【作者】 游伟倩；

【导师】 陈怀海；

【作者基本信息】 南京航空航天大学 ， 工程力学， 2010， 博士

【摘要】 结构振动控制在航空航天、机械制造、车辆与船舶、桥梁与建筑等众多工程领域有着广泛的应用背景。振动控制方法的研究和应用对于结构减振或振动利用都具有重要的意义。在处理振动控制问题时,关键是决定所采用的控制方法。经典的振动控制方法,例如PID或LQR（LQG）等方法在实践中已获得了广泛应用,解决了大量实际问题。但是这些经典控制方法存在着诸多局限性。例如PID控制方法一般仅适用于单输入单输出系统的频域控制;LQR（LQG）虽可用于时域多输入多输出系统,但需要建立系统精确的状态空间模型。为了打破经典振动控制方法所存在的局限性,必须探索新的振动控制理论和技术。H₂和H∞控制理论的崛起与不断发展为解决结构振动控制问题开辟了新的途径。本文以多输入多输出线性系统控制理论为基础,以多振动台振动控制系统的研究和应用为工程背景,利用现代控制理论的新方法对结构振动控制问题进行广泛而深入的研究,针对振动控制中的实际问题提出新的控制方法和解决途径。以双振动台随机振动试验控制系统为对象,进行了深入的理论分析、算法模拟和试验研究。论文的主要工作有:对振动控制中的H₂范数和H∞范数进行了深入的研究。提出了一种计算H∞范数的新方法。重点介绍了H₂和H∞范数空间在理论上的定义、计算方法和计算步骤。研究了振动控制中的H₂和H∞范数的物理含义及其区别。提出了一种利用优化算法计算H∞范数的新方法并以一悬臂梁模型为仿真对象与传统的对分法计算结果进行了比较,验证了所提算法的可行性和有效性。研究了LQG/H₂控制算法以及其在振动控制中的应用。指出经典的LQG问题实际上是输出反馈控制问题,是最优状态反馈的LQR方法和最优状态估计Kalman滤波器的综合。研究了LQG控制理论在结构振动控制领域中的应用。用一悬臂梁进行了仿真验证,通过几种类型激励力作用下的控制结果分析,阐明了LQG控制算法在处理随机干扰作用下系统的振动控制问题所具有的优良效果。对H∞控制算法在结构振动控制中的应用进行了深入研究。阐述了基于H∞控制理论的一些具体控制方法,包括基于信号的H∞控制理论,混合灵敏度的H∞控制理论,双自由度H∞控制算法,H∞回路整形控制方法以及H∞滤波问题,给出了各种方法的控制器设计过程。着重研究了混合灵敏度H∞控制理论和双自由度H∞控制算法。在应用混合灵敏度H∞控制理论处理高阶柔性结构的振动抑制问题中,提出了一种新的权函数的选择方法,并通过仿真算例验证了其可行性。应用双自由度H∞控制算法研究了双振动台随机振动控制问题,通过悬臂梁模型进行了仿真验证,结果表明设计的控制器,能有效的抑制结构振动高阶模态的溢出,在20²000Hz频带内,能使输出控制谱和参考谱的自谱密度误差控制在±1dB以内,且没有超标谱线,总均方根值误差控制在±10%以内,完全满足双振动台控制器在工程上的设计要求。应用双自由度H∞控制算法完成了双振动台随机振动控制试验验证。控制系统基于PC机、VXI等硬件平台。在实验室针对一悬臂梁结构,对文中所提出的控制算法进行了大量的试验研究。试验结果验证了所提控制算法的有效性和可行性,各项试验指标均能达到工程应用要求。更多还原

【Abstract】 The structural vibration control has been widely used in many fields such as aviation, machinery manufacturing, vehicle engineering, shipping and marine project, bridge and building engineering and so on. Research and application on vibration control algorithm is of great importance both in vibration reduction and the use of the good vibration. The key problem which needs to be solved is the control method when deal with the control problems. The classical control algorithms such as the PID control and the LQR （LQG） control theory have played a big role in control field. But they also have many demerits. For example, the PID control is just suitable for frequency domain control of the single-input-single-output （SISO） systems. Though the LQR （LQG） control method can be used in time domain control of the multiple-input-multiple-output （MIMO） systems, the accurate state space model must be obtained. To eliminate the problems in classical methods from the root, new vibration control theory and technology must be introduced. The pathways for solving structural vibration control are broadened by the continuous improvement of the H₂ and H∞control theory.In the background of research and development of multi-shaker control system, the paper extensively discusses and studies the aspects of structural control problems using the new methods in advanced modern control theory. Many new control strategies are proposed to solve the application problems of vibration control. Based on multiple-input-multiple-output （MIMO） linear system theory, theoretical analysis, numerical simulation and experimental research are performed in the dissertation. The main tasks of the dissertation are presented as follow:Profound research has been made of the H₂ norm and the H∞norm in vibration control. A new optimization algorithm for the H∞norm computation is set forth. The H₂ norm and the H∞norm spaces to describe the properties of vibration systems are summarized as well as the computation methods and the detailed calculation procedure. Then the difference between the H₂ norm and the H∞norm in engineering application is performed. At last, the traditional calculation method for H∞norm is recounted and a new optimization algorithm is set forth. A cantilever beam is used to verify the new algorithm. The simulation result shows that the proposed algorithm is feasible and valid.Research on the application of the LQG/H₂ control algorithm in structural vibration control is recounted. The traditional LQG problem is actually output feedback control theory, which is the combine of optimal state feedback and optimal state estimation. The application of the LQG control algorithm in structural vibration control is studied. At last, a cantilever beam is used to verify the LQG control algorithm. Based on the control results obtained from different exciting forces on the beam, the conclusion is drawn that the LQG algorithm is suitable for dealing with the structural vibration problems with random exogenous disturbances.Profound research has been made of the H∞control algorithm in structural vibration control. Many specific control methods based on H∞control algorithm are introduced, which include signal-based H∞control, mixed-sensitivity H∞control, two-degrees-of-freedom H∞control, H∞loop-shaping design and the H∞filtering theory. The specific design procedures are summarized. A summarization of the selection methods for the weighting function matrix in mixed-sensitivity H∞control is presented. A new idea for the weighting function matrix selection is proposed for the vibration control of high order flexible structures. The simulation results show that the technique for the weighting function matrix selection is effective to meet the specifications of robust stability and the performance of external disturbance rejection. A new approach is presented for dual-shaker random vibration test using H∞-based optimal decoupling method with two degrees-of-freedom controller. The results demonstrated that, in the frequency range from 20 Hz to 2000 Hz, the controller could make the error between the output PSD （power spectrum density） and the reference PSD within±1dB and the root mean square error within±10%, which is perfect for the dual-shaker random vibration control test.The dual-shaker random vibration control test is firstly implemented by using the two-degrees-of-freedom H∞control algorithm. The control system is developed on a computer with the VXI modules and so on as hardware platforms for signal acquisition and generation. The two-degrees-of-freedom H∞control algorithm is verified and corrected by lots of tests with a small cantilever beam in the laboratory. The test results demonstrated the feasibility of this method. Every specification of the test results has met the requirements of application in engineering.更多还原