkissian D, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proc MTNS'2002, Notre Dame, Aug 2002
[36] Nichols N K, Robustness in partial pole placement, IEEE Transactions on Automatic Control, 1987,32: 728-732
[37] Misra P, Patel R V, Numerical algorithms for eigenvalue assignment by constant and dynamic output feedback, IEEE Transactions on Automatic Control, 1989,34: 579-588
[38]陈春晖,输出反馈极点配置问题的一个算法,计算数学,1988,2:138-145
[39] Chu E K, Nichols N K and Kausky J, Robust pole assignment for output feedback, Proc 4th IMA Conference on Control Theory, 1984
[40] Chu E K, Approximate pole assignment, Int J Control, 1993, 58: 471-484
[41]陈春晖,关于鲁棒的输出反馈极点配置问题的算法,计算数学,1988,1:59-67
[42] Sun J G, On numerical methods for robust pole assignment in control system design (Ⅱ), J Comp Math, 1987, 5(4): 352-363
[43] Juang Y T, Hong Z C and Wang Y T, Lyapunov approach to robust pole-assignment analysis, Int J Control, 1989, 921-927
[44]刘志东,极点配置在指定区域的一种鲁棒性分析方法,黑龙江自动化技术与应用,1994,13:1-3
[45] Syrmos V L, Lewis F L, Robust eigenvalue assignment for generalized systems, Automatica, 1992, 28: 1223-1228
[46] Kautsky J, Nichols N K, Algorithms for robust pole assignment in singular systems, Proceedings of the American Control Conference, 1986, 433-436
[47] Gobb R G, Liebst B S, Structural damage identification using assignment partial eigenstructure, AIAA Journal, 1997, 35: 152-158
[48] Elsner L, Sun J G, Perturbation theorems for the generalized eigenvalue problem, Linear Algebra Appl, 1982, 48: 341-357
[49] Higham D J, Higham L J, Structured backward error and condition of generalized eigenvalue problems, SIAM J Matrix Anal Appl, 1999, 20: 493-512
[50] Stewart G W, Perturbation Theory for the Generalized Eigenvalue Problem, New York Academic Press, 1978
[51] Stewart G W, On the sensitivity of the eigenvalue problem Ax =λBx, SIAM J Numer Anal, 1972, 9: 669-686
[52] Fletcher L R, Kausky J, Nichols N K, Eigenstructure assignment in descriptor system, IEEE Transactions on Automatic Control, 1986, 31: 1138-1141
[53] Fahmy M M, O’Reilly J, Parametric eigenstructure assignment for continuous-time descriptorsystems, Int J Control, 1989, 49: 129-143
[54] Duan G R, Solution to matrix equation AV + BW = EVFand eigenstructure assignment for descriptor systems, Automatica, 1992, 25: 639-643
[55] Duan G R, Patton R J, Eigenstructure assignment in descriptor system via state feedback—a new complete parametric approach, Int J Systems Science, 1998, 29: 167-178
[56] Duan G R, Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control, Int J control, 1998, 65: 663-694
[57] Fletcher, L R, Eigenstructure assignment by output feedback in descriptor systems, IEE Proc Part D: Control Theory and Applications, 1988, 135: 302-308
[58] Duan G R, Eigenstructure assignment in descriptor systems via output feedbak: a new complete parametric approach, Int J Control, 1997, 72: 345-364
[59] Duan G R, Patton R J, Robust pole assignment in descriptor systems via proportional plus partial derivative state feedback, Int J Control, 1999, 72: 1193-1203
[60] Vagar A, A numerical reliable approach to robust pole assignment for descriptor systems, Future Generation Computer Systems, 2003, 19: 1221-1230
[61] Balas M J, Trends in large space structure control theory: fondest hopes wildest dreams, IEEE Transactions on Automatic Control, 1982, 27: 522-535
[62] Bhaya A, Desoer C, On the design of large flexible space structures, IEEE Transactions on Automatic Control, 1985, 30: 1118-1120
[63] Joshi S M, Control of large flexible space structures, Lecture Notes in Control and Inform Sci, 1989, 131, Berlin, Springer-Verlag
[64] Meirovitch L, Baruh H and Oz H, A comparison of control techniques for large flexible systems, Journal of Guidance, Contorl and Dynamics, 1983, 6: 302-310
[65] Clough R W, Mojtahedi S, Earthquake response analysis condidering non-proportional damping, Earthquake Engrg Structural Dynam, 1976, 4: 489-496
[66] Smith H A, Singh R K and Sorensen D C, Formulation and solution of the non-linear damped eigenvalue problem for skeletal systems, Internat J Numer Methods Engrg, 1995, 38, 3071-3085
[67] Laub A J, Arnold W F, Controllability and observability criteria for multivariate linear second order models, IEEE Transactions on Automatic Control, 1984, 29: 163-165
[68] Inman D J, Kress A, Eigenstructure assignment via inverse eigenvalue methods, AIAA J Guidance, Control and Dynamics, 1995, 18: 625-627
[69] Duan G R, Liu G P, Complete parametric approach for eigenstructure assignment in a class of second-order linear systems , Automatica, 2002, 38 : 725-729
[70]王国胜,段广仁,二阶动力学系统输出反馈特征结构配置,系统工程与电子技术, 2004, 26 (8): 1080-1083
[71] Chu E K, Datta B N, Numerically robust pole assignment for second-order Systems, Int J Control, 1996, 64: 1113-1127
[72] Chu E K, Pole assignment for second-order systems, Mechanical Systems and Signal Processing, 2002, 16: 39-59
[73] Juang J, Maghami P G, Robust eigensystem assignment for second-order dynamics systems, Mechanics and Control of Large Flexible Structures, Progress in Astronautics and Aeronautics, 1990, 129(Washington DC:AIAA): 373-388
[74] Nichols N K, Kautsky J, Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case, SIAM J Matrix Anal and Appl, 2001, 23 : 77-102
[75] Tisseur F, Backward error and condition of polynomial eigenvalue problems, Lin Algebra Appl, 2000, 339: 309-361
[76] Langer H, Najman B and Veselic K, Perturbation of the eigenvalues of quadratic matrix polynomials, SIAM J Matrix Anal Appl, 1992, 13: 474-489
[77] Radjabalipour M, Salem A, On eigenvalues of quadratic matrix polynomials and their perturbations, SIAM J Matrix Anal Appl, 1996, 17: 563-569
[78] Gohberg I, Lancaster P, Rodman L, Matrix Polynomials, New York, Academic Press, 1982
[79] Chan H C, Lam J and Ho D W C, Robust eigenvalue assignment in second-order systems: A gradient flow approach, Optim Control Appl Methods, 1997, 18: 283-296
[80] Henrion D, Sebek M and Kucera V, Robust pole placement for second-order systems: an LMI approach, Kybernetika, 2005, 41 (1): 1-14
[81] Datta B N, Numerical Methods for Linear Control Systems Design and Analysis, Elsevier Academic Press, 2003
[82] Datta B N, Elhay S and Ram Y, Orthogonality and partial pole assignment for the symmetric definite quadratic pencil, Linear Algebra and its Applications, 1997, 257: 29-48
[83] Datta B N, Elhay S and Ram Y, An algorithm for the partial multi-input pole assignment of a second-order control system, Proc Conference on Decision and Control, 1996, 2025-2029
[84] Datta B N, Sarkissian D R, Theory and computations of some inverse eigenvalue problems for the quadratic pencil, Contemporary Mathematics Volume Structured Matrices in Operator Theory, Control, Signal and Image Processing, American Mathematical Society, 2001,280: 221-240
[85] Datta B N, Sarkissian D R, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proc. MTNS'2002 , Notre Dame, Aug 2002
[86] Datta B N, Elhay S and Ram Y M et al, Partial eigenstructure assignment for the quadratic pencil , J Sound and Vibration, 2000, 230: 101-110
[87] Lin W W, Wang J N, Partial pole assignment for the quadratic pencil by output feedback control with feedback designs, Numerical Linear Algebra with Applications, 2005, 12, 967-979
[88] Zimmerman D, Widengren M, Correcting finite element models using a symmetric eignenstructure assignment technique , AIAA Journal, 1990, 28(9): 1670-1676
[89] Carvalho J, Datta B N and Lin W W et al, Symmetric preserving eigenvalue embedding in finite element model updating of vibrating structures, J Sound and Vibration, 2006, 290(3-5): 839-864
[90] Guo Y C, Lin W W, Xu S F, A new model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment, AIAA Journal, 2005, 43 (12): 2593-2598
[91] Mottershead J E, Friswell M I, Model updating in structural dynamics: a survey, J Sound and Vibration, 1993, 167: 347-375
[92] Qian J, Xu S F, Robust partial eigenvalue assignment problem for the second-order system, J Sound and Vibration , 2005, 282: 937-948
[93]钱江,极点配置问题的数值解法,北京大学博士学位论文,2004
[94] Datta B N, Ram Y and Sarkissian D, Single-input partial pole-placement for gyroscopic operator pencil, Proc Mathematical Theory of Networks and Systems , 2000
[95] Datta B N, Ram Y and Sarkissian D, Multi-input partial pole-placement for undamped gyroscopic distributed parameter systems, Proc IEEE Conference on Decision and Control, 2000, 4661-4665
[96] Datta B N, Ram Y and Sarkissian D, Multi-input partial pole placement for distributed parameter gyroscopic systems, Proc IEEE International Conference on Decision and Control , Sidney, Dec 2000
[97] Datta B N, Sarkissian D, Feedback control in distributed parameter gyroscopic systems : a solution of the partial eigenvalue assignment problem, Mechanical Systems and Signal Processing , , 2001, 16: 3-17
[98] Lin W W, Wang J N, Partial pole assignment for the vibrating system with aerodynamic effect, Numerical Linear Algebra with Applications, 2004, 11: 41–58
[99] Datta B N, Lin W W and Wang J N, Robust partial pole assignment for the vibrating system with aerodynamic effect, IEEE Transactions on Automatic Control, 2006, 51(12): 1979-1984
[100] Xu S F, An Introduction to Inverse Algebraic Eigenvalue Problems, Peking University Press,Beijing, 1998
[101]黄红选,韩继业,数学规划,北京:清华大学出版社,2006
[102]孙继广,矩阵扰动分析,北京:科学出版社,2001
[103]马扣根,顾仲权,最优极点配置法在梁式结构振动主动控制中的应用,振动与冲击,1991,3: 63-66
[104]张德文,魏阜旋,模型修正与破损诊断,北京:科学出版社,1999
[105]戴华,矩阵论,北京:科学出版社,2001
[106]解惠青,特征值问题的灵敏度分析,南京航空航天大学博士学位论文,2003
[107]袁永新,结构动力模型修正中的若干问题研究,南京航空航天大学博士学位论文,2006
[108] Paige C C, Saunders M A, Towards a generalized singular value decomposition, SIAM J Numer Anal, 1981, 18: 398~405
[109] Golub G H, Van Loan C F, Matrix Computations, The Johns Hopkins University Press, Baltimore, 1996
[110] Aubin J P, Appliced Functional Analysis, John Wiley & Sons, Inc, 1979
[111] Luenberger D G, Introduction to linear and nonlinear programming, Addison-Wesley Publishing Company, Inc, 1973
[112] Horst P, Relations among on m set of measures, Psychometrika, 1961, 26: 129-149
[113]王国胜,动力学系统特征结构配置设计及其应用,哈尔滨工业大学博士学位论文,2004
[114] Albert A, Conditions for positive and nonnegative in terms of pseudoinverse, SIAM J Appl Math, 1969, 17: 434-440