分段阻尼隔振系统的动力学特性分析

针对传统线性隔振器在降低共振峰值的同时会牺牲隔振性能的矛盾,设计了一种含分段阻尼的隔振器.首先,采用移动凸轮变阻尼装置,通过凸轮廓线的设计使系统的垂向阻尼系数的受振动位移大小控制并呈现分段线性特征,分析了该装置的阻尼特性.然后将分段阻尼装置应用于隔振器中,建立了含分段阻尼的积极隔振系统模型及其动力学方程,通过能量等效原理求出了分段阻尼系统的等效线性阻尼系数,求解了简谐力激励下系统响应的理论解,并用四阶龙格—库塔法数值仿真验证了理论解的正确性.最后研究了分段阻尼隔振系统的动态特性,分析了主要参数对幅频响应特性与力传递率特性的影响.结果表明,通过合理的参数选择,分段阻尼隔振器可兼顾无阻尼隔振器与线性阻尼隔振器的优点,既能有效降低系统的共振峰值,又能保证高频区域的优秀隔振性能,为新型非线性隔振器的设计提供了理论依据.     

基于泰勒级数拟合的机器人模糊连续变增益H∞控制

针对n关节刚性机器人，提出一种新的保证在整个运动范围内始终具有良好动态性能的模糊连续变增益控制器的设计方法。首先结合变增益H∝理论和LMI方法，运用泰勒级数拟合设计连续变增益H∞控制器，使其适合系统状态变化快的对象；然后引入模糊控制，使控制器在误差较大时具有快速特性，误差较小时具有良好阻尼特性，从而使系统随状态变化始终具有很高的动态性能。仿真和实验结果验证了此控制器的有效性。     

基于等效模态阻尼的复合隔振系统振动计算方法

基于线性黏弹性假设,将应变能阻尼理论推广到复合隔振系统的等效模态阻尼计算中,运用Python和Abaqus编制相应的计算程序,该程序可考虑材料阻尼的频变特性。以多种材料组成的船舶双层复合隔振系统为算例,计算其等效模态阻尼和隔振器等效阻尼系数。分别采用直接积分法和模态叠加法计算系统振动响应,对比设备、筏架、船底壳的振动加速度响应,验证基于等效模态阻尼的模态叠加法的准确性。结果表明,该方法可以准确计算复杂组合模型的模态阻尼,算例的振动响应计算结果一致性较好,用模态叠加法可以大幅提高复合隔振系统稳态振动响应的计算效率。     

线性定常系统电网络阻尼动态特性仿真研究

该文用李亚普诺夫定理推导出的综合阻尼系数方法研究分析了四阶线性系统电网络阻尼特性，对其电路的动态特性进行了计算机仿真。仿真结果证明，采用综合阻尼系数方法研究分析线性定常系统的阻尼特性的方法是合删、可行的，综合阻尼系数反映的是整个线性系统的综合阻尼效应，具有完善的物理意义，可以在整个系统的最佳阻尼下选择不同的参数。特别对系统特征方程次数较高时原则上可不受方程阶数限制，可以准确分析说明线性系统参数变化对阻尼的影响和对阻尼的大范围判定。文中的方法和结论对高阶线性系统的分析是可行的，可用以研究大系统动态过程振荡稳定性问题。     

二自由度自激振荡系统中阻尼对粘滑运动的调控作用

二自由度自激振荡系统中由摩擦引起的粘滑运动具有复杂性，其产生机理及调控方式有重要的学术和工程应用价值。重点探讨了二自由度自激振荡系统中阻尼对粘滑运动的影响，对摩擦的不连续性采取光滑连续处理，应用改进型Hénon算法对系统方程进行数值求解，并根据庞加莱图对系统运动状态和特性进行确认。研究发现：保持系统其他参数不变，由小到大调节阻尼，滑块的运动依次出现混沌粘滑、周期粘滑、周期滑动和阻滑4种状态；混沌粘滑-周期粘滑、周期粘滑-周期滑动为渐变过程，而周期滑动-阻滑为突变过程，其中突变行为对阻尼的变化相当敏感，当阻尼从2.501变为2.502时系统运动状态发生了临界转变。初步探明了阻尼对自激振荡系统运动状态和粘滑行为的作用规律，结果将为粘滑运动调控及阻尼自适应控制提供理论指导。     

弹支-刚性转子系统过共振瞬态响应特性研究

针对结合弹支-刚性转子系统的动力学特点,利用Lagrange能量法建立了考虑变速特性的转子系统瞬态响应动力学方程,模型中区别考虑了非旋转阻尼和旋转阻尼的影响.采用精细积分算法计算获得过临界区的转子瞬态响应特性,进一步对比分析了角加速度和阻尼特性对转子系统瞬态振动响应幅频特性和相频特性的影响规律.研究结果表明：变转速引起系统的刚度矩阵变化并产生附件的激励力;瞬态过共振响应幅值明显小于稳态响应幅值,且过共振越快速、阻尼越大时系统瞬态振动响应幅值越小.针对过瞬态相频特性,在临界转速附近出现一个新的相位角(加速过共振小于90°),此相位不受角加速度值和旋转阻尼比的影响,但随着非旋转阻尼比的增大呈增大趋势.     

基于动量守恒的变质量系统振动分析方法

为了研究变质量系统的动态响应,提出一种基于动量守恒的变质量系统振动分析方法.与现有变质量系统振动分析方法不同,在建立动力系统微分方程时,无需考虑质量变化率对阻尼的影响,而在计算过程中,由某一时刻计算下一时刻系统响应时,考虑质量变化对系统速度的影响,速度变化遵守动量守恒定律.利用算例和实验分别对提出的振动分析方法进行验证,结果表明:该方法可用于变质量动力系统振动分析.     

大阻尼杆振动的广义多辛算法

本文基于Bridges教授建立的多辛算法理论及其Hamilton变分原理,采用广义多辛算法研究了大阻尼杆的阻尼振动特性.引入正交动量后,首先将描述大阻尼杆振动的控制方程降阶为一阶Hamilton近似对称形式,即广义多辛形式;随后采用中点离散方法构造形式广义多辛形式的中点Box广义多辛离散格式;最后通过计算机模拟研究大阻尼杆振动过程中的耗散效应.研究结果表明,本文构造的广义多辛算法不仅能够保持系统守恒型几何性质,同时能够再现系统的耗散效应.     

水平阻尼作为干扰的平台式惯导统一控制方程

研究惯导系统统一控制的优化设计。传统的统一控制采用一体化设计方案,通用性不强。为简捷高效地实现惯导计算机的程序编排,提出了将水平阻尼作为干扰项的平台式惯导统一控制。通过改变系统框图结构,将无阻尼惯导系统和阻尼网络人为分离,水平阻尼网络的输出可视为干扰项。系统控制方程始终采用无阻尼条件下的表达式,惯导系统控制和阻尼网络可以实现模块化设计,使控制的实现形式和推导过程大为简化。给出了惯导计算机的运算流程,并分别在静、动基座条件下,对无阻尼、内水平阻尼和外水平阻尼状态的惯导系统做了仿真。结果表明新的统一控制模型有效体现了惯导系统的参数变化,且设计简便,具有更好的实用性。     

汽车电动助力转向系统的混杂控制与试验

汽车电动助力转向(EPS)系统以蓄电池为能源,以电动机为动力元件,汽车EPS控制系统的设计是提高EPS系统性能和电动机效率的关键.分析了汽车EPS系统的混杂特性,可分为助力工况、回正工况和阻尼工况.设计了汽车EPS混杂控制系统,助力工况采用由Bang-bang控制和变参数双模糊控制组成的双模态控制器;回正工况采用PID控制器;阻尼控制采用电动机制动转矩控制方式.设计了实车试验系统,进行了转向手感实车试验和回正控制实车试验.汽车EPS系统的混杂控制充分反映了汽车EPS系统的工作状况,优化了EPS系统的功能和控制效果,增强了转向操纵的安全性,提高了EPS电动机的工作效率和节能环保能力.     

Large errors in approximate decoupling of nonclassically damped linear second-order systems under harmonic excitations

A simple and commonly used approximate technique of solving the normalized equations of motion of a nonclassically damped linear second-order system is to decouple the system equations by neglecting the offdiagonal elements of the normalized damping matrix, and then to solve the decoupled equations. This approximate technique can result in a solution with large errors, even when the off-diagonal elements of the normalized damping matrix are small. Large approximation errors can arise in lightly damped systems under harmonic excitations when some of the undamped natural frequencies of the system are close to the excitation frequency. In this article, a rigorous analysis of the approximation error in lightly damped systems is given. Easy-to-check conditions under which neglecting the off-diagonal elements of the normalized damping matrix can result in large approximation errors are presented.     

半主动分支电路压电可控减振技术仿真与实验

通过仿真，研究了半主动分支电路压电可控减振技术中电感的变化对减振效果的影响．以振动能耗比例评价减振效果。仿真结果表明，分支电路电感的最优值在电路谐振时的电感值附近，而偏离电路谐振电感时，减振效果迅速下降。实验中通过测得的振动能耗比例随电感变化曲线．验证了仿真得到的结论。进一步说明了具有RL分支电路的半主动悬臂梁结构阻尼控制技术的可行性和有效性。     

Passivity‐based asymptotic stabilization for switched nonlinear systems using the sampled integral stabilization technique

The asymptotic stabilization problem is studied for a cascade connection of passive switched nonlinear systems and a passive switched nonlinear system in this paper. When each subsystem is asymptotically zero state detectable and passive on active time intervals, asymptotic stabilization is achieved via co‐design of switching laws and controllers without damping injection. First, an output‐feedback controller is designed to asymptotically stabilize a cascade connection of two passive switched systems if outputs are measurable. Second, when the output of the first switched system is noisy or unmeasurable, a sampled integral stabilization (SIS) technique is employed to investigate asymptotical stabilization of a cascade connection by measuring only the storage function of the second switched system. Finally, as a special case of a cascade connection, the SIS technique is used to stabilize a passive switched system without damping injection. Under this circumstance, the controller is designed by sampling the integral of the passive output. The two‐link robot manipulator is provided to illustrate the effectiveness of the SIS technique.     

Composite nonlinear feedback control for linear systems with input saturation: theory and an application

We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.     

Regulation of flexible structures via nonlinear coupling

In this article, we propose an active/passive vibration controller for a cantilever beam using a sliding mass-spring-dashpot mechanism. The controller is placed at the free end of the beam, introducing Coriolis, inertia, and centripetal nonlinearities into the system, resulting in nonlinear coupling that may be used to quench the transient vibration of the beam. When the natural frequency of the slider is twice the fundamental beam frequency (2:1 internal resonance), the two systems will be coupled through nonlinearities that cause the oscillatory energy to be transferred back and forth between the beam and the slider. Control is achieved once the vibration of the beam is absorbed by the slider and dissipated through the slider damping. Numerical results show that this technique can improve the effective damping ratio of the structure by a factor of 15. This technique is particularly useful for reducing large-amplitude oscillations to levels that may be managed using conventional methods.Due to the nonlinearities in the system, for small or zero controller damping, chaotic transient oscillations can occur depending on the amplitude of the initial disturbance of the beam. Editor: T. Vincent     

On tracking control of flexible robot arms

A controller for solving the tracking problem of flexible robot arms is presented. In order to achieve this goal, the desired trajectory for the link (flexible) coordinates is computed from the dynamic model of the robot arm and is guaranteed to be bounded, and the desired trajectory for the joint (rigid) coordinates can be assigned arbitrarily. The case of no internal damping is also considered, and a robust control technique is used to enhance the damping of the system     

Optimal pole-placement in discrete systems

A technique for increasing the damping in a closed-loop discrete-time system by modifying a nominal linear quadratic performance criterion is developed. The technique uses the multiple solutions of the discrete-time algebraic Riccati equation to modify the nominal criterion. These criterion modifications increase the damping by moving the nominal closed-loop eigenvalues to an exact location along the radial line segment connecting the nominal eigenvalues with the origin     

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper studies the technique of the composite nonlinear feedback (CNF) control for a class of cascade nonlinear systems with input saturation. The objective of this paper is to improve the transient performance of the closed-loop system by designing a CNF control law such that the output of the system tracks a step input rapidly with small overshoot and at the same time maintains the stability of the whole cascade system. The CNF control law consists of a linear feedback control law and a nonlinear feedback control law. The linear feedback law is designed to yield a closed-loop system with a small damping ratio for a quick response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system when the system output approaches the target reference to reduce the overshoot. The result has been successfully demonstrated by numerical and application examples including a flight control system for a fighter aircraft.     

Improvement of damping performance by splitting damping material

Damping materials in the carriage arm of a hard disk drive reduce flow-induced vibrations. As recording tracks become narrower, better damping is required. In this paper, a technique of splitting damping materials to improve the damping performance is described. We assumed a structural damping and examined the damping performance using the strain energy stored in a viscoelastic material. At first, we classified deformations of the viscoelastic material into three kinds: bending, shearing and thickness deformation (change in thickness). For the bending and the shearing deformation, we clarified that the splitting technique does not increase the strain energy. For the thickness deformation, we derived equations for the deformation shape and the strain energy. Then we found the splitting increases the strain energy if the parameter ϕ, which is proportional to the length and related to the stiffness of the damping material, is more than 5. Finally, we demonstrated the effectiveness of the splitting technique by numerical simulations and experiments.     

Construction of control Lyapunov functions for damping stabilization of control affine systems

This paper considers the stabilization of nonlinear control affine systems that satisfy Jurdjevic–Quinn conditions. We first obtain a differential one-form associated to the system by taking the interior product of a non vanishing two-form with respect to the drift vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point that decomposes the system into an exact part and an anti-exact one. Integrating the exact one-form, we obtain a locally-defined dissipative potential that is used to generate the damping feedback controller. Applying the same decomposition approach on the entire control affine system under damping feedback, we compute a control Lyapunov function for the closed-loop system. Under Jurdjevic–Quinn conditions, it is shown that the obtained damping feedback is locally stabilizing the system to the desired equilibrium point provided that it is the maximal invariant set for the controlled dynamics. The technique is also applied to construct damping feedback controllers for the stabilization of periodic orbits. Examples are presented to illustrate the proposed method.