基于压电叠堆惯性作动器的随机振动控制研究

本文主要研究了基于压电叠堆惯性作动器的随机振动控制方法并分析了控制力时滞对控制效果的影响规律。首先,对压电叠堆惯性作动器的动力学特性进行分析,建立了考虑惯性作动器动力学的主结构的随机动力学模型;接着,提出主结构随机振动"线性"二次高斯控制(linear quadratic Gaussian,LQG)方法,并探讨了作动器惯性质量和刚度等对控制效果的影响规律;最后,研究了控制力时滞对控制效果的影响,并提出了利用时滞优化控制效果的方法。研究结果表明,压电叠堆惯性作动器对结构的随机振动具有较好的控制效果,当控制时滞时间τ=0.025 s时控制效果可以得到进一步优化。     

振动控制作动器的数目和位置优化设计

提出一种确定作动器的数目和优化设计作动器位置的方法。以独立模态最优控制方法为基础,将模态控制力和作动器作动力处理为随机变量,建立了模态控制力能量的自相关矩阵和作动器作动力能量的自相关矩阵。进一步通过作动力能量的自相关阵包含的能量确定了作动器的数目,在此基础上,建立了基于控制系统作动力消耗能量最小,优化设计控制系统的作动器最优位置。通过数值算例证明了该方法的有效性。     

柔性结构作动器／传感器优化配置研究

从有效衰减振动能量的角度出发,在对位配置作动器／传感器的情况下,通过最小化系统总储能积分,对柔性结构振动主动控制中的作动器／传感器位置及反馈增益进行了优化。在优化方法上,作者提出了一种快速收敛的遗传算法,即“适应度缩放” 加引入“有偏外来移民”的遗传算法。实验结果表明了该方法的有效性和控制系统的良好减振效果。     

介电弹性作动器主动隔振模糊控制试验研究

采用模糊控制策略,开展介电弹性作动器的主动隔振性能试验研究。基于介电弹性材料的Maxwell应力模型建立了作动器的力电耦合模型,分析了作动器的非线性特性;针对隔振系统设计了Mamdani型模糊控制器,建立了控制电压信号与振动响应之间的关系;在此基础上,开展了介电弹性作动器主动隔振试验研究,并与加速度反馈控制进行了对比。试验结果表明,在相同驱动电压的情况下,基于模糊控制策略的主动隔振性能要优于加速度反馈控制,且能够显著降低由于非线性驱动力导致的倍频响应幅值,有助于提高隔振系统的稳定性。     

基于压电叠堆惯性作动器的随机振动控制研究 1)

本文主要研究了基于压电叠堆惯性作动器的随机振动控制方法并分析了控制力时滞对控制效果的影响规律。首先,对压电叠堆惯性作动器的动力学特性进行分析,建立了考虑惯性作动器动力学的主结构的随机动力学模型;接着,提出主结构随机振动 "线性"二次高斯控制(linear quadratic Gaussian,LQG)方法,并探讨了作动器惯性质量和刚度等对控制效果的影响规律;最后,研究了控制力时滞对控制效果的影响,并提出了利用时滞优化控制效果的方法。研究结果表明,压电叠堆惯性作动器对结构的随机振动具有较好的控制效果,当控制时滞时间$\tau = 0.025$s时控制效果可以得到进一步优化。     

含饱和作动器的基准建筑物混合控制研究

当作动器所提供的控制力小于所需控制力时会出现控制力饱和现象,这一现象在大型结构的实际控制过程中经常出现,为此,本文根据饱和控制力,采用线性矩阵不等式来设计控制器。考虑作动器饱和时,单纯采用作动器来控制结构在地震作用下的响应往往不足于保护结构,此时需附加阻尼器。最优阻尼的确定需要大量的计算,为了减少计算量,本文借鉴临界激励的概念来简化最优阻尼的选择。最后,以三层非线性基准结构为例来说明本文方法的可行性。     

形状记忆合金作动器的设计及优化

采用Ｂｒｉｓｉｏｎ［１］等提出的ＳＭＡ材料的本构关系，分析了形状记忆合金作动器在三种热交换方式（自然冷却、强制冷却和采用半导体热泵技术）下的动力特性，同时研究了ＳＭＡ丝在恒载和载荷变化时对完成正逆相变所用时间的影响，并简单讨论了影响作动器响应的几个因素和改进方法     

多自由度柔性结构非线性随机振动响应分析方法

随机等效线性化方法是多自由度结构非线性随机振动分析的有效方法,然而柔性结构隐式的系统方程限制了该方法的应用.本文首先提出了把多自由度柔性结构隐式系统方程显式化的等效非线性系统建立方法,该方法结合模态分析,将系统几何非线性作用等效为模态坐标的高次多项式组合,把多自由度物理系统转化为容易求解的模态系统;在此基础上运用随机等效线性化技术建立柔性结构非线性随机振动响应分析方法.该方法通过引入虚拟激励原理,大幅提高了计算效率,使对多自由柔性结构的非线性随机振动响应分析成为可能.通过算例分析,本文分析结果和精确解与数值模拟解的比较结果表明,本文方法具有较好的计算精度和较高的计算效率,能够应用于实际柔性工程结构的随机振动响应分析.     

考虑压电驱动元件布局的作动器拓扑优化设计

工程中常需要设计各种各样的作动器以满足一定的驱动要求。本文采用拓扑优化的方法设计以压电材料为驱动的作动器。通过拓扑描述方法和RAMP（Rational Approximation of Material Properties）材料插值模型相结合的建模方式,建立了压电驱动元件布局与柔性机构构型协同设计的优化模型;以电压的...     

层叠式PVDF压电作动器及圆柱壳的振动主动控制

设计了一个层叠式PVDF压电作动器用于壳结构的振动控制。考虑压电层、粘接层、壳体耦合关系,推导了表面局部粘贴层叠式PVDF压电作动器的圆柱壳的振动控制方程,给出了作动力与压电层和粘接层层数、厚度之间的关系以及作动力与作动器粘贴位置之间的关系。针对一端固定、另一端自由的圆柱壳,进行了振动控制仿真。结果表明层叠式PVDF压电作动器作动力与作动器层数近似成线性关系,增大作动器层数能有效增大作动力,在低控制电压下能显著抑制圆柱壳振动,作动器周向不完全粘贴时,在径向产生的径向作动力对壳体横向振动控制非常有利。说明了层叠式PVDF压电作动器是一种可用于壳体结构振动并具有良好作动效果的作动器。     

Optimal Bounded Control of First-Passage Failure of Quasi-Integrable Hamiltonian Systems with Wide-Band Random Excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged Itô equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.     

Random Vibration of Strongly Nonlinear Systems

Procedures developed recently to extend the quasi-conservativeaveraging method to the case of non-white broad-band excitations arefurther extended and presented in a unified framework. The excitationscan be stationary or nonstationary with known evolutionary spectra, andthey can be additive, or multiplicative, or both. Relative merits ofthese procedures are compared, and their accuracies are substantiated byMonte Carlo simulations.     

主动振动控制中传感／作动元件配置问题的全局优化方法研究

提出了一种主动振动控制中作动／传感元件位置的复合优化方法，它能有效地解决全局优化配置问题；通过对单点并置问题的优化，证明了该优化方法的有效性，并对多点配置问题也具有一定的参考价值。     

An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems

A strategy for optimal nonlinear feedback control of randomlyexcited structural systems is proposed based on the stochastic averagingmethod for quasi-Hamiltonian systems and the stochastic dynamicprogramming principle. A randomly excited structural system isformulated as a quasi-Hamiltonian system and the control forces aredivided into conservative and dissipative parts. The conservative partsare designed to change the integrability and resonance of the associatedHamiltonian system and the energy distribution among the controlledsystem. After the conservative parts are determined, the system responseis reduced to a controlled diffusion process by using the stochasticaveraging method. The dissipative parts of control forces are thenobtained from solving the stochastic dynamic programming equation. Boththe responses of uncontrolled and controlled structural systems can bepredicted analytically. Numerical results for a controlled andstochastically excited Duffing oscillator and a two-degree-of-freedomsystem with linear springs and linear and nonlinear dampings, show thatthe proposed control strategy is very effective and efficient.     

Optimal Bounded Control for Minimizing the Response of Quasi Non-Integrable Hamiltonian Systems

A strategy for designing optimal bounded control to minimize theresponse of quasi non-integrable Hamiltonian systems is proposed basedon the stochastic averaging method for quasi non-integrable Hamiltoniansystems and the stochastic dynamical programming principle. Theequations of motion of a controlled quasi non-integrable Hamiltoniansystem are first reduced to an one-dimensional averaged Itô stochasticdifferential equation for the Hamiltonian by using the stochasticaveraging method for quasi non-integrable Hamiltonian systems. Then, thedynamical programming equation for the control problem of minimizing theresponse of the averaged system is formulated based on the dynamicalprogramming principle. The optimal control law is derived from thedynamical programming equation and control constraints without solvingthe equation. The response of optimally controlled systems is predictedthrough solving the Fokker–Planck–Kolmogrov (FPK) equation associatedwith completely averaged Itô equation. Finally, two examples are workedout in detail to illustrate the application and effectiveness of theproposed control strategy.     

Bounded Control of Random Vibration: Hybrid Solution to HJB Equations

Problems of optimal bounded control for randomly excited systems are studied by the Dynamic Programming approach. An effective hybrid solution method has been developed for the corresponding Hamilton–Jacobi–Bellman (HJB) equations for the optimized functional of the response energy. These PDEs are shown to be amenable to an exact analytical solution within a certain outer domain of the phase space. The solution provides boundary conditions for numerical study within the remaining inner domain. The simple dry-friction law had been shown previously to be optimal for a SDOF system within the outer domain and to become asymptotically optimal within the whole phase plane for the important case of so-called long-term control, whereby steady-state response is to be optimized according to the integral cost functional. These results are extended in this paper to MDOF systems by using modal transformation. Thus, the multidimensional dry-friction law is shown to be the optimal one for the case of long-term control. The expected response energy is predicted for this case by a direct energy balance based on application of the SDE Calculus to the energy equation. Stochastic averaging is also used in order to obtain certain reliability estimates. In particular, numerical results for the expected time to first-passage failure are presented, illustrating reduction of reliability due to the imposed bound on the control force. Monte-Carlo simulation results are presented, which demonstrate adequate accuracy of the predictions far beyond the expected applicability range of the asymptotic approaches.     

磁悬浮列车系统的随机最优控制

本文根据磁悬浮列车和车行道的结构特点，将总系统模型按分块原则分成列车、磁执行环节和车行道系统，并在平衡点附近对非线性方程线性化处理，形成末加控制的总系统的状态方程，它是一组考虑外干扰情况下线性时变系统模型。而基于电磁关系原则建立的磁悬浮列车系统模型在末加控制状态下是不稳定的，为了保证列车的行驶舒适性、稳定性及可靠性，承重磁铁与导向磁铁必须加以控制。附加控制方程后，就形成了被控制的总系统的状态方程，从而实现车、磁及车行道模型的有机组合。对于实际工程问题，被控制的总系统的动力学性质由于维数较高，直接计算比较困难，本文采用计算机进行数值仿真，利用随机最优控制理论，对系统悬浮气隙和垂向加速度的变化规律进行了研究，并通过实例给出时变系统的仿真结果。     

LS-SVM在随机振动在线自适应逆控制中的应用

针对随机振动试验中波形再现实现中的非线性和不确定性的特点,提出了一种基于最小二乘支持向量机的自适应逆控制方法.首先根据试验样本数据利用模糊贝叶斯推断确定最小二乘支持向量机的参数,然后给出了基于最小二乘支持向量机的自适应逆控制器的设计方法,最后给出了随机振动在线自适应逆控制结构.实验结果表明该方法的有效性.     

Response of Uncertain Nonlinear Vibration Systems with 2D Matrix Functions

This paper extends the response of uncertain nonlinear vibration systems to vector-valued and matrix-valued functions. Random variables and system derivatives are conveniently arranged into 2D matrices. The method is based on a second order expansion of the governing equations and matrix calculus, Kronecker algebra are used in the mathematical development. The results derived are easily amenable to computational procedures.