复杂激励环境下分布式结构的振动主动控制研究
|
摘要
复杂激励作用下的振动控制涉及到结构动力学，控制理论，信号处理，计算机应用等多个交叉学科领域。分布式结构在复杂激励作用下具有复杂的动力学行为，长期以来一直吸引着广大学者的关注。复杂激励会使这类结构产生分叉、混沌等非线性动力学行为。由于这类受控结构具有连续性特点，拥有无穷维数，对其进行理论分析具有相当大的困难。另外，通过计算机或DSP等硬件设施进行控制器设计时，容易引起观测和控制溢出的问题，从而导致系统失稳，这对控制算法的鲁棒性和抗干扰性能提出了更高的要求。因此，研究复杂激励作用下分布式结构的控制问题具有极大的挑战性，同时具有很强的工程应用背景和科学意义。
本文以风洞测力模型受跨声速风载作用下的振动控制为背景，研究分布式结构受复杂激励作用下的系统动力学控制问题。论文的主要研究内容和学术贡献如下：
1.针对模型参数已知的受控对象，进行输入估计控制方法的研究。为提高系统控制效果，得到更为可靠的控制输入，将未知外扰引入到控制器的设计和求解过程中。研究表明，结合随机游走模型能够将系统转换为不显含系统外扰的状态方程。针对该新方程进行Kalman滤波估计得到系统状态，其中包含未知外扰的估计值。因此，就可以采用线性二次型Gauss方法得到含外扰的控制器表达式。
2.研究了滤波器时滞对受控系统稳定性的影响。为消除分布式受控系统输出信号中的高频和噪声干扰，引入抗混滤波器和高阶低通数字滤波器作为信号处理手段。不考虑滤波器过渡带非线性相频的影响，将通带范围内的相频特性近似成线性关系，研究滤波器产生的固定时滞现象。并进一步分析该时滞对控制系统动力学的影响，通过分析得到系统稳定时滞区域。
3.研究了系统存在输出时滞情况下的控制方法，提出基于时滞利用和消除的控制器设计方法。在时滞利用方面，根据系统稳定时滞区域内的脉冲响应衰减速度，确定接近最佳控制效果时的时滞量，以此为依据对系统时滞重新设定以提升控制效果。另外，在时滞消除控制方法的研究方面，建立了不显含时滞的离散状态方程，结合LQ控制方法实现基于固定时滞的振动主动控制研究。
4.考虑滤波器过渡带非线性相频特性，研究由此产生的可变时滞现象。在处理这一问题过程中采用相位补偿法将原本含有可变时滞的系统转换为固定时滞系统，为进一步研究消除总体时滞建立可靠的输出时间序列。
5.进行时间序列预测方法的研究，建立关于系统输出的ARMA模型。通过变换将该模型转换为AR模型，同时采用随机近似方法对其进行求解，得到无时滞的估计输出序列。这一过程从根本上消除了时滞的影响，为不依赖模型的控制算法提供有效的控制器输入。
6.根据实际工程应用和试验研究的需求，分别建立工程控制系统和地面试验系统。结合Borland C++软件开发平台编制控制软件，通过对DAQ2206数采卡进行接口和信号传输操作，实现计算机与恒流源、功率放大器等外部设备的通讯。采用多线程技术实现数据接收、输送以及计算机内部运算的同步进行，为控制系统的实时工作提供保障。
7.结合地面试验控制系统对文中提出的控制方法进行试验验证，同时将部分控制方法应用于工程控制系统。
The active vibration control of structures suffering from complex excitations is aninterdisciplinary subject involving the scientific research fields of structural dynamics, control theory,signal processing, computer application, etc. The kinetic study of distributed structures suffering fromcomplex excitations has long attracted the attention of scholars. However, complex excitationsprovide this type of structure with nonlinear dynamical behaviors such as bifurcation, chaos, etc.These complicated phenomena are induced by the infinite dimensional characteristic of continuousstructures, and it is easy to induce observation and control spillover when discrete time controlalgorithms are applied. This problem will influence the system’s instability. Therefore, the system’srobustness and anti-jamming performance should be further considered. In general, studying problemsinvolving distributed structures suffering from complex excitations is a great challenge, with a strongengineering background and scientific significance.
Based on the vibration control of a wind tunnel model suffering from a transonic wind load, thisstudy examines the dynamical phenomena and control methods for a distributed structure sufferingfrom complex excitations. The main research contents and contributions are as follows:
1. A control algorithm based on the input estimation method is studied, using a system withdeterminate model parameters. An unknown disturbance is introduced into the controllerdesign to improve control effect. Systems can be converted to a new state equation withoutan explicit disturbance in combination with a random walk model. Thus, it is easy to acquirethe estimated value of the new state equation by using a Kalman filter, which contains theestimated value of the unknown disturbance. Therefore, the estimated value can be used inthe linear quadratic gauss method to express the math of a controller with a disturbance.
2. An anti-aliasing filter and high-order low-pass digital filter are introduced to avoid theinfluence of noise induced by the high-order mode of the distributed structures. The linearrelationship is regarded approximately as the phase-to-frequency characteristic in thepass-band of the filters. Considering the invariant time delay induced by the filters, thestability of the controlled system is studied, and the stability regions of the system areconfirmed by the stability switch theory.
3. Delay usage and elimination methods are studied to design controllers adapted to the case ofsystems with output time delays. From the aspect of delay usage, an appropriate time delaycan be determined according to the decay rate of the impulse response. The controlled effect can be greatly improved through a time delay reset. From the aspect of delay elimination, adiscrete state equation is constructed without an explicit time delay, and is combined with alinear quadratic control method to obtain a controller with a time delay.
4. Considering the nonlinear phase-to-frequency characteristic in the transition bandwidth offilters, the problem induced by a system’s variable time delay is studied. To deal with thisnew problem, the variable time delay system is converted to a fixed one using a phasecompensation method. A credible output time series is established for further study on theelimination of overall delay.
5. A time series forecasting method is studied, and an ARMA model is established based on thesystem output. To obtain a serial output without a time delay, the model is transferred to theAR form, and is solved using a stochastic approximation method. This process essentiallyeliminates the influence of time delay and provides an effective controller input for thecontrol algorithm independent of the model parameters.
6. Based on an actual engineering application and experimental research, an engineeringcontrol system and ground test system are established. Application software is developed forthe control system based on the Borland C++software development platform. In addition,the connections between a computer and a constant current source, power amplifier, andother peripheral equipment are established by using a data acquisition card (DAQ2206). Toprovide protection for real-time applications, multithreading technology is adopted to ensurecomputer and data transfer synchronization.
7. The proposed control methods are validated on the ground test system, and some of them areapplied in the engineering control system.
本文以风洞测力模型受跨声速风载作用下的振动控制为背景，研究分布式结构受复杂激励作用下的系统动力学控制问题。论文的主要研究内容和学术贡献如下：
1.针对模型参数已知的受控对象，进行输入估计控制方法的研究。为提高系统控制效果，得到更为可靠的控制输入，将未知外扰引入到控制器的设计和求解过程中。研究表明，结合随机游走模型能够将系统转换为不显含系统外扰的状态方程。针对该新方程进行Kalman滤波估计得到系统状态，其中包含未知外扰的估计值。因此，就可以采用线性二次型Gauss方法得到含外扰的控制器表达式。
2.研究了滤波器时滞对受控系统稳定性的影响。为消除分布式受控系统输出信号中的高频和噪声干扰，引入抗混滤波器和高阶低通数字滤波器作为信号处理手段。不考虑滤波器过渡带非线性相频的影响，将通带范围内的相频特性近似成线性关系，研究滤波器产生的固定时滞现象。并进一步分析该时滞对控制系统动力学的影响，通过分析得到系统稳定时滞区域。
3.研究了系统存在输出时滞情况下的控制方法，提出基于时滞利用和消除的控制器设计方法。在时滞利用方面，根据系统稳定时滞区域内的脉冲响应衰减速度，确定接近最佳控制效果时的时滞量，以此为依据对系统时滞重新设定以提升控制效果。另外，在时滞消除控制方法的研究方面，建立了不显含时滞的离散状态方程，结合LQ控制方法实现基于固定时滞的振动主动控制研究。
4.考虑滤波器过渡带非线性相频特性，研究由此产生的可变时滞现象。在处理这一问题过程中采用相位补偿法将原本含有可变时滞的系统转换为固定时滞系统，为进一步研究消除总体时滞建立可靠的输出时间序列。
5.进行时间序列预测方法的研究，建立关于系统输出的ARMA模型。通过变换将该模型转换为AR模型，同时采用随机近似方法对其进行求解，得到无时滞的估计输出序列。这一过程从根本上消除了时滞的影响，为不依赖模型的控制算法提供有效的控制器输入。
6.根据实际工程应用和试验研究的需求，分别建立工程控制系统和地面试验系统。结合Borland C++软件开发平台编制控制软件，通过对DAQ2206数采卡进行接口和信号传输操作，实现计算机与恒流源、功率放大器等外部设备的通讯。采用多线程技术实现数据接收、输送以及计算机内部运算的同步进行，为控制系统的实时工作提供保障。
7.结合地面试验控制系统对文中提出的控制方法进行试验验证，同时将部分控制方法应用于工程控制系统。
The active vibration control of structures suffering from complex excitations is aninterdisciplinary subject involving the scientific research fields of structural dynamics, control theory,signal processing, computer application, etc. The kinetic study of distributed structures suffering fromcomplex excitations has long attracted the attention of scholars. However, complex excitationsprovide this type of structure with nonlinear dynamical behaviors such as bifurcation, chaos, etc.These complicated phenomena are induced by the infinite dimensional characteristic of continuousstructures, and it is easy to induce observation and control spillover when discrete time controlalgorithms are applied. This problem will influence the system’s instability. Therefore, the system’srobustness and anti-jamming performance should be further considered. In general, studying problemsinvolving distributed structures suffering from complex excitations is a great challenge, with a strongengineering background and scientific significance.
Based on the vibration control of a wind tunnel model suffering from a transonic wind load, thisstudy examines the dynamical phenomena and control methods for a distributed structure sufferingfrom complex excitations. The main research contents and contributions are as follows:
1. A control algorithm based on the input estimation method is studied, using a system withdeterminate model parameters. An unknown disturbance is introduced into the controllerdesign to improve control effect. Systems can be converted to a new state equation withoutan explicit disturbance in combination with a random walk model. Thus, it is easy to acquirethe estimated value of the new state equation by using a Kalman filter, which contains theestimated value of the unknown disturbance. Therefore, the estimated value can be used inthe linear quadratic gauss method to express the math of a controller with a disturbance.
2. An anti-aliasing filter and high-order low-pass digital filter are introduced to avoid theinfluence of noise induced by the high-order mode of the distributed structures. The linearrelationship is regarded approximately as the phase-to-frequency characteristic in thepass-band of the filters. Considering the invariant time delay induced by the filters, thestability of the controlled system is studied, and the stability regions of the system areconfirmed by the stability switch theory.
3. Delay usage and elimination methods are studied to design controllers adapted to the case ofsystems with output time delays. From the aspect of delay usage, an appropriate time delaycan be determined according to the decay rate of the impulse response. The controlled effect can be greatly improved through a time delay reset. From the aspect of delay elimination, adiscrete state equation is constructed without an explicit time delay, and is combined with alinear quadratic control method to obtain a controller with a time delay.
4. Considering the nonlinear phase-to-frequency characteristic in the transition bandwidth offilters, the problem induced by a system’s variable time delay is studied. To deal with thisnew problem, the variable time delay system is converted to a fixed one using a phasecompensation method. A credible output time series is established for further study on theelimination of overall delay.
5. A time series forecasting method is studied, and an ARMA model is established based on thesystem output. To obtain a serial output without a time delay, the model is transferred to theAR form, and is solved using a stochastic approximation method. This process essentiallyeliminates the influence of time delay and provides an effective controller input for thecontrol algorithm independent of the model parameters.
6. Based on an actual engineering application and experimental research, an engineeringcontrol system and ground test system are established. Application software is developed forthe control system based on the Borland C++software development platform. In addition,the connections between a computer and a constant current source, power amplifier, andother peripheral equipment are established by using a data acquisition card (DAQ2206). Toprovide protection for real-time applications, multithreading technology is adopted to ensurecomputer and data transfer synchronization.
7. The proposed control methods are validated on the ground test system, and some of them areapplied in the engineering control system.
引文
[1] Meirovitch L. Some problems associated with the control of distributed structures. Journal ofOptimization Theory and Applications,1987,54:1-20.
[2] Meirovitch L. Computational methods in structural dynamics. The Netherlands, Sijthoff&noordhoff,1980.
[3] Balas M J. Active control of flexible systems. Journal of Optimization Theory and Applications,1978,25:415-436.
[4] Mei C. Reduction of control spillover in active vibration control of distributed structures usingmultioptimal shemes. Journal of Sound and Vibration,2002,251(1):184-192.
[5] Counrant R. Variation method for solutions of problems of equilibrium and vibrations. Problemsof Equilibrium and Vibrations,1943,49:1-23.
[6] Jonker B. A finite element dynamics analysis of spatial mechanisms with flexible links. Faculty ofMechanical Engineering,1989,76(1):17-40.
[7] Jonker B. A finite element dynamic analysis of flexible manipulators. The International Journal ofRobotics Research.1990,9(4):59-74.
[8]徐晨,甘小冰.柔性操作器动力学的数值方法.机器人,1992,14(1):52-58.
[9]徐晨,张景绘,史维祥.一个高精度单臂柔性机械手的动力学模型.机器人,1992,14(5):8-13.
[10] Xu C, Shi W, Zhang J. An investigation of the effect of distributed structure flexibility onbehavior of single-link manipulator force-feedback control system. Proceedings of the IEEEInternational Symposium on Industrial Electronics,1992,1:320-323.
[11] Hwu C, Chang W C, Gai H S. Vibration suppression of composite sandwich beams. Journal ofSound and Vibration,2004,272(1-2):1-20.
[12] Zain M Z, Tokhi M O, Mohamed Z. Hybrid learning control schemes with input shaping of aflexible manipulator system. Mechatronics,2006,16(3-4):209-219.
[13] Wong W O, Tang S L, Cheung Y L, Cheng L. Design of a dynamic vibration absorber forvibration isolation of beams under point or distributed loading. Journal of Sound and Vibration,2007,301(3-5):898-908.
[14] Cheung Y L, Wong W O. H∞and H2optimizations of a dynamic vibration absorber forsuppressing vibrations in plates. Journal of Sound and Vibration,2009,320(1-2):29-42.
[15] Chu C L, Wu B S, Lin Y H. Active vibration control of a flexible beam mounted on an elasticbase. Finite Elements in Analysis and Design,2006,43(1):59-67.
[16] Lim C W, Park Y J, Moon S J. Robust saturation controller for linear time-invariant system withstructured real parameter uncertainties. Journal of Sound and Vibration,2006,294(1-2):1-14.
[17] Yaman M, Sen S. Vibration control of a cantilever beam of varying orientation. Solids andStructures,2007,44(3-4):1210-1220.
[18] Dong X J, Meng G, Peng J C. Vibration control of piezoelectric smart structures based on systemidentification technique: Numerical simulation and experimental study. Journal of Sound andVibration,2006,297(3-5):680-693.
[19] zcan K, John C, Bruch J, James M S, Sarp A, Ibrahim S S. Integral equation approach for piezopatch vibration control of beams with various types of damping. Computers&Structures,2008,86(3-5):357-366.
[20]邱志成,吴宏鑫.基于特征模型的压电悬臂板振动控制.机械工程学报,2008,44(10):187-195.
[21] Stavroulakis G E, Foutsitzi G, Hadjigeorgiou E, Marinova D, Baniotopoulos C C. Design androbust optimal control of smart beams with application on vibrations suppression. EngineeringSoftware,2005,36(11-12):806-813.
[22] Wu S T, Shao Y J. Adaptive vibration control using a virtual-vibration-absorber controller.Journal of Sound and Vibration,2007,305(4-5):891-903.
[23] Wu S T, Chiu Y Y, Yeh Y C. Hybrid vibration absorber with virtual passive devices. Journal ofSound and Vibration,2007,299(1-2):247-260.
[24] Zhang Y, Zhang X, Xie S. Adaptive vibration control of a cylindrical shell with laminated PVDFactuator. Acta Mechanic,2010,210(1-2):85-98.
[25] To C W S, Chen T. Optimal control of random vibration in plate and shell structures withdistributed piezoelectric components. Mechanical Sciences,2007,49(12):1389-1398.
[26] Luo Q, Tong L. Exact static solutions to piezoelectric smart beams including peel stresses, Part I:Theoretical formulation. International Journal of Solids and Structures,2002,39(18):4677-4695.
[27] Luo Q, Tong L. Exact static solutions to piezoelectric smart beams including peel stresses, Part II:Numerical results, comparison and discussion. International Journal of Solids and Structures,2002,39(18):4697-4722.
[28] Tong L, Luo Q. Exact dynamic solutions to piezoelectric smart beams including peel stresses, I:Theory and application. International Journal of Solids and Structures,2003,40(18):4789-4812.
[29] Istv á n E. Dynamic equilibrium equations of linear piezoelectric Euler-Bernoulli beams.Mechanics Research Communications,2009,36(2):175-182.
[30] Daví F. Saint-Venant’s problem for linear piezoelectric bodies. Journal of Elasticity,1996,43(3):227-245.
[31] D kmeci M C. Recent progress in the dynamic applications of piezoelectric crystals. The Shockand Vibration Digest,1988,20(2):3-20.
[32] Robert G L. Recent developments in smart structures with aeronautical applications. SmartMaterials and Structures,1997,6(5):11-42.
[33]孙宝元,钱敏,张军.压电式传感器与测力仪研发回顾与展望.大连理工大学学报,2001,41(2):127-134.
[34] Cady W G. Piezoelectricity. New York, Dover Publications,1964.
[35] Tzou H S. Piezoelectric Shells: Distributed Sensing and Control of Continua. Dordrecht,Netherlands, Kluwer Academic Publisher,1993.
[36] Yang J S. Introduction to the Theory of Piezoelectricity. New York, Springer,2005.
[37] Edward F C, Javier L. Use of piezoelectric actuators as elements of intelligent structures. AIAAJournal,1987,25(10):1373-1385.
[38]胡海岩,孙久厚,陈怀海.机械振动与冲击.北京:航空工业出版社,1998.
[39] Valverde J C, Pelayo F L, Martinez J A, Miralles J J. Stability of continuous systems byRouth-Hurwitz and Mathematica. Journal of Computational Methods in Science and Engineering,2004,4(1-2):125-134.
[40] Chang J R, Lin W J, Huang C J, Choi S T. Vibration and stability of an axially moving Rayleighbeam. Applied Mathematical Modelling,2010,34(6):1482-1497.
[41] Yang X D, Tang Y Q, Chen L Q, Lim C W. Dynamic stability of axially accelerating Timoshenkobeam: Averaging method. European Journal of Mechanics A/Solids,2010,29(1):81-90.
[42] Wang P K C, Wei J D. Vibrations in a moving flexible robot arm. Journal of Sound and Vibration,1987,116(1):149-160.
[43] Ding H, Chen L Q. Stability of axially accelerating viscoelastic beams: multi-scale analysis withnumerical confirmations. European Journal of Mechanics A/Solids,2008,27(6):1108-1120.
[44] Chen L Q, Yang X D. Stability in parametric resonance of axially moving viscoelastic beamswith time-dependent speed. Journal of Sound and Vibration,2005,28(3-5):879-891.
[45] Young T H, Juan C S. Dynamic stability and response of fluttered beams subjected to randomfollower forces. International Journal of Non-Linear Mechanics,2003,38(6):889-901.
[46] Meirovitch L. Some problems associated with the control of distributed structures. Journal ofOptimization Theory and Applications.1987,54(1):1-20.
[47] Meirovitch L. Dynamics and Control of Structures. New York, John Wiley&Sons,1989.
[48] Meirovitch L, Bennighof J K. Modal control of traveling waves in flexible structures. Journal ofSound and Vibration.1986,111(1):131-144.
[49] Mei C, Mace B R, Jones R W. Hybrid wave/mode active vibration control. Journal of Sound andVibration,2001,274(5):765-784.
[50] Piazzi A, Visioli A. A noncausal approach for PID control. Journal of Process Control,2006,16(8):831-843.
[51] Khoury G M, Saad M, Kanaan H Y, Asmar C. Fuzzy PID control of five DOF robot arm. Journalof Intelligent and Robotic Systems,2004,40(3):299-320.
[52] Astr m K J, H gglund T. The future of PID control. Control Engineering Practice,2001,9(11):1163-1175.
[53] Li Y, Sheng A, Wang Y. Synthesis of PID-type controllers without parametric models: a graphicalapproach. Energy Conversion and Management,2008,49(8):2392-2402.
[54]李超,马玉玲,张伟平.模糊增益调整PID控制在VAV系统中的应用.控制系统,2006,22(16):35-37.
[55]苏绍兴.基于变速积分PID的温度控制系统设计.机电工程,2002,19(6):28-30.
[56] Liu Z, Wang D, Hu H, Yu M. Measures of Modal Controllability and Observability in VibrationControl of flexible Structures. Engineering Notes,1994,17(6):1377-1380.
[57] Hurlebaus S, St bener U, Gaul L. Vibration reduction of curved panels by active modal control.Computers&Structures,2008,86(3-5):251-257.
[58] Houlston P R, Garvey S D, Popov A A. Modal control of vibration in rotating machines and othergenerally damped systems. Journal of Sound and Vibration,2007,302(1-2):104-116.
[59] Datta B N. Recent developments on nonmodal and partial modal approaches for control ofvibration. Applied Numerical Mathematics,1999,30(1):41-52.
[60] Wang D A, Huang Y M. Modal space vibration control of a beam by using the feedforward andfeedback control loops. International Journal of Mechanical Sciences,2002,44(1):1-19.
[61] Librescu L, Na S, Qin Z, Lee B. Active aeroelastic control of aircraft composite wings impactedby explosive blasts. Journal of Sound and Vibration,2008,318(1-2):1-19.
[62] Magdalene M, Yannis M, Georgios E S. Vibration control of beams with piezoelectric sensorsand actuators using particle swarm optimization. Expert Systems with Applications,2011,38(6):6872-6883.
[63] Yang F, Esmailzadeh E, Sedaghati R. Optimal vibration control of beam-type structures usingmultiple-tuned-mass-dampers. Proceedings of the Institution of Mechanical Engineers, Park K:Journal of Multi-body Dynamics,2010,244(2):191-202.
[64] Yang J, Chen G. Optimal placement and configuration direction of actuators in plate structurevibration control system.2nd International Asia Conference on Informatics in Control, Automationand Robotics,2010:124-8.
[65] Choi S B, Hong S R, Sung K G, Sohn J W. Optimal control of structural vibrations using amixed-mode magnetorheological fluid mount. International Journal of Mechanical Sciences,2008,50(3):559-568.
[66]李书,孙忠凯,向锦武.结构控制中输出反馈鲁棒极点配置优化方法.力学学报,2001,33(1):71-78.
[67] Jiang D, Wang J. Augmented gradient flows for on-line robust pole assignment via state andoutput feedback. Automatica,2002,38(2):279-286.
[68] Toshkov A. Distributed control linear systems design with pole assignment. Annual Review inAutomatic Programming,1985,12(1):429-432.
[69] Wei M, Wang Q, Cheng X. Some new results for system decoupling and pole assignmentproblems. Automatica,2010,46(5):937-944.
[70] Tsui C. A new dynamic output feedback compensator design for pole assignment. Journal of TheFranklin Institute,1999,366():665-674.
[71] Ouyang H. Pole assignment of friction-induced vibration for stabilisation through state-feedbackcontrol. Journal of Sound and Vibration,2010,329(11):1985-1991.
[72]刘金琨.先进PID控制MATLAB仿真(第二版).北京:电子工业出版社,2004.
[73]陈卫东,邵敏强,杨兴华,路波,徐庆华.跨声速风洞测力模型主动减振系统的试验研究.振动工程学报,2007,20(1):91-96.
[74] Liu G P, Daley S. Optimal-tuning PID control for industrial systems. Control EngineeringPractice,2001,9(11):1185-1194.
[75] Hayashi K, Otsubo A, Murakami S, Maeda M. Realization of nonlinear and linear PID controlsusing simplified indirect fuzzy inference method. Fuzzy Sets and Systems,1999,105(3):409-414.
[76] Mizumoto M. Realization of PID controls by fuzzy control methods. Fuzzy Sets and Systems,1995,70(2-3):171-182.
[77] Ji W, Li Q, Xu B, Zhao D, Fang S. Adaptive fuzzy PID composite control with hysteresis-bandswitching for line of sight stabilization servo system. Aerospace Science and Technology,2011,15(1):25-32.
[78] Sanchez E N, Becerra H M, Velez C M. Combining fuzzy, PID and regulation control for anautonomous mini-helicopter. Information Sciences,2007,177(10):1999-2022.
[79] Lan L H. Stability analysis for a class of Takagi–Sugeno fuzzy control systems with PIDcontrollers. International Journal of Approximate Reasoning,2007,46(1):109-119.
[80] Soyguder S, Karakose M, Alli H. Design and simulation of self-tuning PID-type fuzzy adaptivecontrol for an expert HVAC system. Expert Systems with Applications,2009,36(3):4566-4573.
[81] Dieulot J Y, Colas F. Robust PID control of a linear mechanical axis: A case study. Mechatronics,2009,19(2):269-273.
[82] Mattei M. Robust multivariable PID control for linear parameter. Automatica,2001,37(12):1997-2003.
[83] Tan K K, Lee T H, Jiang X. Robust on-line relay automatic tuning of PID control systems. ISATransactions,2000,39(2):219-232.
[84] Amer A F, Sallam E A, Elawady W M. A novel robust adaptive sliding mode control using fuzzyself-tunning PID controller for3DOF planar robot manipulators. ISA Transactions,2011,
[85] Mizumoto I, Ikeda D, Hirahata T, Iwai Z. Design of discrete time adaptive PID control systemswith parallel feedforward compensator. Control Engineering Practice,2010,18(2):168-176.
[86] Tang K Z, Huang S N, Tan K K, Lee T H. Combined PID and adaptive nonlinear control forservo mechanical systems. Mechatronics,2004,14(6):701-714.
[87] Eker. Sliding mode control with PID sliding surface and experimental application to anelectromechanical plant. ISA Transactions,2006,45(1):109-118.
[88] Petukhov L V, Troitskii V A. Some optimal problems of the theory of longitudinal vibrations ofrods: PMM. Journal of Applied Mathematics and Mechanics,1972,36(5):895-904.
[89] Blachut J. Parametrical optimal design of funicular arches against buckling and vibration.International Journal of Mechanical Sciences,1984,26(5):305-310.
[90]胡寿松,王执铨,胡维礼.最优控制理论与系统.北京:科学出版社,2005.
[91] Sadek I S, Adali S, Sloss J M, Bruch J C. Vibration damping of a thin plate by optimal open-andclosed-loop control forces. Journal of the Franklin Institute,1992,329(2):207-214.
[92] Lee H K, Chen S T, Lee A C. Optimal control of vibration suppression in flexible systems viadislocated sensor/actuator positioning, Journal of the Franklin Institute,1996,333(5):789-802.
[93] Bolonkin A A, Khot N S. Optimal Bounded control design for vibration suppression. ActaAstronautic,1996,38(10):803-813.
[94] Zhang X. Integrated optimal design of flexible mechanism and vibration control. InternationalJournal of Mechanical Sciences,2004,46(11):1607-1620.
[95] Qiu Z, Zhang X, Wu H, Zhang H. Optimal placement and active vibration control forpiezoelectric smart flexible cantilever plate. Journal of Sound and Vibration,2007,301(3-5):521-543.
[96] Huan R, Chen L, Jin W, Zhu W. Stochastic optimal vibration control of partially observablenonlinear quasi Hamiltonian systems with actuator saturation. Acta Mechanica Solida Sinica,2009,22(2):143-151.
[97] Gao W, Chen J J, Ma H B, Ma X S. Optimal placement of active bars in active vibration controlfor piezoelectric intelligent truss structures with random parameters. Computers&Structures,2003,81(1):53-60.
[98] Wang X Y, Ni Y Q, Ko J M, Chen Z Q. Optimal design of viscous dampers for multi-modevibration control of bridge cables. Engineering Structures,2005,27(5):792-800.
[99]朱位秋.随机振动.北京:科学出版社,1998.
[100] Zibdeh H S. Stochastic vibration of an elastic beam due to random moving loads anddeterministic axial forces. Engineering Structures,1995,17(7):530-535.
[101] Gao W, Chen J, Cui M, Cheng Y. Dynamic response analysis of linear stochastic truss structuresunder stationary random excitation. Journal of Sound and Vibration,2005,281(1-2):311-321.
[102] Grigoriu M. Linear models for non-Gaussian processes and applications to linear randomvibration. Probabilistic Engineering Mechanics,2011,26(3):461-470.
[103] Dimentberg M F. Random vibrations of a rotating shaft with non-linear damping. InternationalJournal of Non-Linear Mechanics,2005,40(5):711-713.
[104] Chen J B, Li J. Dynamic response and reliability analysis of non-linear stochastic structures,Probabilistic Engineering Mechanics,2005,20(1):33-44.
[105] Bryja D, niady P. Stochastic non-linear vibration of highway suspension bridge under inertialsprung moving load. Journal of Sound and Vibration,1998,216(3):507-519.
[106] Homan C J, Tierney J W. Determination of dynamic characteristics of processes in the presenceof random disturbances. Chemical Engineering Science,1960,12(3):153-165.
[107] Herbert R E. On the stresses in a nonlinear beam subject to random excitation. InternationalJournal of Solids and Structures,1965,1(2):235-242.
[108] Zhu W Q, Soong T T, Lei Y. Equivalent nonlinear system method for stochastically excitedHamiltonian systems. Journal of Applied Mechanics,1994,61(3):618-623.
[109]朱位秋,黄志龙,应祖光.非线性随机振动力学与控制的哈密顿理论框架.力学与实践,2002,24:1-9.
[110]张令弥.振动测试与动态分析.北京:航空工业出版社,1992.
[111] Rong H W, Xu W, Wang X, Meng G, Fang T. Response statistics of two-degree-of-freedomnon-linear system to narrow-band random excitation. International Journal of Non-Linear Mechanics,2002,37(6):1017-1028.
[112] Feng Z H, Lan X J, Zhu X D. Principal parametric resonances of a slender cantilever beamsubject to axial narrow-band random excitation of its base. International Journal of Non-LinearMechanics,2007,42(10):1170-1185.
[113] Feng Z H, Lan X J, Zhu X D. Explanation on the importance of narrow-band random excitationcharacters in the response of a cantilever beam. Journal of Sound and Vibration,2009,325(4-5):923-937.
[114] Gu M, Chang C C, Wu W, Xiang H F. Increase of critical flutter wind speed of long-spanbridges using tuned mass dampers. Journal of Wind Engineering,1998,73(2):111-123.
[115] Shi J, Hitchings D. Calculation of flutter derivatives and speed for2-D incompressible flow bythe finite-element method. Applied Mathematical Modelling,1994,18(10):538-549.
[116] Ge Y J, Xiang H F, Tanaka H. Application of a reliability analysis model tobridge flutter under extreme winds. Journal of Wind Engineering and Industrial Aerodynamics,2000,86(2-3):155-167.
[117] Bobryk R, Stettner L. Moment stability for linear systems with a random parametric excitation.System&Control Letters,2005,54(8):781-786.
[118] Náprstek J. Stochastic exponential and asymptotic stability of simple non-linear systems.Non-Linear Mechanics,1996,31(5):693-705.
[119] Feng C, Zhu W. Stochastic optimal control of strongly nonlinear systems under wide-bandrandom excitation with actuator saturation. Acta Mechanica Solida Sinica,2008,21(2):116-126.
[120] Elbeyli O, Sun J Q. Feedback control optimization of nonlinear systems under randomexcitations. Communications in Nonlinear Science and Numerical Simulation,2006,11(1):125-136.
[121] Montazeri A, Poshtan J. A new adaptive recursive RLS-based fast-array IIR filter for activenoise and vibration control systems. Signal Processing,2011,91(1):98-113.
[122] Gaonkar G H. A general method with shaping filters to study random vibration statistics oflifting rotors with feedback controls. Journal of Sound and Vibration,1972,21(2):213-225.
[123] Cross C F. An adaptive digital filter for broadband active sound control. Journal of Sound andVibration,1980,80(3):381-388.
[124] Sergent P, Duhamel D. The effects of sampling rate and length of an adaptive filter on the activecontrol of a plane sound wave in a lossy semi-infinite waveguide. Journal of Sound and Vibration,1997,203(1):127-150.
[125] Alam S M S, Yamada K, Baba S. A Kalman filter approach for galloping control of a bridgetower. Computer&Structure,1995,57(1):67-79.
[126] Brennan M J, Kim S M. Feedforward and feedback control of sound and vibration: a wienerfilter approach. Journal of Sound and Vibration,2001,246(2):281-296.
[127]于明礼.基于超声电机作动器的二维翼段颤振主动抑制,[博士学位论文].南京:南京航空航天大学,2006.
[128] Liu B, Hu H. Group delay induced instabilities and Hopf bifurcations, of a controlled doublependulum. International Journal of Non-Linear Mechanics,2010,45(4):442-452.
[129] Paola M D, Pirrotta A. Time delay induced effects on control of linear systems under randomexcitation. Probabilistic Engineering Mechanics,2001,16(1):43-51.
[130] Li X P, Liu Z H, Zhu W Q. First-passage failure of quasi linear systems subject tomulti-time-delayed feedback control and wide-band random excitation. Probabilistic EngineeringMechanics,2009,24(2):144-150.
[131] Cai G P, Huang J Z, Yang S X. An optimal method for linear systems with time delay.Computers&Structures,2003,81(15):1539-1546.
[132] K. Satyanarayana, P.M. Bainum. Synthesis of control laws for optimally designed large spacestructures. Acta Astronautic,1987,15(11):901-904.
[133]王亮,陈怀海,贺旭东,游伟倩.轴向运动变长度悬臂梁的振动控制.振动工程学报,2009,22(6):565-570.
[134]于国军,杜成斌,艾亿谋.压电陶瓷用于柔性悬臂梁振动控制的试验研究.河海大学学报(自然科学版),2007,35(1):55-58.
[135]赵永春,季宏丽,裘进浩,朱孔军.基于压电元件的悬臂梁半主动振动控制研究.振动、测试与诊断,2009,29(4):424-429.
[136]田海民.智能悬臂梁的振动控制及其优化配置.兰州理工大学硕士学位论文,2008
[137] Fung R, Liu Y, Wang C. Dynamic model of an electromagnetic actuator for vibration control ofa cantilever beam with a tip mass. Journal of Sound and Vibration,2005,288(4-5):957-980.
[138] Choi S B, Hong S R, Kim S H. Beam vibration control via rubber and piezostack mounts:experimental work. Journal of Sound and Vibration,2004,273(4-5):1079-1086.
[139] Liu Y. Application of a proportional feedback controller for active control of a vibration isolator.Vibration and Active Control of Journal of Low Frequency Noise,2005,24(3):181-90.
[140] Park S H, Kim P S, Kwon O K, Kwon W H. Estimation and detection of unknown inputs usingoptimal FIR filter. Automatica,2000,36(10):1481-8.
[141]Ma C K. Chang J M, Lin D C. Input forces estimation of beam structures by an inverse method.Journal of Sound and Vibration,2003,259(2):387-407.
[142] Ho C C, Ma C K. Active vibration control of structural systems by a combination of the linearquadratic Gaussian and input estimation approaches. Journal of Sound and Vibration,2007,301(3-5):429-49.
[143] Czornik A. On discrete-time linear quadratic control. Systems&Control Letters,1999,36(2):101-107.
[144] Basin M, Dario C A. Optimal LQG controller for linear stochastic systems with unknownparameters. Journal of the Franklin Institute,2008,345(3):293-302.
[145] White J E, Speyer J L. Detection filter design: Spectral theory and algorithms. IEEETransactions on Automatic Control,1987,32(7):593-603.
[146] Frank P. Fault diagnosis in dynamic systems using analytic and knowledge-based redundancy-a survey and some new results. Automatica,1990,26(3):459-474.
[147] Park J, Rizzoni G. An eigenstructure assignment algorithm for the design of fault detectionfilters. IEEE Transactions on Automatic Control,1994,39(7):1521-1524.
[148] Friedland B. Treatment of bias in recursive filtering. IEEE Transactions on Automatic Control,1969,14:359-367.
[149] Ignagni M B. Separate-bias Kalman estimator with bias state noise. IEEE Transactions onAutomatic Control,1990,33(3):338-341.
[150] Kalman R E. A New Approach to Linear Filtering and Prediction Problems. Transactions of theASME of Journal of Basic Engineering,1960,82:35-45.
[151] Ali M S, Hou Z K, Noori M N. Stability and performance of feedback control systems with timedelays. Computer&Structures,1998,66(2-3):241-248
[152]胡海岩.振动主动控制中的时滞动力学问题.1997,10(3):273-279.
[153]陈龙祥,蔡国平.地震作用下建筑结构的多时滞最优控制.振动与冲击,2008,27(4):63-66.
[154] Sipahi R, Olgac N. Degenerate cases in using the direct method. Measurement and Control ofJournal of Dynamic Systems,2003,125:194-201.
[155] Sipahi R, Olgac N. Direct method implementation for the stability analysis of multiple timedelayed systems. Proceedings of2003IEEE Conference on Control Applications,2003,2:88-97.
[156] Udwadia F E, von Bremen H F, Kumar R, et al. Time delayed control of structural systems.Earthquake Engineering and Structural Dynamics,2003,32(4):495-535.
[157] Mohamed A R. Time-delay effects on active damped structures. Journal of EngineeringMechanics,1987,113(11):1709-1719.
[158] Mc Greery S, Soong T T, Reinhorn A M. An experiments study of time delay compensation inactive structural control, Proceedings of sixth International Modal Analysis Conference, SEM,1988:1733-1739.
[159]李卫,孙增圻.包含延时的采样系统的最优控制.控制理论与应用,1987,4(2):10-18.
[160] Cai G P, Huang J. Optimal control method with time delay in control. Journal of Sound andVibration,2002,251(3):383-394.
[161] Chen L X, Cai G P. Design method of multiple time-delay controller for active structuralvibration control. Applied Mathematics and Mechanics,2009,30(11):1405-1411.
[162] Haraguchi M, Hu H Y. Using a new discretization approach to design delayed LQG controller.Journal of Sound and Vibration,2008,314(3-5):558-570
[163] Wang Z H, Hu H Y. Stability switches of time-delayed dynamic systems with unknownparameters. Journal of Sound and Vibration,2000,233(2):215-233.
[164] George Ellis.控制系统设计指南,刘军华,汤晓军译.北京:电子工业出版社,2006:17-18.
[165] Weleratna R. Effects of sampling and aliasing on the conversion of analog signals to digitalformat. Sound and Vibration,2002,36(12):12-13.
[166] Bilinsky I, Mikelsons A. Application of randomized or irregular sampling as an anti-aliasingtechnique. Fifth European Signal Processing Conference1990,1:505-512.
[167] D’Antonia G, Rienzo L D, Ottoboni R. Anti-aliasing analog low pass filter transfer functionparametric spectral estimation for digital compensation. Proceedings of the16th IEEEInstrumentation and Measurement Technology Conference,1999,2:1305-9.
[168] Opperman A P R, Linde L P. Design considerations and applications of a class ofasymmetrically matched Nyquist low pass filters. South African Symposium on Communications andSignal Processing,1991:166-71.
[169] Cai G P, Huang J Z. Instantaneous optimal method for vibration control of linear sampled-datasystems with time delay in control. Journal of Sound and Vibration,2003,262:1057-1071.
[170] Jing Z Q. A new method for digital all-pass filter design. Speech and Signal Processing of IEEEtransactions on Acoustics.1987,35:1557-1564.
[171] Reddy G R, Swamy M N S. Digital all-pass design through discrete Hilbert transform. IEEEInternational Symposium on Circuits and Systems,1990,1:646-649.
[172] Piskorowski J, Anda M A G. A new class of continuous-time delay compensated parameter-varying low-pass elliptic filters with improved dynamic behavior, IEEE Transactions on Circuits andSystems,2009,56(1):179-189.
[173] Jaskula M, Kaszynski R. Using the parametric time-varying analog filter to average-evokedpotential signals. IEEE Transactions on Instrumentation and Measurement,2004,53(3):709-715.
[174] Lee H, Bien Z. Bandpass variable-bandwidth filter for reconstruction of signals with knownboundary in time-frequency domain. IEEE Signal Processing Letters,2004,11(2):160-163.
[175] Friedlander B. Lattice filters for adaptive processing. Proceedings of the IEEE,1982,70(8):829-867.
[176] Paolo G, Mattias V. Forecasting macroeconomic time series with locally adaptive signalextraction. International Journal of Forecasting,2010,26(2):312-325.
[177] Paarmann L D, Najar M D. Adaptive online load forecasting via time series modeling. ElectricPower Systems Research,1995,32(3):219-225.
[178] Wong W K, Xia M, Chu W C. Adaptive neural network model for time-series forecasting.European Journal of Operational Research,2010,207(2):807-816.
[179]戴华.矩阵论.北京:科学出版社,2001:233-242.
[180]刘博,胡海岩.群时延引起的受控小车二级摆失稳及其抑制.振动工程学报,2009,22(5):443-448.
[2] Meirovitch L. Computational methods in structural dynamics. The Netherlands, Sijthoff&noordhoff,1980.
[3] Balas M J. Active control of flexible systems. Journal of Optimization Theory and Applications,1978,25:415-436.
[4] Mei C. Reduction of control spillover in active vibration control of distributed structures usingmultioptimal shemes. Journal of Sound and Vibration,2002,251(1):184-192.
[5] Counrant R. Variation method for solutions of problems of equilibrium and vibrations. Problemsof Equilibrium and Vibrations,1943,49:1-23.
[6] Jonker B. A finite element dynamics analysis of spatial mechanisms with flexible links. Faculty ofMechanical Engineering,1989,76(1):17-40.
[7] Jonker B. A finite element dynamic analysis of flexible manipulators. The International Journal ofRobotics Research.1990,9(4):59-74.
[8]徐晨,甘小冰.柔性操作器动力学的数值方法.机器人,1992,14(1):52-58.
[9]徐晨,张景绘,史维祥.一个高精度单臂柔性机械手的动力学模型.机器人,1992,14(5):8-13.
[10] Xu C, Shi W, Zhang J. An investigation of the effect of distributed structure flexibility onbehavior of single-link manipulator force-feedback control system. Proceedings of the IEEEInternational Symposium on Industrial Electronics,1992,1:320-323.
[11] Hwu C, Chang W C, Gai H S. Vibration suppression of composite sandwich beams. Journal ofSound and Vibration,2004,272(1-2):1-20.
[12] Zain M Z, Tokhi M O, Mohamed Z. Hybrid learning control schemes with input shaping of aflexible manipulator system. Mechatronics,2006,16(3-4):209-219.
[13] Wong W O, Tang S L, Cheung Y L, Cheng L. Design of a dynamic vibration absorber forvibration isolation of beams under point or distributed loading. Journal of Sound and Vibration,2007,301(3-5):898-908.
[14] Cheung Y L, Wong W O. H∞and H2optimizations of a dynamic vibration absorber forsuppressing vibrations in plates. Journal of Sound and Vibration,2009,320(1-2):29-42.
[15] Chu C L, Wu B S, Lin Y H. Active vibration control of a flexible beam mounted on an elasticbase. Finite Elements in Analysis and Design,2006,43(1):59-67.
[16] Lim C W, Park Y J, Moon S J. Robust saturation controller for linear time-invariant system withstructured real parameter uncertainties. Journal of Sound and Vibration,2006,294(1-2):1-14.
[17] Yaman M, Sen S. Vibration control of a cantilever beam of varying orientation. Solids andStructures,2007,44(3-4):1210-1220.
[18] Dong X J, Meng G, Peng J C. Vibration control of piezoelectric smart structures based on systemidentification technique: Numerical simulation and experimental study. Journal of Sound andVibration,2006,297(3-5):680-693.
[19] zcan K, John C, Bruch J, James M S, Sarp A, Ibrahim S S. Integral equation approach for piezopatch vibration control of beams with various types of damping. Computers&Structures,2008,86(3-5):357-366.
[20]邱志成,吴宏鑫.基于特征模型的压电悬臂板振动控制.机械工程学报,2008,44(10):187-195.
[21] Stavroulakis G E, Foutsitzi G, Hadjigeorgiou E, Marinova D, Baniotopoulos C C. Design androbust optimal control of smart beams with application on vibrations suppression. EngineeringSoftware,2005,36(11-12):806-813.
[22] Wu S T, Shao Y J. Adaptive vibration control using a virtual-vibration-absorber controller.Journal of Sound and Vibration,2007,305(4-5):891-903.
[23] Wu S T, Chiu Y Y, Yeh Y C. Hybrid vibration absorber with virtual passive devices. Journal ofSound and Vibration,2007,299(1-2):247-260.
[24] Zhang Y, Zhang X, Xie S. Adaptive vibration control of a cylindrical shell with laminated PVDFactuator. Acta Mechanic,2010,210(1-2):85-98.
[25] To C W S, Chen T. Optimal control of random vibration in plate and shell structures withdistributed piezoelectric components. Mechanical Sciences,2007,49(12):1389-1398.
[26] Luo Q, Tong L. Exact static solutions to piezoelectric smart beams including peel stresses, Part I:Theoretical formulation. International Journal of Solids and Structures,2002,39(18):4677-4695.
[27] Luo Q, Tong L. Exact static solutions to piezoelectric smart beams including peel stresses, Part II:Numerical results, comparison and discussion. International Journal of Solids and Structures,2002,39(18):4697-4722.
[28] Tong L, Luo Q. Exact dynamic solutions to piezoelectric smart beams including peel stresses, I:Theory and application. International Journal of Solids and Structures,2003,40(18):4789-4812.
[29] Istv á n E. Dynamic equilibrium equations of linear piezoelectric Euler-Bernoulli beams.Mechanics Research Communications,2009,36(2):175-182.
[30] Daví F. Saint-Venant’s problem for linear piezoelectric bodies. Journal of Elasticity,1996,43(3):227-245.
[31] D kmeci M C. Recent progress in the dynamic applications of piezoelectric crystals. The Shockand Vibration Digest,1988,20(2):3-20.
[32] Robert G L. Recent developments in smart structures with aeronautical applications. SmartMaterials and Structures,1997,6(5):11-42.
[33]孙宝元,钱敏,张军.压电式传感器与测力仪研发回顾与展望.大连理工大学学报,2001,41(2):127-134.
[34] Cady W G. Piezoelectricity. New York, Dover Publications,1964.
[35] Tzou H S. Piezoelectric Shells: Distributed Sensing and Control of Continua. Dordrecht,Netherlands, Kluwer Academic Publisher,1993.
[36] Yang J S. Introduction to the Theory of Piezoelectricity. New York, Springer,2005.
[37] Edward F C, Javier L. Use of piezoelectric actuators as elements of intelligent structures. AIAAJournal,1987,25(10):1373-1385.
[38]胡海岩,孙久厚,陈怀海.机械振动与冲击.北京:航空工业出版社,1998.
[39] Valverde J C, Pelayo F L, Martinez J A, Miralles J J. Stability of continuous systems byRouth-Hurwitz and Mathematica. Journal of Computational Methods in Science and Engineering,2004,4(1-2):125-134.
[40] Chang J R, Lin W J, Huang C J, Choi S T. Vibration and stability of an axially moving Rayleighbeam. Applied Mathematical Modelling,2010,34(6):1482-1497.
[41] Yang X D, Tang Y Q, Chen L Q, Lim C W. Dynamic stability of axially accelerating Timoshenkobeam: Averaging method. European Journal of Mechanics A/Solids,2010,29(1):81-90.
[42] Wang P K C, Wei J D. Vibrations in a moving flexible robot arm. Journal of Sound and Vibration,1987,116(1):149-160.
[43] Ding H, Chen L Q. Stability of axially accelerating viscoelastic beams: multi-scale analysis withnumerical confirmations. European Journal of Mechanics A/Solids,2008,27(6):1108-1120.
[44] Chen L Q, Yang X D. Stability in parametric resonance of axially moving viscoelastic beamswith time-dependent speed. Journal of Sound and Vibration,2005,28(3-5):879-891.
[45] Young T H, Juan C S. Dynamic stability and response of fluttered beams subjected to randomfollower forces. International Journal of Non-Linear Mechanics,2003,38(6):889-901.
[46] Meirovitch L. Some problems associated with the control of distributed structures. Journal ofOptimization Theory and Applications.1987,54(1):1-20.
[47] Meirovitch L. Dynamics and Control of Structures. New York, John Wiley&Sons,1989.
[48] Meirovitch L, Bennighof J K. Modal control of traveling waves in flexible structures. Journal ofSound and Vibration.1986,111(1):131-144.
[49] Mei C, Mace B R, Jones R W. Hybrid wave/mode active vibration control. Journal of Sound andVibration,2001,274(5):765-784.
[50] Piazzi A, Visioli A. A noncausal approach for PID control. Journal of Process Control,2006,16(8):831-843.
[51] Khoury G M, Saad M, Kanaan H Y, Asmar C. Fuzzy PID control of five DOF robot arm. Journalof Intelligent and Robotic Systems,2004,40(3):299-320.
[52] Astr m K J, H gglund T. The future of PID control. Control Engineering Practice,2001,9(11):1163-1175.
[53] Li Y, Sheng A, Wang Y. Synthesis of PID-type controllers without parametric models: a graphicalapproach. Energy Conversion and Management,2008,49(8):2392-2402.
[54]李超,马玉玲,张伟平.模糊增益调整PID控制在VAV系统中的应用.控制系统,2006,22(16):35-37.
[55]苏绍兴.基于变速积分PID的温度控制系统设计.机电工程,2002,19(6):28-30.
[56] Liu Z, Wang D, Hu H, Yu M. Measures of Modal Controllability and Observability in VibrationControl of flexible Structures. Engineering Notes,1994,17(6):1377-1380.
[57] Hurlebaus S, St bener U, Gaul L. Vibration reduction of curved panels by active modal control.Computers&Structures,2008,86(3-5):251-257.
[58] Houlston P R, Garvey S D, Popov A A. Modal control of vibration in rotating machines and othergenerally damped systems. Journal of Sound and Vibration,2007,302(1-2):104-116.
[59] Datta B N. Recent developments on nonmodal and partial modal approaches for control ofvibration. Applied Numerical Mathematics,1999,30(1):41-52.
[60] Wang D A, Huang Y M. Modal space vibration control of a beam by using the feedforward andfeedback control loops. International Journal of Mechanical Sciences,2002,44(1):1-19.
[61] Librescu L, Na S, Qin Z, Lee B. Active aeroelastic control of aircraft composite wings impactedby explosive blasts. Journal of Sound and Vibration,2008,318(1-2):1-19.
[62] Magdalene M, Yannis M, Georgios E S. Vibration control of beams with piezoelectric sensorsand actuators using particle swarm optimization. Expert Systems with Applications,2011,38(6):6872-6883.
[63] Yang F, Esmailzadeh E, Sedaghati R. Optimal vibration control of beam-type structures usingmultiple-tuned-mass-dampers. Proceedings of the Institution of Mechanical Engineers, Park K:Journal of Multi-body Dynamics,2010,244(2):191-202.
[64] Yang J, Chen G. Optimal placement and configuration direction of actuators in plate structurevibration control system.2nd International Asia Conference on Informatics in Control, Automationand Robotics,2010:124-8.
[65] Choi S B, Hong S R, Sung K G, Sohn J W. Optimal control of structural vibrations using amixed-mode magnetorheological fluid mount. International Journal of Mechanical Sciences,2008,50(3):559-568.
[66]李书,孙忠凯,向锦武.结构控制中输出反馈鲁棒极点配置优化方法.力学学报,2001,33(1):71-78.
[67] Jiang D, Wang J. Augmented gradient flows for on-line robust pole assignment via state andoutput feedback. Automatica,2002,38(2):279-286.
[68] Toshkov A. Distributed control linear systems design with pole assignment. Annual Review inAutomatic Programming,1985,12(1):429-432.
[69] Wei M, Wang Q, Cheng X. Some new results for system decoupling and pole assignmentproblems. Automatica,2010,46(5):937-944.
[70] Tsui C. A new dynamic output feedback compensator design for pole assignment. Journal of TheFranklin Institute,1999,366():665-674.
[71] Ouyang H. Pole assignment of friction-induced vibration for stabilisation through state-feedbackcontrol. Journal of Sound and Vibration,2010,329(11):1985-1991.
[72]刘金琨.先进PID控制MATLAB仿真(第二版).北京:电子工业出版社,2004.
[73]陈卫东,邵敏强,杨兴华,路波,徐庆华.跨声速风洞测力模型主动减振系统的试验研究.振动工程学报,2007,20(1):91-96.
[74] Liu G P, Daley S. Optimal-tuning PID control for industrial systems. Control EngineeringPractice,2001,9(11):1185-1194.
[75] Hayashi K, Otsubo A, Murakami S, Maeda M. Realization of nonlinear and linear PID controlsusing simplified indirect fuzzy inference method. Fuzzy Sets and Systems,1999,105(3):409-414.
[76] Mizumoto M. Realization of PID controls by fuzzy control methods. Fuzzy Sets and Systems,1995,70(2-3):171-182.
[77] Ji W, Li Q, Xu B, Zhao D, Fang S. Adaptive fuzzy PID composite control with hysteresis-bandswitching for line of sight stabilization servo system. Aerospace Science and Technology,2011,15(1):25-32.
[78] Sanchez E N, Becerra H M, Velez C M. Combining fuzzy, PID and regulation control for anautonomous mini-helicopter. Information Sciences,2007,177(10):1999-2022.
[79] Lan L H. Stability analysis for a class of Takagi–Sugeno fuzzy control systems with PIDcontrollers. International Journal of Approximate Reasoning,2007,46(1):109-119.
[80] Soyguder S, Karakose M, Alli H. Design and simulation of self-tuning PID-type fuzzy adaptivecontrol for an expert HVAC system. Expert Systems with Applications,2009,36(3):4566-4573.
[81] Dieulot J Y, Colas F. Robust PID control of a linear mechanical axis: A case study. Mechatronics,2009,19(2):269-273.
[82] Mattei M. Robust multivariable PID control for linear parameter. Automatica,2001,37(12):1997-2003.
[83] Tan K K, Lee T H, Jiang X. Robust on-line relay automatic tuning of PID control systems. ISATransactions,2000,39(2):219-232.
[84] Amer A F, Sallam E A, Elawady W M. A novel robust adaptive sliding mode control using fuzzyself-tunning PID controller for3DOF planar robot manipulators. ISA Transactions,2011,
[85] Mizumoto I, Ikeda D, Hirahata T, Iwai Z. Design of discrete time adaptive PID control systemswith parallel feedforward compensator. Control Engineering Practice,2010,18(2):168-176.
[86] Tang K Z, Huang S N, Tan K K, Lee T H. Combined PID and adaptive nonlinear control forservo mechanical systems. Mechatronics,2004,14(6):701-714.
[87] Eker. Sliding mode control with PID sliding surface and experimental application to anelectromechanical plant. ISA Transactions,2006,45(1):109-118.
[88] Petukhov L V, Troitskii V A. Some optimal problems of the theory of longitudinal vibrations ofrods: PMM. Journal of Applied Mathematics and Mechanics,1972,36(5):895-904.
[89] Blachut J. Parametrical optimal design of funicular arches against buckling and vibration.International Journal of Mechanical Sciences,1984,26(5):305-310.
[90]胡寿松,王执铨,胡维礼.最优控制理论与系统.北京:科学出版社,2005.
[91] Sadek I S, Adali S, Sloss J M, Bruch J C. Vibration damping of a thin plate by optimal open-andclosed-loop control forces. Journal of the Franklin Institute,1992,329(2):207-214.
[92] Lee H K, Chen S T, Lee A C. Optimal control of vibration suppression in flexible systems viadislocated sensor/actuator positioning, Journal of the Franklin Institute,1996,333(5):789-802.
[93] Bolonkin A A, Khot N S. Optimal Bounded control design for vibration suppression. ActaAstronautic,1996,38(10):803-813.
[94] Zhang X. Integrated optimal design of flexible mechanism and vibration control. InternationalJournal of Mechanical Sciences,2004,46(11):1607-1620.
[95] Qiu Z, Zhang X, Wu H, Zhang H. Optimal placement and active vibration control forpiezoelectric smart flexible cantilever plate. Journal of Sound and Vibration,2007,301(3-5):521-543.
[96] Huan R, Chen L, Jin W, Zhu W. Stochastic optimal vibration control of partially observablenonlinear quasi Hamiltonian systems with actuator saturation. Acta Mechanica Solida Sinica,2009,22(2):143-151.
[97] Gao W, Chen J J, Ma H B, Ma X S. Optimal placement of active bars in active vibration controlfor piezoelectric intelligent truss structures with random parameters. Computers&Structures,2003,81(1):53-60.
[98] Wang X Y, Ni Y Q, Ko J M, Chen Z Q. Optimal design of viscous dampers for multi-modevibration control of bridge cables. Engineering Structures,2005,27(5):792-800.
[99]朱位秋.随机振动.北京:科学出版社,1998.
[100] Zibdeh H S. Stochastic vibration of an elastic beam due to random moving loads anddeterministic axial forces. Engineering Structures,1995,17(7):530-535.
[101] Gao W, Chen J, Cui M, Cheng Y. Dynamic response analysis of linear stochastic truss structuresunder stationary random excitation. Journal of Sound and Vibration,2005,281(1-2):311-321.
[102] Grigoriu M. Linear models for non-Gaussian processes and applications to linear randomvibration. Probabilistic Engineering Mechanics,2011,26(3):461-470.
[103] Dimentberg M F. Random vibrations of a rotating shaft with non-linear damping. InternationalJournal of Non-Linear Mechanics,2005,40(5):711-713.
[104] Chen J B, Li J. Dynamic response and reliability analysis of non-linear stochastic structures,Probabilistic Engineering Mechanics,2005,20(1):33-44.
[105] Bryja D, niady P. Stochastic non-linear vibration of highway suspension bridge under inertialsprung moving load. Journal of Sound and Vibration,1998,216(3):507-519.
[106] Homan C J, Tierney J W. Determination of dynamic characteristics of processes in the presenceof random disturbances. Chemical Engineering Science,1960,12(3):153-165.
[107] Herbert R E. On the stresses in a nonlinear beam subject to random excitation. InternationalJournal of Solids and Structures,1965,1(2):235-242.
[108] Zhu W Q, Soong T T, Lei Y. Equivalent nonlinear system method for stochastically excitedHamiltonian systems. Journal of Applied Mechanics,1994,61(3):618-623.
[109]朱位秋,黄志龙,应祖光.非线性随机振动力学与控制的哈密顿理论框架.力学与实践,2002,24:1-9.
[110]张令弥.振动测试与动态分析.北京:航空工业出版社,1992.
[111] Rong H W, Xu W, Wang X, Meng G, Fang T. Response statistics of two-degree-of-freedomnon-linear system to narrow-band random excitation. International Journal of Non-Linear Mechanics,2002,37(6):1017-1028.
[112] Feng Z H, Lan X J, Zhu X D. Principal parametric resonances of a slender cantilever beamsubject to axial narrow-band random excitation of its base. International Journal of Non-LinearMechanics,2007,42(10):1170-1185.
[113] Feng Z H, Lan X J, Zhu X D. Explanation on the importance of narrow-band random excitationcharacters in the response of a cantilever beam. Journal of Sound and Vibration,2009,325(4-5):923-937.
[114] Gu M, Chang C C, Wu W, Xiang H F. Increase of critical flutter wind speed of long-spanbridges using tuned mass dampers. Journal of Wind Engineering,1998,73(2):111-123.
[115] Shi J, Hitchings D. Calculation of flutter derivatives and speed for2-D incompressible flow bythe finite-element method. Applied Mathematical Modelling,1994,18(10):538-549.
[116] Ge Y J, Xiang H F, Tanaka H. Application of a reliability analysis model tobridge flutter under extreme winds. Journal of Wind Engineering and Industrial Aerodynamics,2000,86(2-3):155-167.
[117] Bobryk R, Stettner L. Moment stability for linear systems with a random parametric excitation.System&Control Letters,2005,54(8):781-786.
[118] Náprstek J. Stochastic exponential and asymptotic stability of simple non-linear systems.Non-Linear Mechanics,1996,31(5):693-705.
[119] Feng C, Zhu W. Stochastic optimal control of strongly nonlinear systems under wide-bandrandom excitation with actuator saturation. Acta Mechanica Solida Sinica,2008,21(2):116-126.
[120] Elbeyli O, Sun J Q. Feedback control optimization of nonlinear systems under randomexcitations. Communications in Nonlinear Science and Numerical Simulation,2006,11(1):125-136.
[121] Montazeri A, Poshtan J. A new adaptive recursive RLS-based fast-array IIR filter for activenoise and vibration control systems. Signal Processing,2011,91(1):98-113.
[122] Gaonkar G H. A general method with shaping filters to study random vibration statistics oflifting rotors with feedback controls. Journal of Sound and Vibration,1972,21(2):213-225.
[123] Cross C F. An adaptive digital filter for broadband active sound control. Journal of Sound andVibration,1980,80(3):381-388.
[124] Sergent P, Duhamel D. The effects of sampling rate and length of an adaptive filter on the activecontrol of a plane sound wave in a lossy semi-infinite waveguide. Journal of Sound and Vibration,1997,203(1):127-150.
[125] Alam S M S, Yamada K, Baba S. A Kalman filter approach for galloping control of a bridgetower. Computer&Structure,1995,57(1):67-79.
[126] Brennan M J, Kim S M. Feedforward and feedback control of sound and vibration: a wienerfilter approach. Journal of Sound and Vibration,2001,246(2):281-296.
[127]于明礼.基于超声电机作动器的二维翼段颤振主动抑制,[博士学位论文].南京:南京航空航天大学,2006.
[128] Liu B, Hu H. Group delay induced instabilities and Hopf bifurcations, of a controlled doublependulum. International Journal of Non-Linear Mechanics,2010,45(4):442-452.
[129] Paola M D, Pirrotta A. Time delay induced effects on control of linear systems under randomexcitation. Probabilistic Engineering Mechanics,2001,16(1):43-51.
[130] Li X P, Liu Z H, Zhu W Q. First-passage failure of quasi linear systems subject tomulti-time-delayed feedback control and wide-band random excitation. Probabilistic EngineeringMechanics,2009,24(2):144-150.
[131] Cai G P, Huang J Z, Yang S X. An optimal method for linear systems with time delay.Computers&Structures,2003,81(15):1539-1546.
[132] K. Satyanarayana, P.M. Bainum. Synthesis of control laws for optimally designed large spacestructures. Acta Astronautic,1987,15(11):901-904.
[133]王亮,陈怀海,贺旭东,游伟倩.轴向运动变长度悬臂梁的振动控制.振动工程学报,2009,22(6):565-570.
[134]于国军,杜成斌,艾亿谋.压电陶瓷用于柔性悬臂梁振动控制的试验研究.河海大学学报(自然科学版),2007,35(1):55-58.
[135]赵永春,季宏丽,裘进浩,朱孔军.基于压电元件的悬臂梁半主动振动控制研究.振动、测试与诊断,2009,29(4):424-429.
[136]田海民.智能悬臂梁的振动控制及其优化配置.兰州理工大学硕士学位论文,2008
[137] Fung R, Liu Y, Wang C. Dynamic model of an electromagnetic actuator for vibration control ofa cantilever beam with a tip mass. Journal of Sound and Vibration,2005,288(4-5):957-980.
[138] Choi S B, Hong S R, Kim S H. Beam vibration control via rubber and piezostack mounts:experimental work. Journal of Sound and Vibration,2004,273(4-5):1079-1086.
[139] Liu Y. Application of a proportional feedback controller for active control of a vibration isolator.Vibration and Active Control of Journal of Low Frequency Noise,2005,24(3):181-90.
[140] Park S H, Kim P S, Kwon O K, Kwon W H. Estimation and detection of unknown inputs usingoptimal FIR filter. Automatica,2000,36(10):1481-8.
[141]Ma C K. Chang J M, Lin D C. Input forces estimation of beam structures by an inverse method.Journal of Sound and Vibration,2003,259(2):387-407.
[142] Ho C C, Ma C K. Active vibration control of structural systems by a combination of the linearquadratic Gaussian and input estimation approaches. Journal of Sound and Vibration,2007,301(3-5):429-49.
[143] Czornik A. On discrete-time linear quadratic control. Systems&Control Letters,1999,36(2):101-107.
[144] Basin M, Dario C A. Optimal LQG controller for linear stochastic systems with unknownparameters. Journal of the Franklin Institute,2008,345(3):293-302.
[145] White J E, Speyer J L. Detection filter design: Spectral theory and algorithms. IEEETransactions on Automatic Control,1987,32(7):593-603.
[146] Frank P. Fault diagnosis in dynamic systems using analytic and knowledge-based redundancy-a survey and some new results. Automatica,1990,26(3):459-474.
[147] Park J, Rizzoni G. An eigenstructure assignment algorithm for the design of fault detectionfilters. IEEE Transactions on Automatic Control,1994,39(7):1521-1524.
[148] Friedland B. Treatment of bias in recursive filtering. IEEE Transactions on Automatic Control,1969,14:359-367.
[149] Ignagni M B. Separate-bias Kalman estimator with bias state noise. IEEE Transactions onAutomatic Control,1990,33(3):338-341.
[150] Kalman R E. A New Approach to Linear Filtering and Prediction Problems. Transactions of theASME of Journal of Basic Engineering,1960,82:35-45.
[151] Ali M S, Hou Z K, Noori M N. Stability and performance of feedback control systems with timedelays. Computer&Structures,1998,66(2-3):241-248
[152]胡海岩.振动主动控制中的时滞动力学问题.1997,10(3):273-279.
[153]陈龙祥,蔡国平.地震作用下建筑结构的多时滞最优控制.振动与冲击,2008,27(4):63-66.
[154] Sipahi R, Olgac N. Degenerate cases in using the direct method. Measurement and Control ofJournal of Dynamic Systems,2003,125:194-201.
[155] Sipahi R, Olgac N. Direct method implementation for the stability analysis of multiple timedelayed systems. Proceedings of2003IEEE Conference on Control Applications,2003,2:88-97.
[156] Udwadia F E, von Bremen H F, Kumar R, et al. Time delayed control of structural systems.Earthquake Engineering and Structural Dynamics,2003,32(4):495-535.
[157] Mohamed A R. Time-delay effects on active damped structures. Journal of EngineeringMechanics,1987,113(11):1709-1719.
[158] Mc Greery S, Soong T T, Reinhorn A M. An experiments study of time delay compensation inactive structural control, Proceedings of sixth International Modal Analysis Conference, SEM,1988:1733-1739.
[159]李卫,孙增圻.包含延时的采样系统的最优控制.控制理论与应用,1987,4(2):10-18.
[160] Cai G P, Huang J. Optimal control method with time delay in control. Journal of Sound andVibration,2002,251(3):383-394.
[161] Chen L X, Cai G P. Design method of multiple time-delay controller for active structuralvibration control. Applied Mathematics and Mechanics,2009,30(11):1405-1411.
[162] Haraguchi M, Hu H Y. Using a new discretization approach to design delayed LQG controller.Journal of Sound and Vibration,2008,314(3-5):558-570
[163] Wang Z H, Hu H Y. Stability switches of time-delayed dynamic systems with unknownparameters. Journal of Sound and Vibration,2000,233(2):215-233.
[164] George Ellis.控制系统设计指南,刘军华,汤晓军译.北京:电子工业出版社,2006:17-18.
[165] Weleratna R. Effects of sampling and aliasing on the conversion of analog signals to digitalformat. Sound and Vibration,2002,36(12):12-13.
[166] Bilinsky I, Mikelsons A. Application of randomized or irregular sampling as an anti-aliasingtechnique. Fifth European Signal Processing Conference1990,1:505-512.
[167] D’Antonia G, Rienzo L D, Ottoboni R. Anti-aliasing analog low pass filter transfer functionparametric spectral estimation for digital compensation. Proceedings of the16th IEEEInstrumentation and Measurement Technology Conference,1999,2:1305-9.
[168] Opperman A P R, Linde L P. Design considerations and applications of a class ofasymmetrically matched Nyquist low pass filters. South African Symposium on Communications andSignal Processing,1991:166-71.
[169] Cai G P, Huang J Z. Instantaneous optimal method for vibration control of linear sampled-datasystems with time delay in control. Journal of Sound and Vibration,2003,262:1057-1071.
[170] Jing Z Q. A new method for digital all-pass filter design. Speech and Signal Processing of IEEEtransactions on Acoustics.1987,35:1557-1564.
[171] Reddy G R, Swamy M N S. Digital all-pass design through discrete Hilbert transform. IEEEInternational Symposium on Circuits and Systems,1990,1:646-649.
[172] Piskorowski J, Anda M A G. A new class of continuous-time delay compensated parameter-varying low-pass elliptic filters with improved dynamic behavior, IEEE Transactions on Circuits andSystems,2009,56(1):179-189.
[173] Jaskula M, Kaszynski R. Using the parametric time-varying analog filter to average-evokedpotential signals. IEEE Transactions on Instrumentation and Measurement,2004,53(3):709-715.
[174] Lee H, Bien Z. Bandpass variable-bandwidth filter for reconstruction of signals with knownboundary in time-frequency domain. IEEE Signal Processing Letters,2004,11(2):160-163.
[175] Friedlander B. Lattice filters for adaptive processing. Proceedings of the IEEE,1982,70(8):829-867.
[176] Paolo G, Mattias V. Forecasting macroeconomic time series with locally adaptive signalextraction. International Journal of Forecasting,2010,26(2):312-325.
[177] Paarmann L D, Najar M D. Adaptive online load forecasting via time series modeling. ElectricPower Systems Research,1995,32(3):219-225.
[178] Wong W K, Xia M, Chu W C. Adaptive neural network model for time-series forecasting.European Journal of Operational Research,2010,207(2):807-816.
[179]戴华.矩阵论.北京:科学出版社,2001:233-242.
[180]刘博,胡海岩.群时延引起的受控小车二级摆失稳及其抑制.振动工程学报,2009,22(5):443-448.