Dynamics and control of an active pendulum system

The work focuses on autoparametric vibrations of system composed of a non-linear oscillator with an attached pendulum. A combination of semi-active damper together with a non-linear spring mounted in the suspension of system is proposed. The spring is made from a shape memory alloy (SMA) while damping is realized through a magnetorheological (MR) damper. The MR damper is used for controlling damping of the system, SMA spring is used to change system׳s stiffness. The system is solved numerically and verified experimentally on a custom made experimental rig. Specifically, non-linear resonances are investigated, and their influence on the system dynamics and absorption effect.     

时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

摆式调谐质量阻尼器因其便于安装、维修、更换,且经济实用,广泛应用于结构减振.它通过将摆的自振频率调谐到接近主系统的控制频率,使摆产生与主系统相反的振动,从而抑制或消除主系统的振动.本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计,实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制.首先,建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程,通过对主系统无阻尼的被动减振系统进行等峰优化,获得了减振系统的最优频率比和质量摆的最优阻尼比.对于主系统存在阻尼的被动减振系统,在该优化参数下主系统的幅频响应曲线等峰优化失效.其次,对于主系统存在阻尼的时滞反馈优化控制系统,采用CTCR方法得到了反馈增益系数和时滞的稳定区域.在保证系统稳定的前提下,通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制.再次,对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析,表明共振点幅值对反馈增益系数比对时滞更为敏感.最后,通过实验分别在频域和时域内对理论结果进行了验证.研究表明,通过采用时滞反馈对摆式调...     

磁流体特性对磁流变火炮后坐阻尼器性能的影响

针对火炮后坐磁流变阻尼器的特点,以某单管25 mm火炮实验用磁流变阻尼器为研究对象,基于Herschel-Bulkley本构模型,建立了该炮磁流变后坐阻尼器的轴对称一维层流模型,获得了不同磁场作用下阻尼力随活塞速度的变化规律。运用火炮的后坐运动方程,计算了不同磁流体特性指数下,火炮的后坐位移和后坐速度。计算结果表明,磁流体特性指数的变化对磁流变后坐阻尼器的性能影响显著。     

The application of inerter in tuned mass absorber

In this paper we investigate the dynamics of tuned mass absorber with additional viscous damper and inerter attached to the pendulum. The devices are used to damp out oscillations of non-linear Duffing oscillator. Analysis of how these devices influence the dynamics of tuned mass absorber and its damping properties is shown. We calculate the detailed bifurcation diagrams and show how by changing the parameters of damper and inerter one can eliminate dangerous dynamic instabilities from the systems. Finally, in the last section we present an optimization of TMA׳s parameters in order to achieve best efficiency in damping of the main body vibrations.     

结构振动的滑模变结构半主动控制

研究应用磁流变阻尼器(MRD)对结构振动半主动控制的算法和原理。研制并对磁流变阻尼器进行了阻尼特性实验，采用非线性滞回双粘性模型描述磁流变阻尼器的阻尼特性，模型结果与实验结果非常一致。采用滑模控制算法和趋近律方法设计了半主动控制器。利用滑模控制方法所建立的控制器，本文给出了地震激励下结构振动半主动控制算例。计算分析表明，半主动滑模控制具有控制效果明显、鲁棒性好等优点，是一种非常有发展前途的控制方法。     

MR阻尼器的半主动控制研究

MR阻尼器能提供可以调节的阻尼力,适合用作减少结构地震响应的半主动控制器。本文对MR阻尼器的半主动控制进行研究,提出了状态跳跃算法,根据结构响应的大小实现MR阻尼器的状态切换,使结构响应得到有效的控制。这种控制策略简便,不需要在线计算,便于实施。由于速度响应直接影响MR阻尼器的阻尼力,建议用速度响应作为MR阻尼器进行状态切换的变量。文中给出了两个算例,进行了计算分析和比较,说明了状态跳跃控制算法的特点。     

剪切阀式磁流变减振器力学特性实验研究

本文对剪切阀式磁流变减振器的结构和工作原理作了介绍,基于平板模型对其结构进行简化,采用叠加法得出了其阻尼力的理论计算模型。利用材料试验机(MTS)分别在不同电流、振幅、速度和频率等条件下,对自行研制的剪切阀式磁流变减振器的动态特性进行了实验研究,得出了相应的实验曲线。实验结果表明剪切阀式磁流变减振器具有优良的电控阻尼力特性,且振幅、速度和频率等因素对其阻尼力有着重要影响,另外也对其阻尼力的理论计算公式作了验证。     

Nonlinear Stiffness of a Magneto-Rheological Damper

The last decade has witnessed an important role of magneto-rheological dampers in the semi-active vibration control on the basis of empirical models. Those models established by fitting experimental data, however, do not offer any explicit expressions for the stiffness and the damping of magneto-rheological dampers. Hence, it is not easy for engineers to get any intuitive information about the effects of stiffness and damping of a magneto-rheological damper on the dynamic performance of a controlled system. To manifest the nonlinear properties of a magneto-rheological damper, this paper presents the hysteretic phenomena and the additional nonlinear stiffness of a typical magneto-rheological damper in terms of equivalent linear stiffness and equivalent linear damping. Then, it gives a brief discussion about the effect of nonlinear stiffness on the vibration control through the numerical simulations and an experiment for the semi-active suspension of a quarter car model with a magneto-rheological damper installed. Both numerical simulations and experimental results show that the additional nonlinear stiffness in the magneto-rheological damper is remarkable, and should be taken into consideration in the design of vibration control.     

A NEW STOCHASTIC OPTIMAL CONTROL STRATEGY FOR HYSTERETIC MR DAMPERS

I. INTRODUCTION Magneto-rheological (MR) ?uid as a smart material possesses fairly good essential characteristics suchas reversible change between liquid and semi-solid in milliseconds with a controllable yield strengthwhen exposed to a magnetic ?eld. A…     

On damping properties of a frictionless physical pendulum with a moving mass

The damping effects are generated in a frictionless oscillating physical pendulum by a continuous motion of an auxiliary mass. The main parameters affecting the damping properties of the pendulum-mass system are identified. In particular, the effective damping ratio for a cycle is introduced and derived in a closed form from the energy considerations and then independently from Mathieu's equation. It is shown that a continuous damping can be achieved if the mass motion is synchronized with the pendulum rotation. Otherwise the system becomes prone to ‘beating’ phenomenon. The results presented may be useful for design of active control strategy of autonomous systems with negligible passive damping.     

基于分数阶磁流变液阻尼器模型的车辆悬架组合控制

磁流变液阻尼器的分数阶Bingham模型结构形式简单, 而且可以更好地描述系统的滞回特性. 建立了含有分数阶Bingham模型的单自由度1/4车辆悬架系统模型, 利用磁流变液阻尼器对在路面简谐激励下的非线性车辆悬架系统进行振动控制. 研究了含有分数阶Bingham模型的悬架系统在天棚阻尼半主动控制下的主共振响应, 利用平均法得到了系统的近似解析解. 求解了系统定常解的幅频响应方程, 并根据李雅普诺夫稳定性理论得到了悬架系统的稳定性条件. 通过绘制数值解和解析解的幅频响应曲线对比图, 验证了近似解析解的正确性. 利用簧载质量垂直方向的加速度均方根值分析了半主动控制对车辆乘坐舒适性的影响, 发现天棚阻尼半主动控制策略在低频激励区域反而会降低车辆的乘坐舒适性. 因此提出了一种被动控制与半主动控制相结合的组合控制策略, 并分析了半主动控制参数对振动控制效果的影响. 分析结果表明, 该组合控制策略不但能够提高车辆的乘坐舒适性, 而且能有效抑制悬架系统的主共振振动幅值.      

Study on the force transmissibility of vibration isolators with geometric nonlinear damping

By a special layout of the damper in a vibration isolation system, the velocity-nth power damping of the damper can be transformed into the velocity-displacement dependent damping in the moving direction due to geometric nonlinearity. This study is mainly concerned with the mechanism of this geometric nonlinear damping and tries to find some guidelines for designing isolators with high performance, regardless of the isolator is passive or active. The model used in this study is an unconstrained two-degree-of-freedom isolation system, which is suitable for investigating vibration isolation in space vehicles. The motion equation is solved by the averaging method to obtain the amplitude–frequency equation. The influence of damping coefficients on the force transmissibility is analyzed. Results show that this kind of damping has some advantages in improving isolation performance at both the resonance and higher frequencies. Meanwhile, it can also degrade the isolation performance if unreasonable parameters are chosen.     

Inner mass impact damper for attenuating structure vibration

The behaviors of a vibration system suppressed with an impact damper are investigated, where the impact damper is simplified as a combination of spring and viscous damping. The analytical theory for the optimal impact control algorithms for impact damper is developed, and the accurate expressions are derived for the optimal values of the impact damper damping and initial displacement in a single-degree-of-freedom structure. The relation between coefficient of restitution and impact damping ratio is obtained. The investigation shows that the effective reduction of the vibration response is nearly independent of the number of impacts, but primarily related to the type of collision which the impact mass collides with the main mass face-to-face. This theory is generalized to continuous structures. An example of an impact damper in a rotating cantilever beam demonstrates that the impact dampers are suitable for attenuating the impulse response of structures unconditional stable without the requirement of the accuracy of the modal information.     

磁流变阻尼器半主动控制方法的实验研究

由于磁流变阻尼器是一种高度非线性的装置,因此建立与之相适应的控制系统是半主动控制问题的关键。本文采用改进的Bingham模型建立了磁流变阻尼器的动力学特性模型,根据天棚阻尼开关控制、天棚阻尼连续控制和模糊控制三种控制方法,确立了从系统速度响应到磁流变阻尼器励磁电流之间的关系,并开发了一套半主动控制系统。在一个两自由度的简化车辆试验平台上进行半主动控制试验,对比研究了三种控制方法的控制效果。实验结果表明,在1.3Hz~2.0Hz的低频段内,开关控制的最佳减振效果为15.1%,连续控制的最佳减振效果为14.9%,模糊控制的最佳减振效果为20.1%。可见,三种控制方法都能有效的减小车体的振动,模糊控制的减振效果最佳。     

Stability and instability of controlled motions of a two-mass pendulum of variable length

The problem of parametric control of plane motions of a two-mass pendulum (swing) is considered. The swing model is a weightless rod with two lumped masses one of which is fixed on the rod and the other slides along it within bounded limits. The control is the distance from the suspension point to the moving point. The proposed control law of swing excitation and damping consists in continuously varying the pendulumsuspension length depending on the phase state. The stability of various controlled motions, including the motions near the upper and lower equilibria, is studied. The Lyapunov functions that prove the asymptotic stability and instability of the pendulum lower position in the respective cases of the pendulum damping and excitation are constructed for the proposed control law. The influence of the viscous friction forces on the pendulum stable motions and the onset of stagnation regions in the case of its excitation is analyzed. The theoretical results are confirmed by graphical representation of the numerical results.     

内通道式磁流变阻尼器研究

设计制作了一种新型的内通道式磁流变液阻尼器,该阻尼器的流场通道位于线圈内部,磁流变效应发生在两层固定的平板区域之间,并能保持磁流变液的流向与磁感应方向垂直,即保证磁流变液的大面积成链,产生大的可控阻尼力,又具备失效安全性;根据宾汉模型,建立了阻尼器的准静态力学模型;最后对研制的阻尼器进行动力学实验研究,并与理论结果进行比较,二者吻合较好。     

一类非线性磁流变系统局部分岔特性研究

讨论了一类基于磁流变阻尼器非线性系统的局部分岔与控制问题，建立了该系统的动力 学模型，运用中心流形定理和范式理论，得到该系统双零特征值问题的规范形及其普适开折， 进而探讨了此系统的分岔行为和稳定性；给出了分岔曲线、转迁集；并给出了此类非线性系 统的数值仿真结果.     

Analytical investigation of an SDOF building structure equipped with a friction damper

The purpose of this study is to investigate analytically a single-degree-of-freedom (SDOF) building structure equipped with a friction damper for assessing its vibration control effect. Friction dampers are installed between stories to reduce inter-story displacements of building structures subjected to external loading. They are in general regarded to generate damping forces characterized by Coulomb damping, of which the directions are opposite to the inter-story velocities of building structures. Hence, the building structure model with friction dampers can be represented by a mass-spring-viscous-Coulomb damping system. The building response reduction as a result of damper installation can be provided by observing the damping ratio rather than the friction force contributed by the dampers. Since a large friction damper force is required to attenuate the response of the building due to strong excitation, friction force ratio is directly related to building response reduction, which is the friction force of the damper versus external force. Therefore, damping and friction force ratios are key parameters, playing a main role in selecting an optimal friction damper, which satisfies target response reduction. This study first identifies an SDOF building structure installed with a friction damper for free vibration with initial conditions. A?closed-form expression of normalized displacement is derived in terms of friction force ratio in the time domain. Peak and valley of displacements are also found and then the time when the structure stops is derived with recursive interval number. This study is extended to identify steady-state vibration of the structure by deriving closed-form solution in case of resonance in terms of friction force ratio. Then, the dissipated energy balance is identified for both free and steady-state vibrations. Finally, equivalent viscous damping ratios are derived by using friction force ratio based on dissipated energy balance equation. The derived equations in terms of viscous damping ratio and friction force ratio can provide insight to design a friction damper for reducing structural displacement under external loadings.     

Comparative research on semi-active control strategies for magneto-rheological suspension

This paper presents the comparison results of a study to identify an appropriate semi-active control algorithm for a MR suspension system from a variety of semi-active control algorithms for use with MR dampers. Five representative control algorithms are considered including the skyhook controller, the hybrid controller, the LQG controller, the sliding mode controller and the fuzzy logic controller. To compare the control performances of the five control algorithms, a quarter car model with a MR damper is adopted as the baseline model for our analysis. After deriving the governing motion equations of the proposed dynamic model, five controllers are developed. Then each control policy is applied to the baseline model equipped with a MR damper. The performances of each control algorithm under various road conditions are compared along with the equivalent passive model in both time and frequency domains through the numerical simulation. Subsequently, a road test is performed to validate the actual control performance. The results show that the performance of a MR suspension system is highly dependent on the choice of algorithm employed, and the sliding mode control strategy exhibits an excellent integrated performance.