非线性振动一种稳定的模糊控制方法研究

由于非线性振动系统的非线性本质,在于传统控制理论的线性控制器用于非线性振动控制效果不佳。本文针对非线性振动系统提出了一种模糊自适应滑模控制方案。     

The effect of time-delayed feedback controller on an electrically actuated resonator

This paper presents a study of the effect of a time-delayed feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated as a resonator by DC and AC voltage loads. A linearization analysis is conducted to determine the stability chart of the linearized system equations as a function of the time delay period and the controller gain. Then the method of multiple-scales is applied to determine the response and stability of the system for small vibration amplitude and voltage loads. It is shown that negative time-delay feedback control gain can lead to unstable responses, even if AC voltage is relatively small compared to the DC voltage. On the other hand, positive time delay can considerably strengthen the system stability even in fractal domains. We also show how the controller can be used to control damping in MEMS, increasing or decreasing, by tuning the gain amplitude and delay period. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved.     

斜拉索振动的模糊半主动控制研究

考虑拉索垂度及抗弯刚度的影响,得出了索-阻尼器系统振动偏微分方程;用中心差分法将偏微分方程在空间内离散,导出了系统的面内振动常微分方程组;提出了使用MR阻尼器(Magnetorheological Damper)作为控制设备,模糊集为基础的半主动控制算法,并运用提出的算法对索-阻尼器系统进行了振动控制分析。本文方法的优势在于算法自身的鲁棒性、处理非线性问题的能力强和不需要结构的精确数学模型,算法需要的输入变量少,可以解决实际工程中斜拉索的振动响应信息难以测量的困难。模糊算法的输出直接控制MR阻尼器的输入电压。与LQR-Clipped算法不同,MR阻尼器的输入电压可以是零与最大值之间的任意值。本文以实际斜拉桥拉索为例,分析了拉索的振动控制效果,结果表明本文提出的模糊半主动控制算法,使MR阻尼器的功能得到了更好的发挥,比MR被动控制效果好,且可以减小控制力。     

Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber

A nonlinear adaptive vibration absorber to control the vibrations offlexible structures is investigated. The absorber is based on thesaturation phenomenon associated with dynamical systems possessingquadratic nonlinearities and a two-to-one internal resonance. Thetechnique is implemented by coupling a second-order controller with thestructure through a sensor and an actuator. Energy is exchanged betweenthe structure and the controller and, near resonance, the structure'sresponse saturates to a small value.Experimental results are presented for the control of a rectangularplate and a cantilever beam using piezoelectric ceramics andmagnetostrictive alloys as actuators. The control technique isimplemented using a digital signal processing board and a modelingsoftware. The control strategy is made adaptive by incorporating anefficient frequency-measurement technique. This is validated bysuccessfully testing the control strategy for a nonconventionalproblem, where nonlinear effects hinder the application of thenonadaptive controller.     

Intrinsic localized modes in microresonator arrays and their relationship to nonlinear vibration modes

Intrinsic Localized Modes (ILMs) are defined as localizations due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators. Such nonlinear phenomena have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Here, such mode localization is studied in the context of microcantilever arrays and microresonator arrays, and it is explored if an ILM can be realized as a forced nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to construct nonlinear normal modes are used to study nonlinear vibrations of microresonator arrays. Investigations reported in this article suggest that it is possible to realize an ILM as a forced nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.     

动力吸振器复合非线性能量阱对线性镗杆系统的振动控制

研究了线性动力吸振器复合非线性能量阱对线性镗杆在外部简谐激励下的振动控制. 忽略镗杆系统中的非线性因素, 建立了附加线性动力吸振器和非线性能量阱的镗杆系统的三自由度运动方程, 研究了附加复合式动力吸振器的镗杆系统的受迫振动. 通过平均法得到了附加复合式动力吸振器的镗杆系统的近似解析解, 并利用数值解验证了近似解析解的准确性, 两者具有很好的一致性. 利用近似解析解详细分析了线性动力吸振器和非线性能量阱的参数对镗杆振动抑制性能的影响. 对给定质量的复合式动力吸振器进行了参数优化, 其中线性动力吸振器参数采用H_∞优化方法的近似解析解进行了优化, 非线性能量阱的阻尼利用系统的近似解析解进行了优化. 分析结果表明, 线性动力吸振器与非线性能量阱组合可以有效抑制线性镗杆系统的振动, 而且采用参数优化后的复合式动力吸振器可以获得更好的减振效果. 通过附加非线性能量阱, 不但可以提高线性动力吸振器的振动抑制效果, 而且还可以提高振动控制系统的鲁棒性.      

Thermal and tensile loading effects on size-dependent vibration response of traveling nanobeam by wavelet-based spectral element modeling

This paper presents a novel approach for size-dependent vibration response of a nanostructure under tensile and thermal loads, traveling in its axial direction at a constant velocity. The traveling nanostructure is modeled as an Euler–Bernoulli nanobeam based on modified couple stress theory. Wavelet-based spectral element model (WSEM) is performed for analyzing vibration of the system. Imposing WSEM reduces the governing partial differential equation of the system to a set of ordinary differential equations. The roles of nanobeam velocity, tensile and thermal loads on vibration and wave characteristics, and divergence/flutter instability are scrutinized by WSEM. The validity and accuracy of resulting responses are inspected by comparing with numeric values obtained from spectral element and finite element methods, and whenever possible, with those available in the literature.     

全柔性空间机器人运动振动一体化输入受限重复学习控制

探究基座、臂、关节全柔性影响下空间机器人动力学模拟、运动控制及基座、臂、关节三重柔性振动主动抑制的问题, 设计了不基于系统模型信息的运动振动一体化输入受限重复学习控制算法. 将柔性基座与关节等效为线性弹簧与扭转弹簧, 柔性臂视为欧拉-伯努利梁模型, 利用拉格朗日方程与假设模态法建立动力学模型, 然后, 用奇异摄动理论将模型分解为包含刚性变量与臂柔性振动的慢变子系统, 包含基座、关节柔性振动的快变子系统, 并分别设计相应的子控制器, 构成了带关节柔性补偿的一体化控制算法. 针对慢变子系统, 提出输入受限重复学习控制算法, 由双曲正切函数, 饱和函数与重复学习项构成, 双曲正切函数与饱和函数实现输入力矩受限要求, 重复学习项补偿周期性系统误差, 以完成对基座姿态、关节铰周期轨迹的渐进稳定追踪. 然而, 为了同时抑制慢变子系统臂的柔性振动, 运用虚拟力的概念, 构造同时反映臂柔性振动与系统刚性运动的混合轨迹, 提出了基于虚拟力概念的输入受限重复学习控制器, 保证基座、关节轨迹精确追踪的同时, 对臂的柔性振动主动抑制. 针对快变子系统, 采用线性二次最优控制算法抑制基座与关节的柔性振动. 仿真结果表明: 控制器适用于一般柔性非线性系统, 满足输入力矩受限要求, 实现对周期信号的高精度追踪, 有效抑制基座、臂、关节的柔性振动, 证实算法的可行性.      

Aeroelastic analysis and active flutter control of nonlinear lattice sandwich beams

Nonlinear aeroelastic characteristics of sandwich beams with pyramidal lattice core are investigated, and the active flutter control of the nonlinear structural system is also studied using the piezoelectric actuator/sensor pair. In the structural modeling, Reddy’s third-order shear deformation theory is applied. Aerodynamic pressure is evaluated by the supersonic piston theory. Hamilton’s principle and the assumed mode method are used to derive the equation of motion. The proportional feedback and the optimal H _∞ control methods are performed to design the controller. In the robust control, the uncertainty caused by omitting the nonlinear terms of the control equation is taken into account, and the mixed sensitivity method is used to solve the problem. The nonlinear aeroelastic property of the sandwich beam is analyzed and is compared with that of the equivalent isotropic beam with the same weight to show the superior aeroelastic characteristics of the lattice sandwich beam. Controlled vibration responses under the two different controllers are calculated and compared. Simulation results show that the robust controller is much more effective than the proportional feedback controller in the flutter suppression of the nonlinear sandwich beam.     

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。     

Stability of fluid conveying nanobeam considering nonlocal elasticity

In this study, the nonlocal Euler–Bernoulli beam theory is employed in the vibration and stability analysis of a nanobeam conveying fluid. The nanobeam is assumed to be traveling with a constant mean velocity along with a small harmonic fluctuation. In the considered analysis, the effects of the small-scale of the nanobeam are incorporated into the equations. By utilizing Hamilton’s principle, the nonlinear equations of motion including stretching of the neutral axis are derived. Damping effect is considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The effects of the different value of the nonlocal parameters, mean speed value and ratios of fluid mass to the total mass as well as effects of the simple–simple and clamped–clamped boundary conditions on the linear and nonlinear frequencies, stability, frequency–response curves and bifurcation point are presented numerically and graphically. The solvability conditions are obtained for the three distinct cases of velocity fluctuation frequency. For all cases, the stability areas of system are constructed analytically.     

几何非线性摩擦阻尼隔振系统动力学行为研究

非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的“锁定”现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.      

Infinite-Dimensional Control of Nonlinear Beam Vibrations by Piezoelectric Actuator and Sensor Layers

An infinite-dimensional approach for the active vibration control of a multilayered straight composite piezoelectric beam is presented. In order to control the excited beam vibrations, distributed piezoelectric actuator and sensor layers are spatially shaped to achieve a sensor/actuator collocation which fits the control problem. In the sense of von Kármán a nonlinear formulation for the axial strain is used and a nonlinear initial boundary-value problem for the deflection is derived by means of the Hamilton formalism. Three different control strategies are proposed. The first one is an extension of the nonlinear H-design to the infinite-dimensional case. It will be shown that an exact solution of the corresponding Hamilton–Jacobi–Isaacs equation can be found for the beam under investigation and this leads to a control law with optimal damping properties. The second approach is a PD-controller for infinite-dimensional systems and the third strategy makes use of the disturbance compensation idea. Under certain observability assumptions of the free system, the closed loop is asymptotically stable in the sense of Lyapunov. In this way, flexural vibrations which are excited by an axial support motion or by different time varying lateral loadings, can be suppressed in an optimal manner. A numerical example serves both to illustrate the design process and to demonstrate the feasibility of the proposed methods.     

Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic nonlinear equation of motion with damping is established by employing Hamilton’s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve are analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.     

On the need of nonlinear control for efficient model-based wake stabilization

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input–output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.     

四维超混沌系统Hopf分岔分析与反控制

对超混沌系统进行分岔反控制的研究已成为当前一个重要研究方向,常采用线性控制器实现反控制。首先,对一个四维超混沌系统的Hopf分岔特性进行了分析,利用高维分岔理论推导出分岔特性与参数之间的关系式,以此判断系统的分岔类型。然后,设计一个由线性与非线性组合成的混合控制器对系统进行分岔反控制,控制参数取值不同时,系统会呈现出不同的分岔特性。通过分析得出,调控线性控制器参数可以使系统Hopf分岔提前或延迟发生;同时,调控混合控制器的两个控制参数,可以改变系统Hopf分岔特性,实现分岔反控制。     

Vibration of fluid-conveying pipe with nonlinear supports at both ends

The axial fluid-induced vibration of pipes is very widespread in engineering applications. The nonlinear forced vibration of a viscoelastic fluid-conveying pipe with nonlinear supports at both ends is investigated. The multi-scale method combined with the modal revision method is formulated for the fluid-conveying pipe system with nonlinear boundary conditions. The governing equations and the nonlinear boundary conditions are rescaled simultaneously as linear inhomogeneous equations and linear inhomogeneous boundary conditions on different time-scales. The modal revision method is used to transform the linear inhomogeneous boundary problem into a linear homogeneous boundary problem. The differential quadrature element method (DQEM) is used to verify the approximate analytical results. The results show good agreement between these two methods. A detailed analysis of the boundary nonlinearity is also presented. The obtained results demonstrate that the boundary nonlinearities have a significant effect on the dynamic characteristics of the fluid-conveying pipe, and can lead to significant differences in the dynamic responses of the pipe system.

     

Free torsional vibration of cracked nanobeams incorporating surface energy effects

This paper investigates surface energy effects, including the surface shear modulus, the surface stress, and the surface density, on the free torsional vibration of nanobeams with a circumferential crack and various boundary conditions. To formulate the problem, the surface elasticity theory is used. The cracked nanobeam is modeled by dividing it into two parts connected by a torsional linear spring in which its stiffness is related to the crack severity. Governing equations and corresponding boundary conditions are derived with the aid of Hamilton's principle. Then, natural frequencies are obtained analytically, and the influence of the crack severity and position, the surface energy, the boundary conditions, the mode number, and the dimensions of nanobeam on the free torsional vibration of nanobeams is studied in detail. Results of the present study reveal that the surface energy has completely different effects on the free torsional vibration of cracked nanobeams compared with its effects on the free transverse vibration of cracked nanobeams.     

压电智能结构模糊自学习控制(FSLC)

将模糊逻辑与学习控制的基本思想相结合,根据控制系统的动态输出特性,采用模糊控制对学习控制律中的参数进行实时校正,实现系统的动态学习过程,提出了一种适用于压电智能结构振动控制的模糊自学控制方法FSLC（FuzzySelf-LearningContr01）。分别采用三维8节点实体单元（Solid45）和耦合单元模拟主结构和压电致动器／传感器,基于ANSYS参数化语言编写了压电智能结构振动控制分析的有限元程序。通过数值仿真证明了模糊自学习控制方法能有效控制压电结构的振动,并提高了自学习控制的收敛速度和获得了很好的控制效果。     

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.