不确定结构（系统）控制的性能分析与综合
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摘要
由于不确定性的客观存在,研究不确定性对结构与系统的性能影响程度,以及对不确定性结构和系统控制方法的综合分析与设计越来越受到科学界和工程界的高度重视,并且已成为当前结构力学研究领域和控制理论研究领域中的热点问题之一。本文分别对不确定结构的静力和动力响应分析、不确定结构和系统的控制性能分析与控制器的综合设计等方面进行了分析与研究,主要工作内容如下:
1、模糊性区间参数桁架结构的静力和动力分析
考虑具有模糊性区间参数的桁架结构,用具有区间值隶属函数的区间因子表征参数的不确定性,分别建立了桁架结构的静力学有限元方程和动力学方程。基于区间数学和区间值模糊集合的相关理论,推导出了模糊性区间参数桁架结构静力位移、单元应力和固有频率的求解公式,并且对相关计算结果的区间值隶属函数的求解给出了一种离散数值解法。仿真算例结果表明,该方法可以考察每一参数的不确定性对结构静力和动力分析结果的影响,其分析与求解的过程较为简便易行,且计算量小、计算效率较高。
2、随机参数结构最优控制的闭环响应分析
分别对物理参数和几何参数均具有随机性的随机桁架结构,以及物理参数为随机性的随机平面梁结构,在确定性参数结构的基础上,在模态坐标下对其降阶进行最优控制。基于近似离散化的方法得到了结构最优控制闭环响应的近似解。考虑结构参数的随机性导致的状态方程中矩阵参数的随机性,对上述随机结构最优控制的闭环响应进行了研究分析,揭示了其结构各参数的随机性与结构最优控制闭环响应随机性之间的关系。通过算例考察了结构各个参数的随机性对结构最优控制闭环响应随机性的影响,获得了许多有意义的结论。经与Monte Carlo数值模拟法的结果比较,验证了文中理论分析和计算方法的正确性。
3、随机智能梁结构振动控制的特征值分析
建立了压电智能梁结构的控制模型,在模态坐标下采用极点配置法对其进行振动控制。考虑智能梁结构物理和几何参数的随机性,从随机智能梁结构刚度矩阵和质量矩阵中提取出随机因子并将其引入振动控制方程,用随机因子来表示控制方程中参数的随机性。并利用代数综合法推导出随机智能梁结构振动控制的开环和闭环特征值的均值和方差的表达式。同时,应用3σ准则对随机参数智能梁结构振动控制的闭环稳定性进行了分析,得出了稳定性的判据。仿真算例表明:本文提出的基于概率的随机智能梁结构振动控制特征值的分析和求解方法是可行的,且计算结果表明,对于特征值实部和虚部分散性的影响,几何参数的作用要大于物理参数的作用。
4、不确定智能结构振动的鲁棒PID控制及其时滞稳定性分析
对存在参数不确定性的智能梁结构的振动控制,利用解耦的模态坐标,结合常规PID控制、保成本鲁棒控制以及H∞控制的优点,提出一种鲁棒PID控制的设计方法,并给出了必要的理论依据及具体的推导和论证过程。该方法将PID控制器的参数整定问题转化为线性矩阵不等式凸优化问题的求解,从而针对不确定结构的振动控制设计出一种复合PID控制器。同时,考虑到实际中存在的时滞因素,分析了控制系统的时滞稳定性,得出了能使系统稳定的最大允许时滞量的求解方法。通过仿真算例可以看出,在允许的最大时滞量内,鲁棒PID控制算法能使系统保持稳定。而超出允许的最大时滞量时,控制系统将发散。此外,文中还得出了系统的抗干扰能力和允许的最大时滞量之间是相互制约的这一结论。从而为不确定智能结构的振动控制提供了一种新的设计思路和方法。
5、智能PID控制在不确定电弧炉系统中的应用研究
针对具有参数不确定性且三相电流耦合的电弧炉系统,设计了一种智能PID控制算法,该算法首先利用遗传算法离线优化控制器的参数,在获得初始最优参数后,结合专家经验和积分分离原则,设计出模糊推理规则在线实时整定PID参数。从仿真结果可以看出,对于电弧炉系统,本文提出的智能PID控制器不论是从系统的阶跃响应,抗干扰能力,解耦能力以及鲁棒性等方面,均显示出优良的控制性能。
Due to the uncertainty exists in practical, studying the influence of uncertainty to performance of structures or systems, and the synthesis analysis and design of control methods for uncertainty structures and systems are more and more important problems to scientists and engineers. These problems have been one of the focus researches in present structural mechanics and control theory field. In this dissertation, the static and dynamic responses of uncertainty structures, and the control performance and controller design of uncertainty systems are analyzed. The main research works can be described as follows.
1. The static responses and dynamic characteristics of truss analysis structures with fuzzy interval parameters
When the fuzziness of the truss structures with interval parameters was represented by the interval-valued membership function, the uncertainty of the interval variables was represented by fuzzy interval factors, and the interval variables were expressed as the product of their mean values and interval factors. And then, the static finite element equations and dynamic equations of the structure are built. Based on the interval analysis theory and interval-valued fuzzy sets theory, the explicit calculation expressions of structural displacement responses , stress response and natural frequencies are developed to truss structures with fuzzy interval parameters. The computational method for solving the interval-valued membership function of structural displacement response , stress response and natural frequencies are given. Feasibility and validity of the proposed method are illustrated by two numerical examples. The advantages of this method are that the effect of the uncertainty of one of the structural parameters on the uncertainty of the structural static response and natural frequencies can be reflected expediently and objectively. In additional, it is easy to realized the proposed method with small amount and high calculation efficient.
2. Closed-Loop Response Analysis of Optimal Vibration Control System with Stochastic Parameters
Based on mode coordinate, the optimal vibration control of truss and plane beam structures were designed. By using the approximately discrete method, the approximate solutions of structural closed-loop response are obtained. The approximate solutions can substitute the exact solutions. The randomness of physical and geometric dimensions parameters of truss structure and the randomness of physical of plane beam structure were considered and represented in the form of random factors. And then, the computational expressions of the mean value and the variance of closed-loop response of the stochastic parameters structure under the optimal vibration control are derived by means of the random variable’s functional moment method. Finally, the influences of the randomness of structural parameters on the structural closed-loop responses are analyzed by an example with the proposed method and the Monte Carlo method, which validate the feasibility of the proposed method.
3. Eigenvalues analysis of intelligent beam structure vibration control system with stochastic parameters
The control model of intelligent beam structure was built. And then, under the mode coordinate, the vibration control of intelligent beam was designed by using the method of pole allocation. Considering the randomness of intelligent beam structural physical and geometric dimensions parameters, the random factors were abstracted from the stiffness matrix and the mass matrix, and then, were introduced into the vibration control equation, so the randomness of parameters in the vibration control equation was represented by the random factors. By using the algebra synthesis method, the expressions of the mean value and the standard variance of the open-loop and closed-loop eigenvalues of vibration control equation were developed. The closed-loop stability of the vibration control equation of random structures was discussed and the stability criterion was obtained by the 3σcriterion. Finally, an example of intelligent cantilever beam structure was used to illustrate the feasibility of the proposed method, which show that the effect of the physical parameters on the eigenvalues are bigger than that of the geometric dimensions parameters.
4. Robust PID vibration control of uncertainty intelligent beam structures and its time-delay stability analysis
The design of the robust PID vibration control of uncertainty intelligent beam structures was studied. Considering the uncertainty of the structural mode damping ratio and mode frequency in a intelligent beam structure, and the excellent performance of PID control, guaranteed cost control and H∞control, a new method to design robust PID vibration control was presented, and the processes of derivation and demonstration are given. The optimal parameters of PID controller were obtained by solving a convex optimal problem of LMI. Considering the practical time-delay factors, the analysis of the time-delay stability of the robust PID vibration control system was studied and the value of maximum time-delay of the stable system was obtained. Finally, an example was used to illustrate the feasibility and validity of the method given here. From the example, we can conclude that the robust PID controller can keep the system stable within the range of maximum time-delay, furthermore, the anti-interference performance of system and the accepted value of maximum time-delay restraint each other.
5. Application of intelligent PID controller in an uncertainty arc furnace system
An intelligent PID controller is proposed for an arc furnace system with uncertainty parameters and three-phase current coupled . By using genetic algorithm with real number coding, a group of optimal parameters of this intelligent PID controller are obtained, which are used as the original values for the real-time tuning of PID parameters. Based on the principle of integral detached, a fuzzy decoupled inference is designed for the PID parameters real-time tuning to ensure that the system response has optimal dynamic and steady-state performances. The results of computer simulation show that the intelligent PID controller has the advantages of better dynamic, static, and robust performance over the conventional PID controllers in the uncertainty arc furnace control system.
1、模糊性区间参数桁架结构的静力和动力分析
考虑具有模糊性区间参数的桁架结构,用具有区间值隶属函数的区间因子表征参数的不确定性,分别建立了桁架结构的静力学有限元方程和动力学方程。基于区间数学和区间值模糊集合的相关理论,推导出了模糊性区间参数桁架结构静力位移、单元应力和固有频率的求解公式,并且对相关计算结果的区间值隶属函数的求解给出了一种离散数值解法。仿真算例结果表明,该方法可以考察每一参数的不确定性对结构静力和动力分析结果的影响,其分析与求解的过程较为简便易行,且计算量小、计算效率较高。
2、随机参数结构最优控制的闭环响应分析
分别对物理参数和几何参数均具有随机性的随机桁架结构,以及物理参数为随机性的随机平面梁结构,在确定性参数结构的基础上,在模态坐标下对其降阶进行最优控制。基于近似离散化的方法得到了结构最优控制闭环响应的近似解。考虑结构参数的随机性导致的状态方程中矩阵参数的随机性,对上述随机结构最优控制的闭环响应进行了研究分析,揭示了其结构各参数的随机性与结构最优控制闭环响应随机性之间的关系。通过算例考察了结构各个参数的随机性对结构最优控制闭环响应随机性的影响,获得了许多有意义的结论。经与Monte Carlo数值模拟法的结果比较,验证了文中理论分析和计算方法的正确性。
3、随机智能梁结构振动控制的特征值分析
建立了压电智能梁结构的控制模型,在模态坐标下采用极点配置法对其进行振动控制。考虑智能梁结构物理和几何参数的随机性,从随机智能梁结构刚度矩阵和质量矩阵中提取出随机因子并将其引入振动控制方程,用随机因子来表示控制方程中参数的随机性。并利用代数综合法推导出随机智能梁结构振动控制的开环和闭环特征值的均值和方差的表达式。同时,应用3σ准则对随机参数智能梁结构振动控制的闭环稳定性进行了分析,得出了稳定性的判据。仿真算例表明:本文提出的基于概率的随机智能梁结构振动控制特征值的分析和求解方法是可行的,且计算结果表明,对于特征值实部和虚部分散性的影响,几何参数的作用要大于物理参数的作用。
4、不确定智能结构振动的鲁棒PID控制及其时滞稳定性分析
对存在参数不确定性的智能梁结构的振动控制,利用解耦的模态坐标,结合常规PID控制、保成本鲁棒控制以及H∞控制的优点,提出一种鲁棒PID控制的设计方法,并给出了必要的理论依据及具体的推导和论证过程。该方法将PID控制器的参数整定问题转化为线性矩阵不等式凸优化问题的求解,从而针对不确定结构的振动控制设计出一种复合PID控制器。同时,考虑到实际中存在的时滞因素,分析了控制系统的时滞稳定性,得出了能使系统稳定的最大允许时滞量的求解方法。通过仿真算例可以看出,在允许的最大时滞量内,鲁棒PID控制算法能使系统保持稳定。而超出允许的最大时滞量时,控制系统将发散。此外,文中还得出了系统的抗干扰能力和允许的最大时滞量之间是相互制约的这一结论。从而为不确定智能结构的振动控制提供了一种新的设计思路和方法。
5、智能PID控制在不确定电弧炉系统中的应用研究
针对具有参数不确定性且三相电流耦合的电弧炉系统,设计了一种智能PID控制算法,该算法首先利用遗传算法离线优化控制器的参数,在获得初始最优参数后,结合专家经验和积分分离原则,设计出模糊推理规则在线实时整定PID参数。从仿真结果可以看出,对于电弧炉系统,本文提出的智能PID控制器不论是从系统的阶跃响应,抗干扰能力,解耦能力以及鲁棒性等方面,均显示出优良的控制性能。
Due to the uncertainty exists in practical, studying the influence of uncertainty to performance of structures or systems, and the synthesis analysis and design of control methods for uncertainty structures and systems are more and more important problems to scientists and engineers. These problems have been one of the focus researches in present structural mechanics and control theory field. In this dissertation, the static and dynamic responses of uncertainty structures, and the control performance and controller design of uncertainty systems are analyzed. The main research works can be described as follows.
1. The static responses and dynamic characteristics of truss analysis structures with fuzzy interval parameters
When the fuzziness of the truss structures with interval parameters was represented by the interval-valued membership function, the uncertainty of the interval variables was represented by fuzzy interval factors, and the interval variables were expressed as the product of their mean values and interval factors. And then, the static finite element equations and dynamic equations of the structure are built. Based on the interval analysis theory and interval-valued fuzzy sets theory, the explicit calculation expressions of structural displacement responses , stress response and natural frequencies are developed to truss structures with fuzzy interval parameters. The computational method for solving the interval-valued membership function of structural displacement response , stress response and natural frequencies are given. Feasibility and validity of the proposed method are illustrated by two numerical examples. The advantages of this method are that the effect of the uncertainty of one of the structural parameters on the uncertainty of the structural static response and natural frequencies can be reflected expediently and objectively. In additional, it is easy to realized the proposed method with small amount and high calculation efficient.
2. Closed-Loop Response Analysis of Optimal Vibration Control System with Stochastic Parameters
Based on mode coordinate, the optimal vibration control of truss and plane beam structures were designed. By using the approximately discrete method, the approximate solutions of structural closed-loop response are obtained. The approximate solutions can substitute the exact solutions. The randomness of physical and geometric dimensions parameters of truss structure and the randomness of physical of plane beam structure were considered and represented in the form of random factors. And then, the computational expressions of the mean value and the variance of closed-loop response of the stochastic parameters structure under the optimal vibration control are derived by means of the random variable’s functional moment method. Finally, the influences of the randomness of structural parameters on the structural closed-loop responses are analyzed by an example with the proposed method and the Monte Carlo method, which validate the feasibility of the proposed method.
3. Eigenvalues analysis of intelligent beam structure vibration control system with stochastic parameters
The control model of intelligent beam structure was built. And then, under the mode coordinate, the vibration control of intelligent beam was designed by using the method of pole allocation. Considering the randomness of intelligent beam structural physical and geometric dimensions parameters, the random factors were abstracted from the stiffness matrix and the mass matrix, and then, were introduced into the vibration control equation, so the randomness of parameters in the vibration control equation was represented by the random factors. By using the algebra synthesis method, the expressions of the mean value and the standard variance of the open-loop and closed-loop eigenvalues of vibration control equation were developed. The closed-loop stability of the vibration control equation of random structures was discussed and the stability criterion was obtained by the 3σcriterion. Finally, an example of intelligent cantilever beam structure was used to illustrate the feasibility of the proposed method, which show that the effect of the physical parameters on the eigenvalues are bigger than that of the geometric dimensions parameters.
4. Robust PID vibration control of uncertainty intelligent beam structures and its time-delay stability analysis
The design of the robust PID vibration control of uncertainty intelligent beam structures was studied. Considering the uncertainty of the structural mode damping ratio and mode frequency in a intelligent beam structure, and the excellent performance of PID control, guaranteed cost control and H∞control, a new method to design robust PID vibration control was presented, and the processes of derivation and demonstration are given. The optimal parameters of PID controller were obtained by solving a convex optimal problem of LMI. Considering the practical time-delay factors, the analysis of the time-delay stability of the robust PID vibration control system was studied and the value of maximum time-delay of the stable system was obtained. Finally, an example was used to illustrate the feasibility and validity of the method given here. From the example, we can conclude that the robust PID controller can keep the system stable within the range of maximum time-delay, furthermore, the anti-interference performance of system and the accepted value of maximum time-delay restraint each other.
5. Application of intelligent PID controller in an uncertainty arc furnace system
An intelligent PID controller is proposed for an arc furnace system with uncertainty parameters and three-phase current coupled . By using genetic algorithm with real number coding, a group of optimal parameters of this intelligent PID controller are obtained, which are used as the original values for the real-time tuning of PID parameters. Based on the principle of integral detached, a fuzzy decoupled inference is designed for the PID parameters real-time tuning to ensure that the system response has optimal dynamic and steady-state performances. The results of computer simulation show that the intelligent PID controller has the advantages of better dynamic, static, and robust performance over the conventional PID controllers in the uncertainty arc furnace control system.
引文
[1]王光远.论不确定性结构力学的进展[J].力学进展, 2002, 32(2): 205-211.
[2]王清印,刘志勇,赵秀恒.广义不确定性系统概念及其基本原理[J].华中科技大学学报(自然科学版), 2005, 33(1): 531-534.
[3]钟万勰.计算结构力学与最优控制[M].大连:大连理工大学出版社, 1993.
[4]闻邦椿,刘树英,何琼.振动机械的理论与动态设计方法.北京:机械工业出版社, 2001.
[5] Chen J J, Che J W, Sun H A, et al. Probabilistic dynamic analysis of truss structures[J]. Structural Engineering & Mechanics, 2002, 13(2): 231-239.
[6] Dai J, Chen J J, Li Y G. Dynamic response optimization design for engineering structures based on reliability[J]. Applied Mathematics and Mechanics, 2003, 24(1): 43-52.
[7] Gao W, Chen J J, Ma H B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics, 2003, 15(2): 239-248.
[8]李杰.随机结构系统分析与建模(第一版)[M].北京:科学出版社, 1996.
[9]王光远,陈树勋工程结构系统软设计理论及应用[M].国防工业出版社, 1996.
[10]王光远.未确知信息及其数学处理[J].哈尔滨建筑工程学院学报, 1990, (4): 1-10.
[11]邓聚龙.灰色系统理论教程[M].武汉:华中理工大学出版社, 1996.
[12] Ellishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A M Freudenthal's criticisms to modern convex modeling[J]. Computers & Structures, 1995, 56(6): 871-895.
[13] Elishakoff I. Three versions of the finite element method based on concept of either stochasticity, fuzziness or anti-optimization[J]. Applied Mechanics Review, 1998, 51: 209-218.
[14]刘宁,吕泰仁.随机有限元及其工程应用[J].力学进展, 1995, 25(1): 114-126.
[15] Rao S S, Sawyer J P. Fuzzy finite element approach for the analysis of imprecisely defined systems[J]. AIAA Journal, 1995, 33(12): 2364-2370.
[16] Cherki A, Plessis G, Lallemand B, Tison T, Level P. Fuzry behavior of mechanical systems with uncertain boundary conditions[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 189: 863 -873.
[17] Rao S S, Chen L. Numerical solution of fuzzy linear equations in engineering analysis[J]. International Journal of Numeric Methods in Engineering, 1998, 43: 391-408.
[18] Mullen R L, Muhanna R L. Bounds of structural response for all possible loadingcombinations[J]. Journal of Structural Engineering, 1999, 125: 98-106.
[19] Muhanna R L, Mullen R L. Uncertainty in mechanics problems—interval-based approach[J]. Journal of Engineering Mechanics, 2001, 127: 557-566.
[20] Alefeld G, Claudio D. The basic properties of interval arithmetic, its software realizations and some applications[J]. Computers & Structures, 1998, 67(1/3): 3-8.
[21] Soize C. A nonparametric model of random uncertainties for reduced matrix models in structural dynamics[J]. Probabilistic Engineering Mechanics, 2000, 15: 277-294.
[22] Liu N, Tang W H, Ng CWW. Probabilistic FEM for reliability of strain softening media[J]. Finite Elements in Analysis and Design, 2001, 37: 603-619.
[23] Papadimitriou C, Katafygiotis L S, Beck J L. Approximate analysis of response variability of uncertain linear systems[J]. Probabilistic Engineering Mechanics, 1995,10: 251-264.
[24] Angelova D, Simeonova I, Semerdjiev T. Monte Carlo algorithm for ballistic object tracking with uncertain drag parameter[J]. Lect. Notes Comput. SC, 2003, 2907: 112-120.
[25] Corso G M D, Manzini G. On the randomized error of polynomial methods for eigenvector and eigenvalue estimates[J]. Journal of Complexity, 1997, 13: 419-456.
[26] Chen X J, Zhou K M. Order statistics and probabilistic robust control[J]. Systems & Control Letters, 1998, 35: 175-182.
[27] Gao W, Chen J J, Ma H B, Ma X S. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters[J]. Computers & Structures, 2003, 81(1): 53-60.
[28] Gao W, Chen J J, Ma J, Liang Z T. Dynamic response analysis of stochastic frame structures under nonstationary random excitation[J]. AIAA Journal, 2004, 42(9): 1818-1822.
[29] Hanss M, Willner K. A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters[J]. Mechanics Research Communications, 2000, 27(3): 257-272.
[30] Moens D, Vandepitte D. A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1-Procedure[J]. Journal of Sound and Vibration, 2005, 288: 431-462.
[31] Lau TW, Hui PCL, Ng FSF. A new fuzzy approach to improve fashion product development[J]. Compute. Ind., 2006, 57(1): 82-92.
[32] Park KS, Kim, BJ. Application of fuzzy expert system to estimate dimensional errors of forging products having complicated shape[J]. J Mater. Process Tech., 2007, 187: 720-724.
[33] Slavila CA, Decreuse C. Fuzzy approach for maintainability evaluation in the design process[J]. Concurrent Eng-Res A, 2005, 13 (4): 291-300.
[34] Elishakoff I, Lin YK, Zhu LP. Probabilistic and convex modeling of acoustically excited structures[M]. Amsterdam: Elsevier Science Publishers, 1994.
[35] Ferrara A. A variable structure convex programming based control approach for a class of uncertain linear systems[J]. Systems & Control Letters, 2005, 54: 529– 538.
[36] Costa OLV, Val JBR, Geromel JC. Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis[J]. Automatica, 1999, 35: 259-268.
[37] Schutter BD, Boom T. Model predictive control for max-plus-linear discrete event systems[J]. Automatica, 2001, 37: 1049-1056.
[38] Chu CP. Convexity of the first eigenfunctions of Sturm-Liouville eigenvalue problems[J]. Journal of Mathematical Analysis and Applications, 2004, 291: 237-245.
[39] Moore RE. Interval Analysis[M]. New York: Prentice-Hall, Englewood cliffs, 1966
[40] Lu W, Zhang YM, Lin WY. Nonlinear interval model control of quasi-keyhole arc welding process[J]. Automatica, 2004, 40: 805-813.
[41] Wu WD, Rao SS. Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis[J]. Reliability Engineering and System Safety, 2007, 92(1): 54-64.
[42] Rapaport A, Dochain D. Interval observers for biochemical processes with uncertain kinetics and inputs[J]. Mathematical Biosciences, 2005, 193: 235–253.
[43] Hill RO, Johnson CR, Kroschel BK. Extended interlacing intervals[J]. Linear Algebra and Its Applications, 1997, 254: 227-239.
[44] Deif AS. Rigorous perturbation bounds for eigenvalues and eigenvectors of a matrix[J]. Journal of Computational and Applied Mathematics, 1995, 57: 403-412.
[45] Pe'er I, Shamir R. Satisfiability problems on intervals and unit intervals[J].Theoretical Computer Science, 1997, 175: 349-372.
[46]陈塑寰.结构动态设计的矩阵摄动理论[M].北京:科学出版社, 1999.
[47] Chen SH, Zang XM, Chen YD. Interval eigenvalues of closed-loop systems of uncertain structures[J]. Comput. Struct., 2006, 84(3-4): 243-253.
[48] Chen SH, Wu J. Interval optimization of dynamic response for uncertain structures with natural frequency constraints[J]. Engineering Structures, 2004, 26(2): 221-232.
[49] Krodkiewski JM. Stabilization of motion of helicopter rotor blades using delayed feedback-modelling, computer simulation and experimental verification[J]. Journal of Sound and Vibration, 2000, 234(4): 591-610.
[50] Rauh A, Kletting M, Aschemann H, Hofer EP. Reduction of overestimation in interval arithmetic simulation of biological wastewater treatment processes[J]. Journal of Computational and Applied Mathematics, 2007, 199: 212-217.
[51] Koyluoglu HU, Elishakoff I. A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties[J]. Computers and Structures, 1998, 67: 91-98.
[52] Koyluoglu HU, Elishakoff I. A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties[J]. Computers and Structures, 1998, 67: 91-98.
[53] Muer DT, Botteldooren D. Uncertainty in noise mapping: Comparing a probabilistic and a fuzzy set approach[J]. Lecture Notes in Artificial Intelligence, 2003, 2715: 229-236.
[54]欧进萍.结构振动控制-主动、半主动和智能控制[M].北京:科学出版社. 2003: 18-27.
[55] S. Ikenaga, F. L. Lewis, J. Campos and L. Davis . Active suspension control of ground vehicle based on a full-vehicle model[C]. American Control Conference Chicago, USA.2000:1327-1339.
[56] Zhang, Yisheng, Alleyne, A.,New approach to half-car active suspension control[C]. American Control Conference, Denver, Colorado.2003:1420-1431.
[57] Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited Structures[J]. Engineering Structures. 2004, 26: 279-289.
[58]李桂青,邹祖军.结构振动控制评述.地震工程与工程振动. 1987, 7(1): 83-93
[59] Z. Su, K. Khorasani. Neural network controller for single-link flexible manipulator based on the inverse dynamics structure[C]. Proceeding of the International Joint Conference on Neural Network. 2000, 5: 311-316.
[60] H. A. Talebi. Inverse dynamics control of flexible-link manipulators using neural networks[C]. IEEE International Conference on Robotics & Automation. 1998, 1: 806-811.
[61] Afzal Suleman, Antonio P. Costa , Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators[J]. Computers and Structures, 2004, 82: 1303–1314
[62]牟全臣,黄文虎,郑钢铁等.航天结构主、被动一体化振动控制技术的研究现状和进展,应用力学学报[J]. 2001, 18(3): 1-7
[63] Thomas Bailey, Hubbard JE. Distributed piezoelectric polymer active vibration control of a cantilever beam[J]. Journal of Guidance, Control and Dynamics, 1985, 8(5): 605-611.
[64] S. Hanagud, M. W. Obal and M. Meyyappa. Electronic damping techniques and active vibration control[J]. American Institute of Aeronautics and Astronautics, 1985, 8(5): 443-453.
[65] E. F. Crawley and J. DE Luis. Use of piezoelectric actuators as elements of intelligent structures[J]. American Institute of Aeronautics and Astronautics, 1987, 10(5): 1373-1385.
[66] R. Chandra and I. Chopra. Structural modeling of composite beams with induced-strain actuator[J]. American Institute of Aeronautics and Astronautics, 1993, 31(5): 1692-1701.
[67] S. Im and S. N. Atluri. Effects of a piezo-actuator on a finitely deformed beam subjected to general loading[J]. American Institute of Aeronautics and Astronautics, 1989, 27(5): 1801-1807.
[68] C. H. Gerhold and R. Rocha. Active control of flexural vibrations in beams[J]. Journal ofAerospace Engineering, 1989, 2: 141-154.
[69] C. K. Lee. Theory of laminated piezoelectric plates for the design of distributed sensors/actuator. Part I: Governing equations and reciprocal relationships[J]. Journal of Acoustical Society of American, 1990, 87: 1144-1158.
[70] E. F. Crawley and K. B. Lazarus. Induced strain actuation of isotropic and anisotropic plates[J]. American Institute of Aeronautics and Astronautics, 29: 944-951.
[71] P. F. Pai, A. H. Nayfeh, K. Oh and D. T. Mook. A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors[J]. International Journal of Solids and Structures, 1993, 30: 1603-1630.
[72] H. S. Tzou and M. Gadre. Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls[J]. Journal of Sound and Vibration, 1989, 132: 433-450.
[73]司洪伟,李东旭.小波理论在大型空间智能结构振动控制中的应用[J].国防科技大学学报. 2003,25(3): 14-18.
[74]孙东昌,王大钧.梁振动控制的分布压电单元法[J].北京大学学报. 1996,32(5): 585-592.
[75] Bailey T.L. and Hubbard J.E. Distributed Piezoelectric-polymer Active vibration control of a Cantilever Beam[J]. J. of Guidance, control and Dynamics, 1985,8(5): 605-611.
[76] Hwang W.S. Park H.C. finite element modeling of Piezoelectric Sensors Actuators[J]. AIAA. 1992, 30(3): 930-937.
[77]陈塑寰,王晓明,沈亚鹏.用压电元件实现复合材料层合板振动控制的数值分析[J].振动工程学报. 1999,30(2): 107-115.
[78] M.S. de Queiroz, D.M. Dawson, M. Agarwal, F. Zhang. Adaptive Non-linear Boundary Control of a Flexible Link Robot Arm C]. Proceeding of the 36th Conference on Decision & Control. 1997: 1327-1332.
[79]顾仲权.振动主动控制中低阶控制器的优化设计.振动工程学报. 1990, 3(3):1-8.
[80]谭善光,汪希宣.结构强迫振动最优响应和模态主动控制.振动工程学报, 1989, 2(4): 76-81.
[81] Wodeck K. Gawronski, C. S. Racho, Jeffery A. Mellstrom. Application of the LQG and Feed-forward Controllers to the Deep Space Networked Antennas[J]. IEEE Transactions on Control Systems Technology. 1995, 3(4): 417-421.
[82] Zames G. Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Semi norms, and Inverse[J]. IEEE Trans. Automatic Control. 1981, 26: 301-320.
[83] Doyle J. C., Glover K., Khargonekar P., Francis B. A. State-space Solution to Standard H 2 and H∞Control Problems[J]. IEEE Trans. Automatic Control. 1989, 34(8): 831-342.
[84] Sheng-guo Wang, H. Y. Yeh, Paul N. Roschke. Robust Control for Structural Systems with Parametric and Unstructured Uncertainties[C]. Proceedings of the American Control Conference. 2001: 1109-1114.
[85] Crassids, J, baz, A. Werely. H∞control of Active Constrained Layer Damping [J]. Journal of Vibration and Control. 2000, 6: 113-136.
[86]刘雍,顾家柳.转子动力系统的鲁棒H∞控制器设计.振动工程学报. 1994, 7 (3):251-255.
[87] Zhang X and Shao C. Robust H∞vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators[J]. Journal of Sound and Vibration.2001, 243(1): 145-155.
[88] J. Qiu, J. Tani, Vibration control of a cylindrical shell using distributed piezoelectric sensors and actuators[J]. Journal of Intelligent Material Systems and Structures. 1995(6): 474–481.
[89] Fanson J L, Chu C C.. Active member control of a precision structure with and H∞performance objective[C]. AIAA Dynamic Specialist Conference. 1990: 322-333.
[90] Chu C C, Smith R, Fanson J. The design of H∞controllers for an experimental non-collocated flexible structure problem[J]. IEEE Trans. on Control System Technology, 1994, 2(2): 101-109
[91] Carten Scherer, Pascal Gahinet, Multiobjective output-feedback control via LMI optimization[J]. IEEE Trans. on Automatic Control, 1997, 42(7): 896-910.
[92] Qinglei Hu and Guangfu Ma. Active vibration control of a flexible plate structure using LMI-based H∞output feedback control law[C]. Proceedings of the 5th World Congress on Intelligent Control and Automation. 2004: 2021-2032.
[93] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems[J]. Journal of Intelligent Material System & Structure. 2000, 11: 311-323.
[94] Doyle. J. C., Analysis of Feedback System of Structured Uncertainties[J]. IEE proceedings Pt. D. 1982: 242-250.
[95] Balas. J. C. ,Doyle. J. C. Control of Lightly Damped Flexible Modes on the Controller Cross-over Region [J]. Journal of Guidance, Control, and Dynamics. 1994, 17(2): 370-377.
[96]韩志刚.悬臂梁振动的鲁棒控制方法研究[D].南京理工大学硕士学位论文. 2005.
[97] Fujun Peng, Alfred Ng, Yan-Ru Hu. Actuator Placement Optimization and Adaptive Vibration Control of Plate Smart Structures[J]. Journal of Intelligent Material Systems and Structures. 2005, 16(3): 263-271.
[98] Kwakuo P. A. , Kevin C. C. The application of multi-channel design methods for vibration control of an active structure[J]. Smart Material and Structures.1994, 3: 329-343.
[99] Vipperman J S, Burdisso R A , Fuller C R. Active control of broadband structural vibration using the LMS adaptive algorithm[J]. Journal of Sound and Vibration.1993, 166(2): 283-299.
[100]孙朝晖,王冲,戴扬等.结构振动主动控制理论及实验研究[J].振动工程学报. 1994, 7 (2): 154-160.
[101]刘季,滕军.结构在地震作用下的主动自校正控制计算方法[J].地震工程与工程振动. 1991, 11(2): 73-84.
[102]刘季,滕军.地震作用下结构振型组合自校正控制.地震工程与工程振动. 1992, 12(2): 48-58.
[103] Charles C H, Bayard D S. Experimental study of robustness in adaptive control for large flexible structures[C]. AIAA Guidance, Navigation and Control Conference.1990: 1645-1656.
[104]马扣根,顾仲权.结构振动的一种离散自适应控制策略[C].中国振动工程学会噪声与振动控制学年会论文集.北京, 1991: 260-267.
[105] Matthew Allen, Franco Bernelli-Zazzera, Riccardo Scattolini.Sliding mode control of a large flexible space structure[J]. Control Engineering Practice.2000, 8: 861-871.
[106] M.H.Kim. Reduction of observation spillover in vibration suppression using a sliding mode observer[J]. Journal of Vibration and Control. 2002, 7(7): 1087-1150.
[107] Yon-Ping Chen, Jeang-Lin Chang. Sliding-Mode Force Control of Manipulators[C]. Proc. Natl. Sci. Counc. ROC(A). 1999, 23(2): 281-288.
[108] Sshjendra N. Singh. Variable Structure Robust Flight Control System for the F-14[C]. Proceedings of the American Control Conference. 1995: 815-819.
[109]周军,陈新海.大型柔性空间结构的变结构模型参考自适应控制[J].航空学报. 1992, 13(4): 158-163.
[110]黄一敏,高正,王永.基于混合灵敏度优化的鲁棒特征结构配置[J].控制理论与应用. 2003, 20(3): 411-414.
[111]刘春.不确定性振动控制系统的随机方法[D].吉林大学博士学位论文. 2004.
[112]陈大跃,胡宗武,范祖尧.振动控制的特征结构配置[J].振动工程学报, 1991, 4 (2): 75-81.
[113]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[J].振动与冲击. 1991, 3: 85-89.
[114]林嗣廉,徐博侯.柔性结构振动的独立模态H∞控制[J].浙江大学学报, 2001, 35(1): 23-29.
[115] Meirovitch L, Baruh H, A comparison of control techniques for large flexible systems[J], Journal of Guidance.1983, 6(4): 302-310.
[116] Gustavo Luiz, C. M. de Abteu Jose, F. Riberio. A Self-Organizing Fuzzy Logic Controller for the Active Control of Flexible Structures Using Piezoelectric Actuator [J]. Applied Soft Computing. 2002, 1: 271-283.
[117] Shiuh-Jer Huang and Wei-Cheng Lin. Adaptive fuzzy controller with sliding surface for vehicle suspension control[J]. IEEE Trans. on Fuzzy Systems. 2003, 11(4): 550-560.
[118] Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited structures[J]. Engineering Structures. 2004(26): 279–289.
[119] M T Valoor, K Chandrashekhara, S Agarwal. Active vibration control of smart composite plates using self-adaptive neuro-controller[J]. Smart Material and Structures. 2000(9): 197–204.
[120] Cai GP, Hong JZ, Yang SX. Model study and active control of a rotating flexible cantilever beam[J]. International Journal of Mechanical Sciences, 2004, 46: 871-889.
[121] Nakamura Y, Nakayama M, Yasuda M, Fujita T. Development of active six-degrees-of-freedom micro-vibration control system using hybrid actuators comprising air actuators and giant magnetostrictive actuators[J]. Smart Materials and Structures, 2006, 15: 1133-1142.
[122] Mahmoud MS, Zribi M. Passive control synthesis for uncertain systems with multiple-state delays[J]. Computers and Electrical Engineering, 2002, 28: 195-216.
[123] Beaumont O. Solving interval linear systems with linear programming techniques[J]. Linear Algebra and its Applications, 1998, 281: 293-309.
[124] Kuntsevich AV, Kuntsevich VM. Linear adaptive control for nonstationary uncertain systems under bounded noise[J]. Systems & Control Letters, 1997, 31: 33-40.
[125] Lyshevski SE. Design of the constrained controllers for uncertain nonlinear systems using the Lyapunov stability theory[J]. Journal of the Franklin Institute, 1999, 336: 1075-1092.
[126] Lu Z, Shieh LS, Chen GR, Coleman NP. Simplex sliding mode control for nonlinear uncertain systems via chaos optimization[J]. Chaos, Solitons and Fractals, 2005, 23: 747-755.
[127] Fang JQ, Li QS, Jeary AP. Modified independent modal space control of m.d.o.f. systems[J]. Journal of Sound and Vibration, 2003, 261: 421-441.
[128] Chen JD. Robust control for uncertain neutral systems with time-delays in state and control input via LMI and Gas[J]. Applied Mathematics and Computation, 2004, 157: 535-548.
[129] Wang ZH, Hu HY, Wang HL. Robust stabilization to non-linear delayed systems via delayed state feedback: the averaging method[J]. Journal of Sound and Vibration, 2005, 279: 937-953.
[130] Ge SS, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems[J]. Automatica, 2002, 38: 671-682.
[131] Wang DA, Huang YM. Application of discrete-time variable structure control in the vibration reduction of a flexible structure[J]. Journal of Sound and Vibration, 2003, 261: 483-501.
[132] Tisseur F. Backward error and condition of polynomial eigenvalue problems[J]. LinearAlgebra and its Applications, 2000, 309: 339-361.
[133] Masad J. Computation of linear instability eigenvalue subject to perturbations in mean-flow and stability parameter[J]. Computers & Fluids, 1995, 24(6): 653-662.
[134] Lin TR, Pan J. A closed form solution for the dynamic response of finite ribbed plates[J]. Acoustical Society of America, 2006, 119(2): 917-925.
[135] Han Q, Zheng XF. Chaotic response of a large deflection beam and effect of the second order mode[J]. European Journal of Mechanics A/Solids, 2005, 24: 944-956.
[136] Hall JW. Uncertainty-based sensitivity indices for imprecise probability distributions[J]. Reliability Engineering and System Safety, 2006, 91(10-11): 1443-1451.
[137] Bazan FSV. Sensitivity eigenanalysis for single shift-invariant subspace-based methods[J]. Signal Processing, 2000, 80: 89-100.
[138] Hasan WM, Viola E. Use of the singular value decomposition method to detect ill-conditioning of structural identification problems[J]. Computers & Structures, 1997, 63(2): 267-275.
[139] Mosca E, Agnoloni T. Closed-loop monitoring for early detection of performance losses in feedback-control systems[J]. Automatica, 2003, 39: 2071-2084.
[140] Hespanha JP, Liberzon D, Morse AS. Hysteresis-based switching algorithms for supervisory control of uncertain systems[J]. Automatica, 2003, 39: 263-272.
[141] [Nataraj PSV. Computation of QFT bounds for robust tracking specifications[J]. Automatica, 2002, 38: 327-334.
[142] Hagenmeyer V, Delaleau E. Robustness analysis of exact feedforward linearization based on differential flatness[J]. Automatica, 2003, 39: 1941-1946.
[143] Liang YW, Liaw DC. Robust control non-linear affine systems[J]. Applied Mathematics and Computation, 2003, 137: 337-347.
[144] Mahmoud MS. Robust H∞control of linear neutral systems[J]. Automatica, 2000, 36: 757-764.
[145] Huang YJ, Wang YJ. Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem[J]. ISA Transactions, 2000, 39: 419-431.
[146] Mahmoud MS, Zribi M. Guaranteed cost observer-based control of uncertain time-lag systems[J]. Computers and Electrical Engineering, 2003, 29: 193-212.
[147] R. Lind, K. Snyder , M. Brenner., Wavelet analysis to characterize non-linearities and predict limit cycles of an aero elastic system[J]. Mechanical Systems and Signal Processing. 2001, 15(2): 337-356.
[148] J. Awrejcewicz , A. V. Krysko, Wavelet-based analysis of parametric vibrations of flexible[J]. International Applied Mechanic. 2003, 39(9): 997-1029.
[149] S. Pernot,C.H. Lamarque. A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems[J]. Nonlinear Dynamics, 2003, 32: 33–70.
[150] Chun-Hsiung Fang, Yung-Sheng Liu, Shih-Wei Kau. A new LMI-based approach to relaxed quadratic stabilization of T–S fuzzy control systems[J]. IEEE Trans. On Fuzzy Sysems.2006, 14(3): 386-398.
[151]刘晓东,张庆灵.模糊系统H 2 /H∞控制器设计的LMI方法[J].控制理论与应用. 2004, 21(1):102-124.
[152] Huai-Ning Wu and Kai-Yuan Cai. Mode-independent Robust Stabilization for uncertain markovian jump nonlinear systems via fuzzy Control[J]. IEEE Trans. on Systems.Man,Cybernetics. 2006, 36(3):509-512.
[153]王登刚,李杰.计算具有区间参数结构特征值范围的一种新方法[J].计算力学学报, 2004, 21(1): 56-61.
[154] Chen S H, Qiu Z P. Perturbation method for computing eigenvalue bounds in vibration system with interval parameters[J]. Communication in Numerical Methods in Engineering, 1994, 10: 121-134.
[155]陈塑寰,邱志平,宋大同,等.区间矩阵标准特征值的一种解法[J].吉林工业大学学报, 1993, 23(3): 1-8.
[156] Muhanna R L, Mullen R L. Uncertainty in mechanics problems-interval-based approach[J]. Journal of Engineering Mechanics, 2001, 127(3): 557-566.
[157]吴晓,罗佑新,文会军,等.非确定性结构系统区间分析的泛灰求解方法[J].计算力学学报, 2003, 20(3): 329-334.
[158] Nakagiri S, Suzuki K. Finite element interval analysis of external loads identified by displacement input with uncertainty. Comput Methods Appl Mech Engrg, 1999, 168: 63-72.
[159]王登刚.非线性反演算法及其应用研究[M].大连:大连理工大学, 2001.
[160]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报, 2005, 22(2): 227-231.
[161]王登刚,李杰.结构可靠性分析的区间方法[C]. 12届全国反应堆结构力学会议论文集,烟台, 2002.
[162] Chen S H, Lian H D, Yang X W. Interval displacement analysis for structures with interval parameters[J]. Int J Num Methods in Eng, 2002, 53(2): 393-407.
[163]吴杰,陈塑寰.区间参数结构的动力响应优化[J].固体力学学报, 2004, 25(2): 186-189.
[164] Gorzafczany B. Approximate inference with interval-valued fuzzy Sets– an outline[A]. Proc Polish Symp: on interval and fuzzy math[C]. Poland, 1983, 89-95.
[165] Ben-Haim Y. Convex models of uncertainty in radial pulse buckling of shells[J]. Journal of Applied Mechanics, 1993, 60(3): 683-688.
[166]郭书祥,吕震宙.区间运算和静力区间有限元[J].应用数学和力学, 2001, 22(12): 1249-1254.
[167] Chen S H, Yang X W. Interval finite element method for beam structures[J]. Finite Elements in Analysis and Design, 2000, 34(1): 75-88.
[168]郭书祥,吕震宙.线形区间有限元静力控制方程的组合解法[J].计算力学学报, 2003, 20(1): 34-38.
[169]王登刚,李杰.计算不确定结构系统静态响应的一种可靠方法[J].计算力学学报, 2003, 20(6): 662-669.
[170] Li J , Liao S. Response analysis of stochastic parameter st ructures under non-stationary random excitation[J]. Computational Mechanics, 2001 , 27 (1): 61-68.
[171]王登刚.计算具有区间参数结构的固有频率的优化方法[J].力学学报, 2004, 36(3): 364-372.
[172] David M , Dirk V. An interval finite element approach for t he calculation of envelope f requency response functions[J]. International Journal for Numerical Met hods in Engineering, 2004, 61:2480-2507.
[173] Qiu Z , Wang X. Parameter perturbation met hod for dynamic responses of st ructures with uncertain-but-bounded parameters based on interval analysis[J]. International Journal of Solids and Structures, 2005, 42(18-19) : 4958-4970.
[174] Moor R E. Methods and Applications of Interval Analysis[M]. Philadelphia: SIAM Publications, 1979.
[175] Alefeld G, Herzberger J. Introduction to interval computations[M]. Academic Press, New York, 1983.
[176]沈祖和.区间分析方法及其应用[J].应用数学和计算数学, 1983 (2): 34-58.
[177]胡承毅,徐山鹰,杨晓光.区间算法简介[J].系统工程理论与实践, 2003 (4): 59-62.
[178] Turksen B. Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems. 1986, 20: 191-210.
[179] Zeng Wenyi, Shi Yi. Note on interval-valued fuzzy set[J]. Lecture Notes in Artificial Intelligence, 2005, 3316: 20-24.
[180] Zeng Wenyi, Li Hongxing. Relationship between similarity measures and ent ropy of interval valued fuzzy sets[J]. Fuzzy Set s and Systems, 2006, 157: 1477-1481.
[181] Cornelis C, Deschrijver D, Kerre E E. Advances and challenges in interval-valued fuzzy logic [J]. Fuzzy Sets and Systems, 2006, 157 :622-628.
[182] Chun M G. A similarity-based bidirectional approximate reasoning method for decision2making systems[J]. FuzzySet s and Systems, 2001, 117: 269-276.
[183] Chen S M, Hsiao W H, Jong W T. Bidirectional approximate reasoning based oninterval2valued fuzzy sets[J]. Fuzzy Sets and Systems, 1997, 91: 339-345.
[184] Chen S M, Hsiao W H. Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets[J]. Fuzzy Set s and Systems, 2000, 113: 185-190.
[185]吴望名.区间模糊集和区间值模糊推理[J].模糊系统与数学, 1992, 6(2): 38-47.
[186] Rao S S, Berke L. Analysis of uncertain structural system using interval analysis[J]. AIAA Journal, 1997, 35(4): 727-735.
[187]李杰.结构动力分析的若干发展趋势.世界地震工程, 1993, 2: l-8.
[188]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].西南交通大学博士学位论文, 1996.
[189]李贤兴.强震作用下钢筋混凝土多层结构的空间随机响应分析及其损伤评估[D].西南交通大学博士学位论文, 1991.
[190] SAWADA Y, OHSUMI A. Active vibration control for flexible cantilever beam subject to seismic disturbance[C].∥IEEE International Conference on Systems Engineering. Kobe: IEEE, 1992: 436-439.
[191] PETERSEN I R, POTA H R. Minimax LQG optimal control of a flexible beam[J]. Control Engineering Practice, 2003, 11: 1273-1287.
[192] Z G Ying, W Q Zhu, T T Soong. A Stochastic Optimal Semi-active Control Strategy for ER/MR Dampers[J]. Journal of Sound and Vibration, 2003, 259: 45-62.
[193]赵治国.车辆动力学及其非线性控制理论技术的研究[D].西北工业大学博士学位论文, 2002.
[194]余瑞芬.传感器原理[M].北京:航空工业出版社. 1995.
[195]宋天霞.有限元法理论及应用基础教程[M].武汉:华中工学院出版社, 1987.
[196] Hallauer W L Jr, Barthelemy J F M. Active damping of modal vibrations by force apportioning[C]. Proceedings of the AIAA/ASME/ASCE 21ST Structures, Structural Dynamics, and Materials Conference, 1980: 863-873.
[197] Rajaram S. Optimal independent modal space control of a flexible system including integral feedback[C]. Proceeding of an International Symposium on Engineering Science and Mechancs, Tainan, Taiwan, Dec. 29-31, 1981, 1031-1041.
[198] A STROM K J, HOGGLUND T. PID Controllers: Theory, Design and Tuning [M]. Research Triangle Park: Instrument Society of America, 1995.
[199] TAN W, CHEN T, MARQUEZ H J. Robust Controller design and PID tuning for multivariable process[J]. Asian J of Control, 2002, 4(4): 439-451.
[200] Feng Zheng, Qing-Guo Wang, Tong Heng Lee. On the design of multivariable PID controllers via LMI approach[C]. The 27th Annual Conference of the IEEE Industrial Electronics Society, 2001, 776-781.
[201]蔡国平.存在时滞的柔性梁的振动主动控制[J]..固体力学学报. 2004, 25(1):29-34.
[202]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[203]李志虎,王景成,邵惠鹏.时变不确定离散时滞系统的H∞鲁棒控制.控制理论与应用[J].. 2003.20(1):139-142.
[204] Cai G P, Huang J Z. Optimal control method for seismically excited building structures with time delay in control[J]. Journal of Engineering Mechanics, ASCE, 2002, 128(6): 602-612.
[205]刘金琨.先进PID控制MATLAB仿真[M].北京:电子工业出版社, 2004.
[206]吉林化学工业公司电石厂.电石生产问答[M].北京:化学工业出版社,1979.
[207] Lang Z Q. Gu X Y. Bao Y M. Modelling and Identification of Electrode Position Controller in Electric Arc Furnace[C]. International Conference on Control 1991,.1: 434-439.
[208]陈峻岭,罗安,李正国,等.智能大功率电弧炉自动控制系统[J].中国有色金属学报, 2002, 12(2):.393-397.
[209] Ziegler J G. Nichols N B. Optimum settings for automatic controllers[J]. TransASME, 1942, 64: 745-768.
[210]玄光男,程润伟.遗传算法与工程优化[M].北京:清华大学出版社, 2004.
[211] HUKSDóTTIR. System identification of a three-phase submerged-arc ferrosilicon furnace[J]. IEEE Transactions on Control Systems Technoligy, 1995 3(4): 377-387.
[2]王清印,刘志勇,赵秀恒.广义不确定性系统概念及其基本原理[J].华中科技大学学报(自然科学版), 2005, 33(1): 531-534.
[3]钟万勰.计算结构力学与最优控制[M].大连:大连理工大学出版社, 1993.
[4]闻邦椿,刘树英,何琼.振动机械的理论与动态设计方法.北京:机械工业出版社, 2001.
[5] Chen J J, Che J W, Sun H A, et al. Probabilistic dynamic analysis of truss structures[J]. Structural Engineering & Mechanics, 2002, 13(2): 231-239.
[6] Dai J, Chen J J, Li Y G. Dynamic response optimization design for engineering structures based on reliability[J]. Applied Mathematics and Mechanics, 2003, 24(1): 43-52.
[7] Gao W, Chen J J, Ma H B. Dynamic response analysis of closed loop control system for intelligent truss structures based on probability[J]. Structural Engineering & Mechanics, 2003, 15(2): 239-248.
[8]李杰.随机结构系统分析与建模(第一版)[M].北京:科学出版社, 1996.
[9]王光远,陈树勋工程结构系统软设计理论及应用[M].国防工业出版社, 1996.
[10]王光远.未确知信息及其数学处理[J].哈尔滨建筑工程学院学报, 1990, (4): 1-10.
[11]邓聚龙.灰色系统理论教程[M].武汉:华中理工大学出版社, 1996.
[12] Ellishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A M Freudenthal's criticisms to modern convex modeling[J]. Computers & Structures, 1995, 56(6): 871-895.
[13] Elishakoff I. Three versions of the finite element method based on concept of either stochasticity, fuzziness or anti-optimization[J]. Applied Mechanics Review, 1998, 51: 209-218.
[14]刘宁,吕泰仁.随机有限元及其工程应用[J].力学进展, 1995, 25(1): 114-126.
[15] Rao S S, Sawyer J P. Fuzzy finite element approach for the analysis of imprecisely defined systems[J]. AIAA Journal, 1995, 33(12): 2364-2370.
[16] Cherki A, Plessis G, Lallemand B, Tison T, Level P. Fuzry behavior of mechanical systems with uncertain boundary conditions[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 189: 863 -873.
[17] Rao S S, Chen L. Numerical solution of fuzzy linear equations in engineering analysis[J]. International Journal of Numeric Methods in Engineering, 1998, 43: 391-408.
[18] Mullen R L, Muhanna R L. Bounds of structural response for all possible loadingcombinations[J]. Journal of Structural Engineering, 1999, 125: 98-106.
[19] Muhanna R L, Mullen R L. Uncertainty in mechanics problems—interval-based approach[J]. Journal of Engineering Mechanics, 2001, 127: 557-566.
[20] Alefeld G, Claudio D. The basic properties of interval arithmetic, its software realizations and some applications[J]. Computers & Structures, 1998, 67(1/3): 3-8.
[21] Soize C. A nonparametric model of random uncertainties for reduced matrix models in structural dynamics[J]. Probabilistic Engineering Mechanics, 2000, 15: 277-294.
[22] Liu N, Tang W H, Ng CWW. Probabilistic FEM for reliability of strain softening media[J]. Finite Elements in Analysis and Design, 2001, 37: 603-619.
[23] Papadimitriou C, Katafygiotis L S, Beck J L. Approximate analysis of response variability of uncertain linear systems[J]. Probabilistic Engineering Mechanics, 1995,10: 251-264.
[24] Angelova D, Simeonova I, Semerdjiev T. Monte Carlo algorithm for ballistic object tracking with uncertain drag parameter[J]. Lect. Notes Comput. SC, 2003, 2907: 112-120.
[25] Corso G M D, Manzini G. On the randomized error of polynomial methods for eigenvector and eigenvalue estimates[J]. Journal of Complexity, 1997, 13: 419-456.
[26] Chen X J, Zhou K M. Order statistics and probabilistic robust control[J]. Systems & Control Letters, 1998, 35: 175-182.
[27] Gao W, Chen J J, Ma H B, Ma X S. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters[J]. Computers & Structures, 2003, 81(1): 53-60.
[28] Gao W, Chen J J, Ma J, Liang Z T. Dynamic response analysis of stochastic frame structures under nonstationary random excitation[J]. AIAA Journal, 2004, 42(9): 1818-1822.
[29] Hanss M, Willner K. A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters[J]. Mechanics Research Communications, 2000, 27(3): 257-272.
[30] Moens D, Vandepitte D. A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1-Procedure[J]. Journal of Sound and Vibration, 2005, 288: 431-462.
[31] Lau TW, Hui PCL, Ng FSF. A new fuzzy approach to improve fashion product development[J]. Compute. Ind., 2006, 57(1): 82-92.
[32] Park KS, Kim, BJ. Application of fuzzy expert system to estimate dimensional errors of forging products having complicated shape[J]. J Mater. Process Tech., 2007, 187: 720-724.
[33] Slavila CA, Decreuse C. Fuzzy approach for maintainability evaluation in the design process[J]. Concurrent Eng-Res A, 2005, 13 (4): 291-300.
[34] Elishakoff I, Lin YK, Zhu LP. Probabilistic and convex modeling of acoustically excited structures[M]. Amsterdam: Elsevier Science Publishers, 1994.
[35] Ferrara A. A variable structure convex programming based control approach for a class of uncertain linear systems[J]. Systems & Control Letters, 2005, 54: 529– 538.
[36] Costa OLV, Val JBR, Geromel JC. Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis[J]. Automatica, 1999, 35: 259-268.
[37] Schutter BD, Boom T. Model predictive control for max-plus-linear discrete event systems[J]. Automatica, 2001, 37: 1049-1056.
[38] Chu CP. Convexity of the first eigenfunctions of Sturm-Liouville eigenvalue problems[J]. Journal of Mathematical Analysis and Applications, 2004, 291: 237-245.
[39] Moore RE. Interval Analysis[M]. New York: Prentice-Hall, Englewood cliffs, 1966
[40] Lu W, Zhang YM, Lin WY. Nonlinear interval model control of quasi-keyhole arc welding process[J]. Automatica, 2004, 40: 805-813.
[41] Wu WD, Rao SS. Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis[J]. Reliability Engineering and System Safety, 2007, 92(1): 54-64.
[42] Rapaport A, Dochain D. Interval observers for biochemical processes with uncertain kinetics and inputs[J]. Mathematical Biosciences, 2005, 193: 235–253.
[43] Hill RO, Johnson CR, Kroschel BK. Extended interlacing intervals[J]. Linear Algebra and Its Applications, 1997, 254: 227-239.
[44] Deif AS. Rigorous perturbation bounds for eigenvalues and eigenvectors of a matrix[J]. Journal of Computational and Applied Mathematics, 1995, 57: 403-412.
[45] Pe'er I, Shamir R. Satisfiability problems on intervals and unit intervals[J].Theoretical Computer Science, 1997, 175: 349-372.
[46]陈塑寰.结构动态设计的矩阵摄动理论[M].北京:科学出版社, 1999.
[47] Chen SH, Zang XM, Chen YD. Interval eigenvalues of closed-loop systems of uncertain structures[J]. Comput. Struct., 2006, 84(3-4): 243-253.
[48] Chen SH, Wu J. Interval optimization of dynamic response for uncertain structures with natural frequency constraints[J]. Engineering Structures, 2004, 26(2): 221-232.
[49] Krodkiewski JM. Stabilization of motion of helicopter rotor blades using delayed feedback-modelling, computer simulation and experimental verification[J]. Journal of Sound and Vibration, 2000, 234(4): 591-610.
[50] Rauh A, Kletting M, Aschemann H, Hofer EP. Reduction of overestimation in interval arithmetic simulation of biological wastewater treatment processes[J]. Journal of Computational and Applied Mathematics, 2007, 199: 212-217.
[51] Koyluoglu HU, Elishakoff I. A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties[J]. Computers and Structures, 1998, 67: 91-98.
[52] Koyluoglu HU, Elishakoff I. A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties[J]. Computers and Structures, 1998, 67: 91-98.
[53] Muer DT, Botteldooren D. Uncertainty in noise mapping: Comparing a probabilistic and a fuzzy set approach[J]. Lecture Notes in Artificial Intelligence, 2003, 2715: 229-236.
[54]欧进萍.结构振动控制-主动、半主动和智能控制[M].北京:科学出版社. 2003: 18-27.
[55] S. Ikenaga, F. L. Lewis, J. Campos and L. Davis . Active suspension control of ground vehicle based on a full-vehicle model[C]. American Control Conference Chicago, USA.2000:1327-1339.
[56] Zhang, Yisheng, Alleyne, A.,New approach to half-car active suspension control[C]. American Control Conference, Denver, Colorado.2003:1420-1431.
[57] Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited Structures[J]. Engineering Structures. 2004, 26: 279-289.
[58]李桂青,邹祖军.结构振动控制评述.地震工程与工程振动. 1987, 7(1): 83-93
[59] Z. Su, K. Khorasani. Neural network controller for single-link flexible manipulator based on the inverse dynamics structure[C]. Proceeding of the International Joint Conference on Neural Network. 2000, 5: 311-316.
[60] H. A. Talebi. Inverse dynamics control of flexible-link manipulators using neural networks[C]. IEEE International Conference on Robotics & Automation. 1998, 1: 806-811.
[61] Afzal Suleman, Antonio P. Costa , Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators[J]. Computers and Structures, 2004, 82: 1303–1314
[62]牟全臣,黄文虎,郑钢铁等.航天结构主、被动一体化振动控制技术的研究现状和进展,应用力学学报[J]. 2001, 18(3): 1-7
[63] Thomas Bailey, Hubbard JE. Distributed piezoelectric polymer active vibration control of a cantilever beam[J]. Journal of Guidance, Control and Dynamics, 1985, 8(5): 605-611.
[64] S. Hanagud, M. W. Obal and M. Meyyappa. Electronic damping techniques and active vibration control[J]. American Institute of Aeronautics and Astronautics, 1985, 8(5): 443-453.
[65] E. F. Crawley and J. DE Luis. Use of piezoelectric actuators as elements of intelligent structures[J]. American Institute of Aeronautics and Astronautics, 1987, 10(5): 1373-1385.
[66] R. Chandra and I. Chopra. Structural modeling of composite beams with induced-strain actuator[J]. American Institute of Aeronautics and Astronautics, 1993, 31(5): 1692-1701.
[67] S. Im and S. N. Atluri. Effects of a piezo-actuator on a finitely deformed beam subjected to general loading[J]. American Institute of Aeronautics and Astronautics, 1989, 27(5): 1801-1807.
[68] C. H. Gerhold and R. Rocha. Active control of flexural vibrations in beams[J]. Journal ofAerospace Engineering, 1989, 2: 141-154.
[69] C. K. Lee. Theory of laminated piezoelectric plates for the design of distributed sensors/actuator. Part I: Governing equations and reciprocal relationships[J]. Journal of Acoustical Society of American, 1990, 87: 1144-1158.
[70] E. F. Crawley and K. B. Lazarus. Induced strain actuation of isotropic and anisotropic plates[J]. American Institute of Aeronautics and Astronautics, 29: 944-951.
[71] P. F. Pai, A. H. Nayfeh, K. Oh and D. T. Mook. A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors[J]. International Journal of Solids and Structures, 1993, 30: 1603-1630.
[72] H. S. Tzou and M. Gadre. Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls[J]. Journal of Sound and Vibration, 1989, 132: 433-450.
[73]司洪伟,李东旭.小波理论在大型空间智能结构振动控制中的应用[J].国防科技大学学报. 2003,25(3): 14-18.
[74]孙东昌,王大钧.梁振动控制的分布压电单元法[J].北京大学学报. 1996,32(5): 585-592.
[75] Bailey T.L. and Hubbard J.E. Distributed Piezoelectric-polymer Active vibration control of a Cantilever Beam[J]. J. of Guidance, control and Dynamics, 1985,8(5): 605-611.
[76] Hwang W.S. Park H.C. finite element modeling of Piezoelectric Sensors Actuators[J]. AIAA. 1992, 30(3): 930-937.
[77]陈塑寰,王晓明,沈亚鹏.用压电元件实现复合材料层合板振动控制的数值分析[J].振动工程学报. 1999,30(2): 107-115.
[78] M.S. de Queiroz, D.M. Dawson, M. Agarwal, F. Zhang. Adaptive Non-linear Boundary Control of a Flexible Link Robot Arm C]. Proceeding of the 36th Conference on Decision & Control. 1997: 1327-1332.
[79]顾仲权.振动主动控制中低阶控制器的优化设计.振动工程学报. 1990, 3(3):1-8.
[80]谭善光,汪希宣.结构强迫振动最优响应和模态主动控制.振动工程学报, 1989, 2(4): 76-81.
[81] Wodeck K. Gawronski, C. S. Racho, Jeffery A. Mellstrom. Application of the LQG and Feed-forward Controllers to the Deep Space Networked Antennas[J]. IEEE Transactions on Control Systems Technology. 1995, 3(4): 417-421.
[82] Zames G. Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Semi norms, and Inverse[J]. IEEE Trans. Automatic Control. 1981, 26: 301-320.
[83] Doyle J. C., Glover K., Khargonekar P., Francis B. A. State-space Solution to Standard H 2 and H∞Control Problems[J]. IEEE Trans. Automatic Control. 1989, 34(8): 831-342.
[84] Sheng-guo Wang, H. Y. Yeh, Paul N. Roschke. Robust Control for Structural Systems with Parametric and Unstructured Uncertainties[C]. Proceedings of the American Control Conference. 2001: 1109-1114.
[85] Crassids, J, baz, A. Werely. H∞control of Active Constrained Layer Damping [J]. Journal of Vibration and Control. 2000, 6: 113-136.
[86]刘雍,顾家柳.转子动力系统的鲁棒H∞控制器设计.振动工程学报. 1994, 7 (3):251-255.
[87] Zhang X and Shao C. Robust H∞vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators[J]. Journal of Sound and Vibration.2001, 243(1): 145-155.
[88] J. Qiu, J. Tani, Vibration control of a cylindrical shell using distributed piezoelectric sensors and actuators[J]. Journal of Intelligent Material Systems and Structures. 1995(6): 474–481.
[89] Fanson J L, Chu C C.. Active member control of a precision structure with and H∞performance objective[C]. AIAA Dynamic Specialist Conference. 1990: 322-333.
[90] Chu C C, Smith R, Fanson J. The design of H∞controllers for an experimental non-collocated flexible structure problem[J]. IEEE Trans. on Control System Technology, 1994, 2(2): 101-109
[91] Carten Scherer, Pascal Gahinet, Multiobjective output-feedback control via LMI optimization[J]. IEEE Trans. on Automatic Control, 1997, 42(7): 896-910.
[92] Qinglei Hu and Guangfu Ma. Active vibration control of a flexible plate structure using LMI-based H∞output feedback control law[C]. Proceedings of the 5th World Congress on Intelligent Control and Automation. 2004: 2021-2032.
[93] Sridhar Sana, Vittal S Rao. Application of linear matrix inequalities in the control of smart structural systems[J]. Journal of Intelligent Material System & Structure. 2000, 11: 311-323.
[94] Doyle. J. C., Analysis of Feedback System of Structured Uncertainties[J]. IEE proceedings Pt. D. 1982: 242-250.
[95] Balas. J. C. ,Doyle. J. C. Control of Lightly Damped Flexible Modes on the Controller Cross-over Region [J]. Journal of Guidance, Control, and Dynamics. 1994, 17(2): 370-377.
[96]韩志刚.悬臂梁振动的鲁棒控制方法研究[D].南京理工大学硕士学位论文. 2005.
[97] Fujun Peng, Alfred Ng, Yan-Ru Hu. Actuator Placement Optimization and Adaptive Vibration Control of Plate Smart Structures[J]. Journal of Intelligent Material Systems and Structures. 2005, 16(3): 263-271.
[98] Kwakuo P. A. , Kevin C. C. The application of multi-channel design methods for vibration control of an active structure[J]. Smart Material and Structures.1994, 3: 329-343.
[99] Vipperman J S, Burdisso R A , Fuller C R. Active control of broadband structural vibration using the LMS adaptive algorithm[J]. Journal of Sound and Vibration.1993, 166(2): 283-299.
[100]孙朝晖,王冲,戴扬等.结构振动主动控制理论及实验研究[J].振动工程学报. 1994, 7 (2): 154-160.
[101]刘季,滕军.结构在地震作用下的主动自校正控制计算方法[J].地震工程与工程振动. 1991, 11(2): 73-84.
[102]刘季,滕军.地震作用下结构振型组合自校正控制.地震工程与工程振动. 1992, 12(2): 48-58.
[103] Charles C H, Bayard D S. Experimental study of robustness in adaptive control for large flexible structures[C]. AIAA Guidance, Navigation and Control Conference.1990: 1645-1656.
[104]马扣根,顾仲权.结构振动的一种离散自适应控制策略[C].中国振动工程学会噪声与振动控制学年会论文集.北京, 1991: 260-267.
[105] Matthew Allen, Franco Bernelli-Zazzera, Riccardo Scattolini.Sliding mode control of a large flexible space structure[J]. Control Engineering Practice.2000, 8: 861-871.
[106] M.H.Kim. Reduction of observation spillover in vibration suppression using a sliding mode observer[J]. Journal of Vibration and Control. 2002, 7(7): 1087-1150.
[107] Yon-Ping Chen, Jeang-Lin Chang. Sliding-Mode Force Control of Manipulators[C]. Proc. Natl. Sci. Counc. ROC(A). 1999, 23(2): 281-288.
[108] Sshjendra N. Singh. Variable Structure Robust Flight Control System for the F-14[C]. Proceedings of the American Control Conference. 1995: 815-819.
[109]周军,陈新海.大型柔性空间结构的变结构模型参考自适应控制[J].航空学报. 1992, 13(4): 158-163.
[110]黄一敏,高正,王永.基于混合灵敏度优化的鲁棒特征结构配置[J].控制理论与应用. 2003, 20(3): 411-414.
[111]刘春.不确定性振动控制系统的随机方法[D].吉林大学博士学位论文. 2004.
[112]陈大跃,胡宗武,范祖尧.振动控制的特征结构配置[J].振动工程学报, 1991, 4 (2): 75-81.
[113]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[J].振动与冲击. 1991, 3: 85-89.
[114]林嗣廉,徐博侯.柔性结构振动的独立模态H∞控制[J].浙江大学学报, 2001, 35(1): 23-29.
[115] Meirovitch L, Baruh H, A comparison of control techniques for large flexible systems[J], Journal of Guidance.1983, 6(4): 302-310.
[116] Gustavo Luiz, C. M. de Abteu Jose, F. Riberio. A Self-Organizing Fuzzy Logic Controller for the Active Control of Flexible Structures Using Piezoelectric Actuator [J]. Applied Soft Computing. 2002, 1: 271-283.
[117] Shiuh-Jer Huang and Wei-Cheng Lin. Adaptive fuzzy controller with sliding surface for vehicle suspension control[J]. IEEE Trans. on Fuzzy Systems. 2003, 11(4): 550-560.
[118] Kwan-Soon Park, Hyun-Moo Koh, Chung-Won Seo. Independent modal space fuzzy control of earthquake-excited structures[J]. Engineering Structures. 2004(26): 279–289.
[119] M T Valoor, K Chandrashekhara, S Agarwal. Active vibration control of smart composite plates using self-adaptive neuro-controller[J]. Smart Material and Structures. 2000(9): 197–204.
[120] Cai GP, Hong JZ, Yang SX. Model study and active control of a rotating flexible cantilever beam[J]. International Journal of Mechanical Sciences, 2004, 46: 871-889.
[121] Nakamura Y, Nakayama M, Yasuda M, Fujita T. Development of active six-degrees-of-freedom micro-vibration control system using hybrid actuators comprising air actuators and giant magnetostrictive actuators[J]. Smart Materials and Structures, 2006, 15: 1133-1142.
[122] Mahmoud MS, Zribi M. Passive control synthesis for uncertain systems with multiple-state delays[J]. Computers and Electrical Engineering, 2002, 28: 195-216.
[123] Beaumont O. Solving interval linear systems with linear programming techniques[J]. Linear Algebra and its Applications, 1998, 281: 293-309.
[124] Kuntsevich AV, Kuntsevich VM. Linear adaptive control for nonstationary uncertain systems under bounded noise[J]. Systems & Control Letters, 1997, 31: 33-40.
[125] Lyshevski SE. Design of the constrained controllers for uncertain nonlinear systems using the Lyapunov stability theory[J]. Journal of the Franklin Institute, 1999, 336: 1075-1092.
[126] Lu Z, Shieh LS, Chen GR, Coleman NP. Simplex sliding mode control for nonlinear uncertain systems via chaos optimization[J]. Chaos, Solitons and Fractals, 2005, 23: 747-755.
[127] Fang JQ, Li QS, Jeary AP. Modified independent modal space control of m.d.o.f. systems[J]. Journal of Sound and Vibration, 2003, 261: 421-441.
[128] Chen JD. Robust control for uncertain neutral systems with time-delays in state and control input via LMI and Gas[J]. Applied Mathematics and Computation, 2004, 157: 535-548.
[129] Wang ZH, Hu HY, Wang HL. Robust stabilization to non-linear delayed systems via delayed state feedback: the averaging method[J]. Journal of Sound and Vibration, 2005, 279: 937-953.
[130] Ge SS, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems[J]. Automatica, 2002, 38: 671-682.
[131] Wang DA, Huang YM. Application of discrete-time variable structure control in the vibration reduction of a flexible structure[J]. Journal of Sound and Vibration, 2003, 261: 483-501.
[132] Tisseur F. Backward error and condition of polynomial eigenvalue problems[J]. LinearAlgebra and its Applications, 2000, 309: 339-361.
[133] Masad J. Computation of linear instability eigenvalue subject to perturbations in mean-flow and stability parameter[J]. Computers & Fluids, 1995, 24(6): 653-662.
[134] Lin TR, Pan J. A closed form solution for the dynamic response of finite ribbed plates[J]. Acoustical Society of America, 2006, 119(2): 917-925.
[135] Han Q, Zheng XF. Chaotic response of a large deflection beam and effect of the second order mode[J]. European Journal of Mechanics A/Solids, 2005, 24: 944-956.
[136] Hall JW. Uncertainty-based sensitivity indices for imprecise probability distributions[J]. Reliability Engineering and System Safety, 2006, 91(10-11): 1443-1451.
[137] Bazan FSV. Sensitivity eigenanalysis for single shift-invariant subspace-based methods[J]. Signal Processing, 2000, 80: 89-100.
[138] Hasan WM, Viola E. Use of the singular value decomposition method to detect ill-conditioning of structural identification problems[J]. Computers & Structures, 1997, 63(2): 267-275.
[139] Mosca E, Agnoloni T. Closed-loop monitoring for early detection of performance losses in feedback-control systems[J]. Automatica, 2003, 39: 2071-2084.
[140] Hespanha JP, Liberzon D, Morse AS. Hysteresis-based switching algorithms for supervisory control of uncertain systems[J]. Automatica, 2003, 39: 263-272.
[141] [Nataraj PSV. Computation of QFT bounds for robust tracking specifications[J]. Automatica, 2002, 38: 327-334.
[142] Hagenmeyer V, Delaleau E. Robustness analysis of exact feedforward linearization based on differential flatness[J]. Automatica, 2003, 39: 1941-1946.
[143] Liang YW, Liaw DC. Robust control non-linear affine systems[J]. Applied Mathematics and Computation, 2003, 137: 337-347.
[144] Mahmoud MS. Robust H∞control of linear neutral systems[J]. Automatica, 2000, 36: 757-764.
[145] Huang YJ, Wang YJ. Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem[J]. ISA Transactions, 2000, 39: 419-431.
[146] Mahmoud MS, Zribi M. Guaranteed cost observer-based control of uncertain time-lag systems[J]. Computers and Electrical Engineering, 2003, 29: 193-212.
[147] R. Lind, K. Snyder , M. Brenner., Wavelet analysis to characterize non-linearities and predict limit cycles of an aero elastic system[J]. Mechanical Systems and Signal Processing. 2001, 15(2): 337-356.
[148] J. Awrejcewicz , A. V. Krysko, Wavelet-based analysis of parametric vibrations of flexible[J]. International Applied Mechanic. 2003, 39(9): 997-1029.
[149] S. Pernot,C.H. Lamarque. A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems[J]. Nonlinear Dynamics, 2003, 32: 33–70.
[150] Chun-Hsiung Fang, Yung-Sheng Liu, Shih-Wei Kau. A new LMI-based approach to relaxed quadratic stabilization of T–S fuzzy control systems[J]. IEEE Trans. On Fuzzy Sysems.2006, 14(3): 386-398.
[151]刘晓东,张庆灵.模糊系统H 2 /H∞控制器设计的LMI方法[J].控制理论与应用. 2004, 21(1):102-124.
[152] Huai-Ning Wu and Kai-Yuan Cai. Mode-independent Robust Stabilization for uncertain markovian jump nonlinear systems via fuzzy Control[J]. IEEE Trans. on Systems.Man,Cybernetics. 2006, 36(3):509-512.
[153]王登刚,李杰.计算具有区间参数结构特征值范围的一种新方法[J].计算力学学报, 2004, 21(1): 56-61.
[154] Chen S H, Qiu Z P. Perturbation method for computing eigenvalue bounds in vibration system with interval parameters[J]. Communication in Numerical Methods in Engineering, 1994, 10: 121-134.
[155]陈塑寰,邱志平,宋大同,等.区间矩阵标准特征值的一种解法[J].吉林工业大学学报, 1993, 23(3): 1-8.
[156] Muhanna R L, Mullen R L. Uncertainty in mechanics problems-interval-based approach[J]. Journal of Engineering Mechanics, 2001, 127(3): 557-566.
[157]吴晓,罗佑新,文会军,等.非确定性结构系统区间分析的泛灰求解方法[J].计算力学学报, 2003, 20(3): 329-334.
[158] Nakagiri S, Suzuki K. Finite element interval analysis of external loads identified by displacement input with uncertainty. Comput Methods Appl Mech Engrg, 1999, 168: 63-72.
[159]王登刚.非线性反演算法及其应用研究[M].大连:大连理工大学, 2001.
[160]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报, 2005, 22(2): 227-231.
[161]王登刚,李杰.结构可靠性分析的区间方法[C]. 12届全国反应堆结构力学会议论文集,烟台, 2002.
[162] Chen S H, Lian H D, Yang X W. Interval displacement analysis for structures with interval parameters[J]. Int J Num Methods in Eng, 2002, 53(2): 393-407.
[163]吴杰,陈塑寰.区间参数结构的动力响应优化[J].固体力学学报, 2004, 25(2): 186-189.
[164] Gorzafczany B. Approximate inference with interval-valued fuzzy Sets– an outline[A]. Proc Polish Symp: on interval and fuzzy math[C]. Poland, 1983, 89-95.
[165] Ben-Haim Y. Convex models of uncertainty in radial pulse buckling of shells[J]. Journal of Applied Mechanics, 1993, 60(3): 683-688.
[166]郭书祥,吕震宙.区间运算和静力区间有限元[J].应用数学和力学, 2001, 22(12): 1249-1254.
[167] Chen S H, Yang X W. Interval finite element method for beam structures[J]. Finite Elements in Analysis and Design, 2000, 34(1): 75-88.
[168]郭书祥,吕震宙.线形区间有限元静力控制方程的组合解法[J].计算力学学报, 2003, 20(1): 34-38.
[169]王登刚,李杰.计算不确定结构系统静态响应的一种可靠方法[J].计算力学学报, 2003, 20(6): 662-669.
[170] Li J , Liao S. Response analysis of stochastic parameter st ructures under non-stationary random excitation[J]. Computational Mechanics, 2001 , 27 (1): 61-68.
[171]王登刚.计算具有区间参数结构的固有频率的优化方法[J].力学学报, 2004, 36(3): 364-372.
[172] David M , Dirk V. An interval finite element approach for t he calculation of envelope f requency response functions[J]. International Journal for Numerical Met hods in Engineering, 2004, 61:2480-2507.
[173] Qiu Z , Wang X. Parameter perturbation met hod for dynamic responses of st ructures with uncertain-but-bounded parameters based on interval analysis[J]. International Journal of Solids and Structures, 2005, 42(18-19) : 4958-4970.
[174] Moor R E. Methods and Applications of Interval Analysis[M]. Philadelphia: SIAM Publications, 1979.
[175] Alefeld G, Herzberger J. Introduction to interval computations[M]. Academic Press, New York, 1983.
[176]沈祖和.区间分析方法及其应用[J].应用数学和计算数学, 1983 (2): 34-58.
[177]胡承毅,徐山鹰,杨晓光.区间算法简介[J].系统工程理论与实践, 2003 (4): 59-62.
[178] Turksen B. Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems. 1986, 20: 191-210.
[179] Zeng Wenyi, Shi Yi. Note on interval-valued fuzzy set[J]. Lecture Notes in Artificial Intelligence, 2005, 3316: 20-24.
[180] Zeng Wenyi, Li Hongxing. Relationship between similarity measures and ent ropy of interval valued fuzzy sets[J]. Fuzzy Set s and Systems, 2006, 157: 1477-1481.
[181] Cornelis C, Deschrijver D, Kerre E E. Advances and challenges in interval-valued fuzzy logic [J]. Fuzzy Sets and Systems, 2006, 157 :622-628.
[182] Chun M G. A similarity-based bidirectional approximate reasoning method for decision2making systems[J]. FuzzySet s and Systems, 2001, 117: 269-276.
[183] Chen S M, Hsiao W H, Jong W T. Bidirectional approximate reasoning based oninterval2valued fuzzy sets[J]. Fuzzy Sets and Systems, 1997, 91: 339-345.
[184] Chen S M, Hsiao W H. Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets[J]. Fuzzy Set s and Systems, 2000, 113: 185-190.
[185]吴望名.区间模糊集和区间值模糊推理[J].模糊系统与数学, 1992, 6(2): 38-47.
[186] Rao S S, Berke L. Analysis of uncertain structural system using interval analysis[J]. AIAA Journal, 1997, 35(4): 727-735.
[187]李杰.结构动力分析的若干发展趋势.世界地震工程, 1993, 2: l-8.
[188]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].西南交通大学博士学位论文, 1996.
[189]李贤兴.强震作用下钢筋混凝土多层结构的空间随机响应分析及其损伤评估[D].西南交通大学博士学位论文, 1991.
[190] SAWADA Y, OHSUMI A. Active vibration control for flexible cantilever beam subject to seismic disturbance[C].∥IEEE International Conference on Systems Engineering. Kobe: IEEE, 1992: 436-439.
[191] PETERSEN I R, POTA H R. Minimax LQG optimal control of a flexible beam[J]. Control Engineering Practice, 2003, 11: 1273-1287.
[192] Z G Ying, W Q Zhu, T T Soong. A Stochastic Optimal Semi-active Control Strategy for ER/MR Dampers[J]. Journal of Sound and Vibration, 2003, 259: 45-62.
[193]赵治国.车辆动力学及其非线性控制理论技术的研究[D].西北工业大学博士学位论文, 2002.
[194]余瑞芬.传感器原理[M].北京:航空工业出版社. 1995.
[195]宋天霞.有限元法理论及应用基础教程[M].武汉:华中工学院出版社, 1987.
[196] Hallauer W L Jr, Barthelemy J F M. Active damping of modal vibrations by force apportioning[C]. Proceedings of the AIAA/ASME/ASCE 21ST Structures, Structural Dynamics, and Materials Conference, 1980: 863-873.
[197] Rajaram S. Optimal independent modal space control of a flexible system including integral feedback[C]. Proceeding of an International Symposium on Engineering Science and Mechancs, Tainan, Taiwan, Dec. 29-31, 1981, 1031-1041.
[198] A STROM K J, HOGGLUND T. PID Controllers: Theory, Design and Tuning [M]. Research Triangle Park: Instrument Society of America, 1995.
[199] TAN W, CHEN T, MARQUEZ H J. Robust Controller design and PID tuning for multivariable process[J]. Asian J of Control, 2002, 4(4): 439-451.
[200] Feng Zheng, Qing-Guo Wang, Tong Heng Lee. On the design of multivariable PID controllers via LMI approach[C]. The 27th Annual Conference of the IEEE Industrial Electronics Society, 2001, 776-781.
[201]蔡国平.存在时滞的柔性梁的振动主动控制[J]..固体力学学报. 2004, 25(1):29-34.
[202]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[203]李志虎,王景成,邵惠鹏.时变不确定离散时滞系统的H∞鲁棒控制.控制理论与应用[J].. 2003.20(1):139-142.
[204] Cai G P, Huang J Z. Optimal control method for seismically excited building structures with time delay in control[J]. Journal of Engineering Mechanics, ASCE, 2002, 128(6): 602-612.
[205]刘金琨.先进PID控制MATLAB仿真[M].北京:电子工业出版社, 2004.
[206]吉林化学工业公司电石厂.电石生产问答[M].北京:化学工业出版社,1979.
[207] Lang Z Q. Gu X Y. Bao Y M. Modelling and Identification of Electrode Position Controller in Electric Arc Furnace[C]. International Conference on Control 1991,.1: 434-439.
[208]陈峻岭,罗安,李正国,等.智能大功率电弧炉自动控制系统[J].中国有色金属学报, 2002, 12(2):.393-397.
[209] Ziegler J G. Nichols N B. Optimum settings for automatic controllers[J]. TransASME, 1942, 64: 745-768.
[210]玄光男,程润伟.遗传算法与工程优化[M].北京:清华大学出版社, 2004.
[211] HUKSDóTTIR. System identification of a three-phase submerged-arc ferrosilicon furnace[J]. IEEE Transactions on Control Systems Technoligy, 1995 3(4): 377-387.