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研究了弹性轨道条件下,控制回路中位置反馈信号存在时滞的磁浮系统在亚谐轨道激励作用下的响应问题. 将动力学模型在平衡点处线性化,以时滞为分岔参数,得到了系统出现Hopf分岔的条件. 用中心流形约化方法得到了包含轨道扰动系统的Poincaré规范型. 用多尺度法从理论上推导了时滞磁浮系统的亚谐共振周期解,得到了自由振动的分岔响应方程,分析了周期解中自由振动项的存在条件,研究了控制参数和激励参数与周期解的关系. 最后用数值仿真的方法分析了时滞参数、控制参数对系统响应的影响,分析结果指出,使系统保持稳定的亚谐响应的时滞边界小于无扰动时的时滞边界,时滞参数不但可以抑制亚谐响应,还能够控制混沌的产生,而控制参数可以控制系统响应中自由振动项的出现和受迫振动的幅值,适当选择这些参数可以有效抑制亚谐振动响应.
关键词:
亚谐共振响应
位置时滞反馈控制
非自治磁浮系统
分岔 相似文献
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针对基础水平运动的弹簧摆的非线性动力学响应进行研究,利用拉格朗日方程建立了系统的动力学方程.将离散傅里叶变换、谐波平衡法以及同伦延拓方法相结合,对系统的周期响应进行求解,避免了传统方法计算中使用泰勒展开引起的小振幅的限制,与数值计算结果的对比表明该求解方法具有较高的精确度.利用Floquet理论分析了周期响应的稳定性,给出了基础运动振幅和频率对系统周期响应的影响.研究发现:对应某些基础频率和振幅,系统的周期响应可能发生Hopf分岔;利用数值计算研究了Hopf分岔后系统响应随基础频率和振幅的变化,发现系统出现了倍周期运动、拟周期运动和混沌等复杂的动力学行为.研究表明系统进入混沌的主要路径是拟周期环面破裂和阵发性. 相似文献
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非线性动力系统极易发生共振,在多频激励下可能发生联合共振或组合共振,目前关于非线性系统的主-超谐联合共振的研究少见报道.本文以Duffing系统为对象,研究系统在主-超谐联合共振时的周期运动和通往混沌的道路.应用多尺度法得到系统的近似解析解,并利用数值方法对解析解进行验证,结果吻合良好.基于Lyapunov第一方法得到稳态周期解的稳定性条件,并分析了非线性刚度对稳态周期解的幅值和稳定性的影响.此外,由于近似解只能描述周期运动,不足以描述系统的全局特性,因而应用Melnikov方法对系统进行全局分析,得到系统进入Smale马蹄意义下混沌的条件,依据该条件以及主-超谐联合共振的条件选取一组参数进行数值仿真.分岔图和最大Lyapunov指数显示出两个临界值:当激励幅值通过第一个临界值时,异宿轨道破裂,混沌吸引子突然出现,系统以激变方式进入混沌;激励幅值通过第二个临界值时,系统在混沌态下再次发生激变,进入另一种混沌态.利用Melnikov方法考察了第一个临界值在多种频率组合下的变化趋势,并用数值仿真验证了解析结果的正确性. 相似文献
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Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback 下载免费PDF全文
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied.By considering the energy in the air-gap field of the AC motor,the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system.The characteristic roots and the stable regions of time delay are determined by the direct method,and the relationship between the feedback gain and the length summation of stable regions is analyzed.Choosing the time delay as a bifurcation parameter,we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem.Numerical simulations are also performed,which confirm the analytical results. 相似文献
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The local dynamics of an axially moving string under aerodynamic forces is investigated with a time-delayed velocity feedback controller. The retarded differential difference governing equation is obtained in modal coordinates of a two-degree-of-freedom system through Galerkin’s discretization procedure. The stability of trivial equilibrium is examined with the change of counting multiplicity of eigenvalue with positive real part. The Hopf bifurcation curves are determined in the controlling parameter spaces. With the aid of the center manifold reduction, a functional analysis is carried out to reduce the modal equation to a single ordinary differential equation of one complex variable on the center manifold. The approximate analytical solutions in the vicinity of Hopf bifurcations are derived in the case of primary resonance. The curves of excitation-response and frequency-response curves are shown with the effect of time delay. The stability analysis for steady-state periodic solutions of the reduced system indicates the onset of local control parameter for vibration control and response suppression. Moreover, the Poincaré-Bendixson theorem and energy considerations are used to investigate the existences and characteristics of quasi-periodic solutions when stability of the periodic solution is lost. Numerical results demonstrate the validity of the analytical prediction. Two different kinds of quasi-periodic solutions are found. 相似文献
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We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven
Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect
of the time-delay parameter α and the strength γ of the time-delayed feedback. Applying the perturbation theory we obtain a nonlinear equation for the amplitude of the periodic
response of the system. For a range of values of γ and α, the response amplitude is found to be higher than that of the system in the absence of delayed feedback. The response amplitude
is periodic on the parameter α with period 2π/ω where ω is the angular frequency of the external periodic force. We show the occurrence of multiple branches of the response amplitude
curve with and without hysteresis. 相似文献
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建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性.
关键词:
相对转动
准周期参激
时滞反馈
极限环 相似文献
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建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性.
关键词:
相对转动
非线性动力系统
Lyapunov函数
稳定性 相似文献
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Anna Zakharova Alexey Feoktistov Tatyana Vadivasova Eckehard Schöll 《The European physical journal. Special topics》2013,222(10):2481-2495
We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system. 相似文献
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利用动力系统方法研究一维Tonks-Girardeau原子气区域中Gross-Pitaevskii (GP)方程简化模型的一些精确行波解以及这些精确行波解的动力学行为, 研究系统的参数对行波解的动力学行为的影响. 在不同的参数条件下, 获得了一维Tonks-Girardeau原子气区域中GP方程简化模型的六个行波解的精确参数表达式.
关键词:
动力系统方法
孤立波解
周期波解
扭波解 相似文献
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This paper focuses on a paced genetic regulatory small-world network with time-delayed coupling. How the dynamical behaviors including temporal resonance and spatial synchronization evolve under the influence of time-delay and connection topology is explored through numerical simulations. We reveal the phenomenon of delay-induced resonance when the network topology is fixed. For a fixed time-delay, temporal resonance is shown to be degraded by increasing the rewiring probability of the network. On the other hand, for small rewiring probability, temporal resonance can be enhanced by an appropriately tuned small delay but degraded by a large delay, while conversely, temporal resonance is always reduced by time-delay for large rewiring probability. Finally, an optimal spatial synchrony is detected by a proper combination of time-delay and connection topology. 相似文献
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The dynamical behaviour of an incompressible viscous fluid flow on a two-dimensional torus externally excited by a spatially periodic force is investigated. The flow field, described by Navier-Stokes equations, is found to possess a sequence of time-periodic solutions which bifurcate from a single steady state solution (i.e. Hopf bifurcations). This result is based on a combination of analysis and computations, and each provides corroborative evidence to the findings of the other.Research partially supported by the National Science Foundation of China. 相似文献
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A. V. Gurevich K. P. Zybkin G. A. Él’ 《Journal of Experimental and Theoretical Physics》1999,88(1):182-195
The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed
on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence.
The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having
a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability
density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions
amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of
the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found.
Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation)
is completely solved.
Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999) 相似文献
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One-species competition ecosystem with noise and time delay was investigated as not driven by a periodic force.The results show that the time delay is responsible for stochastic resonance of the system as delay time is smaller than critical point of the Hopf bifurcation. 相似文献