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近几十年来, 时滞系统动力学的研究得到了众多学者的大量关注, 研究者在时滞系统的稳定性、非线性、辨识、时滞消除与利用技术等方面做了大量研究, 取得了许多成果. 本文主要介绍作者十多年来在时滞系统动力学方面的研究成果, 包括时滞辨识、两种基于时滞方程的控制律的设计方法、时滞鲁棒控制律的设计、时滞正反馈控制技术、非线性结构时滞控制律的设计、时滞实验等内容. 相似文献
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考虑含时滞反馈的影响,建立楔式制动系统动力学模型,运用多尺度方法对黏滑界面附近区域进行受迫主共振求解,分析时滞量、楔角与系统刚度对系统幅频响应的影响,应用Routh-Hurwitz判据分析系统稳定性的影响因素。基于解析解的分析表明:稳态幅值和稳定性边界都随时滞量发生周期性变化,周期内较大的时滞量引起鞍结分岔,并发展至不稳定多解;楔角和系统刚度增加引起主共振振幅增大,并扩大了不稳定区域。 相似文献
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考虑间隙反馈控制时滞的磁浮车辆稳定性研究 总被引:1,自引:0,他引:1
常导磁吸型(EMS)磁悬浮列车在悬浮控制中的每个环节,时滞是不可避免的,当时滞超过一定程度后,系统有可能失稳.本文针对EMS磁浮列车控制环节的临界时滞与车辆参数(如运行速度、反馈控制增益、导轨参数和悬挂参数)的关系开展研究.建立了磁浮车辆/导轨耦合动力学模型,车辆包含1节车辆和4个磁浮架,考虑车辆的10个自由度,每个磁浮架上包含4个悬浮电磁铁.导轨模拟为一系列简支Bernoulli-Euler梁,采用模态叠加法对导轨振动方程进行求解.采用传统线性电磁力模型实现车辆和轨道的耦合.采用比例-微分控制算法对电磁铁电流进行反馈控制,实现车辆稳定悬浮,并假设时滞均发生在控制环节,且只考虑间隙反馈控制环节的时滞.采用四阶龙格库塔法对耦合系统动力学方程进行求解,编写了数值仿真程序,计算得到车辆导轨耦合系统在考虑间隙反馈控制时滞时的响应.将系统运动发散时的时滞大小视为临界时滞,开展了参数规律影响分析.通过分析,给出了提高时滞条件下车辆稳定性的方法,包括增大导轨的弯曲刚度和阻尼比,减小间隙反馈控制增益并增大速度反馈控制增益,以及增大二系悬挂阻尼. 相似文献
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建立一种刚性杆-弹簧摆刚柔耦合强非线性动力学系统模型,给出了无量纲的动力学微分方程.该模型同时存在小幅度快速振荡和大范围慢速摆动的快、慢双时间尺度变量.针对工程中此类系统数值求解容易产生的刚性问题,采用一种三次Hermite插值精细积分法进行数值计算.将频率比、摆长比和初始摆角作为控制参数,研究刚性杆-弹簧摆刚柔耦合系统快、慢变量的复杂动力学行为.通过数值仿真分析,发现系统在不同的控制参数组合下呈现出混沌运动状态,并给出了与系统运动状态相关的控制参数范围,为复杂的刚柔耦合多体系统的设计与数值分析提供了参考. 相似文献
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非自治时滞反馈控制系统的周期解分岔和混沌 总被引:9,自引:0,他引:9
研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式.通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路:倍周期分岔和环面破裂.其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”. 相似文献
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悬索在考虑1:3内共振情况下的动力学行为 总被引:2,自引:0,他引:2
研究了悬索在受到外激励作用下考虑1:3内共振情况下的两模态非线性响应.对于一定范围内悬索的弹性-几何参数而言,悬索的第三阶面内对称模态的固有频率接近于第一阶面内对称模态固有频率的三倍,从而导致1:3内共振的存在.首先利用Galerkin方法把悬索的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到主共振情况下的平均方程.接下来对平均方程的稳态解、周期解以及混沌解进行了研究.最后利用Runge-Kutta法研究了悬索两自由度离散模型的非线性响应. 相似文献
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首先基于哈密顿变分原理推导了考虑抗弯刚度影响的拉索二自由度控制微分方程,然后分别采用直接法与间接法处理动张力,结合MATLAB软件对比这两种计算方法对控制微分方程中系数的影响。采用多尺度法分析了拉索可能存在的内共振模式,结合数值法分析了直接法与间接法对拉索振幅的影响,最后对比了两种计算方法下抗弯刚度对拉索幅值造成的影响。针对某座桥梁的斜拉索进行参数分析,其参数分析结果表明:两种计算方法下控制微分方程中系数的大小都随着拉索跨径的增加而减小,其中系数b5、b5’、b6、b6’、c5、c5’的值在跨径到达30m时趋于稳定不再变化,系数b4、b4’、b8、b8’、b9、b9’、c6、c6’、c7、c7’的值在跨径到达10m时趋于稳定不再变化,且两种计算方法所得系数的比值接近1.5。内共振分析表明,直接法与间接法不会影响拉索耦合共振的幅值,抗弯刚度对拉索幅值... 相似文献
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文章提出了一种利用时滞反馈对飞机起落架扭转摆振系统进行等峰优化的方法.首先,建立了考虑支柱扭转角、侧向位移、轮胎变形的振动微分方程,并得到了振动系统的解析解.其次,设计了一种等峰优化方法,根据优化准则,对不同当量轮胎侧偏刚度系数,通过调节反馈增益系数和时滞量实现了对支柱扭转角幅频响应曲线的等峰优化.同时,为了保证系统在稳定的前提下工作,采用CTCR方法有效的判定了时滞动力系统的稳定性.研究表明,对任意的当量轮胎侧偏刚度系数,都存在一对最优的反馈增益系数和时滞的最优值,能够实现对支柱扭转角振幅的最大抑制.最后,通过频域分析证明了时滞反馈控制等峰优化结果的有效性,通过时域分析证明了数据的可靠性. 相似文献
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时滞现象广泛地存在于结构振动的反馈控制过程中.考察在以前的研究中所忽略的时滞,对于柔性悬臂梁振动的饱和控制究竟可以产生什么影响.考虑了在反馈信号和控制信号中存在的时滞,研究了主共振和2∶1内共振同时发生的情形,利用多尺度方法求解了时滞微分方程,获得了包含时滞项的近似解析解,了解到时滞对于饱和控制的影响.理论和数值的结果均表明:时滞能够改变饱和控制器开始工作的门限值,如果考虑时滞现象,饱和控制器的有效频率范围将会改变.在某些情况下,可以通过加入时滞并适当地调节时滞参数的大小,来扩大饱和控制器的有效工作范围;在另外一些情况下,则要对所忽略的时滞量的大小有所估计并加以考虑,否则原来的控制策略就有可能失效. 相似文献
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This paper studies the delayed feedback control of flutter of a two-dimensional airfoil using a sliding mode control (SMC) method. The dynamic equation of airfoil flutter is firstly established using the Lagrange method, in which the cubic hardening spring nonlinearity of pitch stiffness is considered. Then, the state equation with time delay is transformed into a standard state equation with implicit time delay by a special integral transformation. Next a nonlinear time-delay controller is designed using the SMC method. Finally the effectiveness of the proposed controller is verified through numerical simulations. Simulation results indicate that time delay in the control system has significant influence on the control performance. Control failure may happen if time delay is not considered in control design. The time-delay controller proposed is effective in suppressing the airfoil flutter with either small or large control time delay. 相似文献
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Guo-Ping Cai·Long-Xiang Chen Department of Engineering Mechanics State Key Laboratory of Ocean Engineering Shanghai Jiaotong University Shanghai China 《Acta Mechanica Sinica》2010,26(6):951-965
In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward. 相似文献
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The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results. 相似文献
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In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation
is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and
a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop
system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries
are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore,
the second-order solution is presented and the corresponding results are compared with those of the first-order solution.
It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant
and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding
numerical results. Good agreement between the two sets of results is observed. 相似文献
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研究了悬索在受到外激励作用和考虑1∶3内共振情况下的两模态非线性响应。对于一定范围内的悬索弹性-几何参数而言,悬索第三阶面内对称模态的固有频率接近于第一阶面内对称模态的固有频率的3倍,从而导致1∶3内共振的存在。首先利用Galerkin方法把悬索的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动,可得到两组不同主共振情况下的平均方程。 相似文献
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CHAOTICBEHAVIOUROFFORCEDOSCILLATORCONTAININGASQUARENONLINEARTERMONPRINCIPALRESONANCECURVESPeiQin-yuan(裴钦元)(ChangshaRailwayUni... 相似文献
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Time delay is an important parameter in the problem of internet congestion control. According to some researches, time delay is not always constant and can be viewed as a periodic function of time for some cases. In this work, an internet congestion control model is considered to study the time-varying delay induced bursting-like motion, which consists of a rapid oscillation burst and quiescent steady state. Then, for the system with periodic delay of small amplitude and low frequency, the method of multiple scales is employed to obtain the amplitude of the oscillation. Based on the expression of the asymptotic solution, it can be found that the relative length of the steady state increases with amplitude of the variation of time delay and decreases with frequency of the variation of time delay. Finally, an effective method to control the bursting-like motion is proposed by introducing a periodic gain parameter with appropriate amplitude. Theoretical results are in agreement with that from numerical method. 相似文献
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Chaos in a pendulum with feedback control 总被引:4,自引:0,他引:4
K. Yagasaki 《Nonlinear dynamics》1994,6(2):125-142
We study chaotic dynamics of a pendulum subjected to linear feedback control with periodic desired motions. The pendulum is assumed to be driven by a servo-motor with small inductance, so that the feedback control system reduces to a periodic perturbation of a planar Hamiltonian system. This Hamiltonian system can possess multiple saddle points with non-transverse homoclinic and/or heteroclinic orbits. Using Melnikov's method, we obtain criteria for the existence of chaos in the pendulum motion. The computation of the Melnikov functions is performed by a numerical method. Several numerical examples are given and the theoretical predictions are compared with numerical simulation results for the behavior of invariant manifolds. 相似文献