自激振荡

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自激振荡作为正反馈回路的图示。振荡器[math]\displaystyle{ V }[/math]产生一个反馈信号[math]\displaystyle{ B }[/math]。位于[math]\displaystyle{ R }[/math]的控制器使用这个信号来调制作用于振荡器的外部源[math]\displaystyle{ S }[/math]。如果源与振荡器的速度同相调制,则产生负阻尼导致振荡增大,直至达到非线性的限制。



Self-oscillation is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from forced and parametric resonators, in which the power that sustains the motion must be modulated externally. In linear systems, self-oscillation appears as an instability associated with a negative damping term, which causes small perturbations to grow exponentially in amplitude. This negative damping is due to a positive feedback between the oscillation and the modulation of the external source of power. The amplitude and waveform of steady self-oscillations are determined by the nonlinear characteristics of the system. Self-oscillations are important in physics, engineering, biology, and economics.

自激振荡 Self-oscillation是指不外加任何激励信号时,自行产生的恒稳且持续的振荡。如果在运算放大器的输入端不加任何激励信号,输出端仍然会出一定幅值和频率的输出信号。[1]


自激振荡是由缺乏相应周期性的动力源产生并维持周期性运动。其中振子本身控制着作用于它的相位的外部源。因此,自激振荡器不同于受迫和参数共振器,后者维持运动的源必须由外部调制。在线性系统 linear systems中,自激振荡表现为与负阻尼项相关的失稳,导致小扰动振幅呈指数增长。这种负阻尼是由于振荡和外部源调制之间的正反馈 positive feedback。系统的非线性特性决定了系统稳态自激振荡的幅值和波形。自激振荡在物理学、工程学、生物学和经济学中都有着很重要的作用。


History of the subject 学科历史

The study of self-oscillators dates back to Robert Willis, George Biddell Airy, James Clerk Maxwell, and Lord Rayleigh in the 19th century. The term itself (also translated as "auto-oscillation") was coined by the Soviet physicist Aleksandr Andronov, who studied them in the context of the mathematical theory of the structural stability of dynamical systems. Other important work on the subject, both theoretical and experimental, was due to André Blondel, Balthasar van der Pol, Alfred-Marie Liénard, and Philippe Le Corbeiller in the 20th century.[2]

The study of self-oscillators dates back to Robert Willis, George Biddell Airy, James Clerk Maxwell, and Lord Rayleigh in the 19th century. The term itself (also translated as "auto-oscillation") was coined by the Soviet physicist Aleksandr Andronov, who studied them in the context of the mathematical theory of the structural stability of dynamical systems. Other important work on the subject, both theoretical and experimental, was due to André Blondel, Balthasar van der Pol, Alfred-Marie Liénard, and Philippe Le Corbeiller in the 20th century.

自激振荡器的研究者可以追溯到19世纪的 Robert Willis、 George Biddell Airy、 James Clerk Maxwell 和 Lord Rayleigh。这个术语(也可以翻译成“自振荡”)本身是由苏联物理学家 Aleksandr Andronov 提出的,他在动力系统结构稳定性的数学理论的背景下研究了这些现象。其他关于这个主题的重要工作,包括理论和实验,是由于20世纪的 André Blondel, Balthasar van der Pol, Alfred-Marie Liénard 以及 Philippe Le Corbeiller 来完成的。


The same phenomenon is sometimes labelled as "maintained", "sustained", "self-exciting", "self-induced", "spontaneous", or "autonomous" oscillation. Unwanted self-oscillations are known in the mechanical engineering literature as hunting, and in electronics as parasitic oscillations.[2] Important early studied examples of self-oscillation include the centrifugal governor[3] and railroad wheels.

The same phenomenon is sometimes labelled as "maintained", "sustained", "self-exciting", "self-induced", "spontaneous", or "autonomous" oscillation. Unwanted self-oscillations are known in the mechanical engineering literature as hunting, and in electronics as parasitic oscillations.Important early studied examples of self-oscillation include the centrifugal governor and railroad wheels.

同样的现象有时也被称为“维持”、“持续”、“自我激发”、“自我诱导”、“自发”或“自主”振荡。有害的自激振荡在机械工程文献中被称为追逐,在电子学中被称为寄生振荡 parasitic oscillations。自激振荡早期的重要研究包括离心调速器和火车车轮。

Mathematical basis 数学基础


Self-oscillation is manifested as a linear instability of a dynamical system's static equilibrium. Two mathematical tests that can be used to diagnose such an instability are the Routh–Hurwitz and Nyquist criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude. This can produce a steady and sustained oscillation. In some cases, self-oscillation can be seen as resulting from a time lag in a closed loop system, which makes the change in variable xt dependent on the variable xt-1 evaluated at an earlier time.[2]

Self-oscillation is manifested as a linear instability of a dynamical system's static equilibrium. Two mathematical tests that can be used to diagnose such an instability are the Routh–Hurwitz and Nyquist criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude. This can produce a steady and sustained oscillation. In some cases, self-oscillation can be seen as resulting from a time lag in a closed loop system, which makes the change in variable xt dependent on the variable xt-1 evaluated at an earlier time.

自振荡表现为动力系统静态平衡的线性不稳定性。可用劳斯-赫尔维茨准则和奈奎斯特准则这两个两个数学检验方法来判断这种不稳定性的。不稳定系统振动的振幅随时间呈指数增长(例如负阻尼下的小振荡),直到非线性变得重要并限制振幅。这可以产生一个稳定和持续的振荡。在某些情况下,自激振荡可以看作是闭环系统中时滞的结果,这使得变量 xt 的变化依赖于变量xt-1 的早期估值。

Examples in engineering 工程中的例子

Railway and automotive wheels 铁路和汽车车轮

Hunting oscillation in railway wheels and shimmy in automotive tires can cause an uncomfortable wobbling effect, which in extreme cases can derail trains and cause cars to lose grip.

Hunting oscillation in railway wheels and shimmy in automotive tires can cause an uncomfortable wobbling effect, which in extreme cases can derail trains and cause cars to lose grip.

铁路车轮上的追逐运动和汽车轮胎的摆振会引起令人不舒服的摇晃效应,在极端情况下,这种摇晃(振荡)会使火车脱轨,导致机车失去抓地力。


Central heating thermostats 集中供热恒温器

Early central heating thermostats were guilty of self-exciting oscillation because they responded too quickly. The problem was overcome by hysteresis, i.e., making them switch state only when the temperature varied from the target by a specified minimum amount.

Early central heating thermostats were guilty of self-exciting oscillation because they responded too quickly. The problem was overcome by hysteresis, i.e., making them switch state only when the temperature varied from the target by a specified minimum amount.

早期的集中供热恒温器由于响应速度太快而被自激振荡所困扰。这个问题可以用磁滞效应克服,例如说只有当温度与目标相差一定的最小值时,它们才会处于切换状态。


Automatic transmissions 自动变速器

Self-exciting oscillation occurred in early automatic transmission designs when the vehicle was traveling at a speed which was between the ideal speeds of 2 gears. In these situations the transmission system would switch almost continuously between the 2 gears, which was both annoying and hard on the transmission. Such behavior is now inhibited by introducing hysteresis into the system.

Self-exciting oscillation occurred in early automatic transmission designs when the vehicle was traveling at a speed which was between the ideal speeds of 2 gears. In these situations the transmission system would switch almost continuously between the 2 gears, which was both annoying and hard on the transmission. Such behavior is now inhibited by introducing hysteresis into the system.

自激振荡在早期的自动变速器设计中出现过,当时车辆的行驶速度介于理想的2个齿轮之间。在这些情况下,传动系统将几乎连续切换两个齿轮,这是恼人的和硬的变速器。这种行为现在已被系统中引入的滞后现象所抑制。


Steering of vehicles when course corrections are delayed 航向修正的延迟时的车辆驾驶

There are many examples of self-exciting oscillation caused by delayed course corrections, ranging from light aircraft in a strong wind to erratic steering of road vehicles by a driver who is inexperienced or drunk.

There are many examples of self-exciting oscillation caused by delayed course corrections, ranging from light aircraft in a strong wind to erratic steering of road vehicles by a driver who is inexperienced or drunk.

有很多由于航向修正的延迟造成的自激振荡的例子,如强风中的轻型飞机、没有经验或醉酒驾驶的司机不规则地操纵公路车辆。


SEIG (self-excited induction generator 自励异步发电机)

If an induction motor is connected to a capacitor and the shaft turns above synchronous speed, it operates as a self-excited induction generator.

If an induction motor is connected to a capacitor and the shaft turns above synchronous speed, it operates as a self-excited induction generator.

将一个感应电动机连接到一个电容器上,并且轴转到同步速度以上,就构建了一个自励感应发电机。

Self-exciting transmitters 自激励发射器

Many early radio systems tuned their transmitter circuit so the system automatically created radio waves of the desired frequency. This design has generally given way to designs that use a separate oscillator to provide a signal that is then amplified to the desired power.

Many early radio systems tuned their transmitter circuit so the system automatically created radio waves of the desired frequency. This design has generally given way to designs that use a separate oscillator to provide a signal that is then amplified to the desired power.

许多早期的无线电系统通过调整发射器电路,来自动产生所需频率的无线电波。这种设计通常让位于使用一个单独的振荡器来提供信号,然后将信号放大到所需的功率。

Examples in other fields 跨领域应用

Population cycles in biology 生物学中的种群周期

模板:Details

For example a reduction in population of a herbivore species because of predation, this makes the populations of predators of that species decline, the reduced level of predation allows the herbivore population to increase, this allows the predator population to increase, etc. Closed loops of time-lagged differential equations are a sufficient explanation for such cycles - in this case the delays are caused mainly by the breeding cycles of the species involved.

For example a reduction in population of a herbivore species because of predation, this makes the populations of predators of that species decline, the reduced level of predation allows the herbivore population to increase, this allows the predator population to increase, etc. Closed loops of time-lagged differential equations are a sufficient explanation for such cycles - in this case the delays are caused mainly by the breeding cycles of the species involved.

例如,食草动物种群由于被捕食而减少,这导致食肉动物种群也随之减少,而食肉动物种群减少又使得食草动物种群增加,这又使得食肉动物种群增加,等等。时滞微分方程的闭环能够充分解释这种循环——在这种情况下,延迟主要是由有关物种的繁殖循环造成的。

See also 另请参见

References 参考资料

  1. https://kknews.cc/news/j9em45l.html
  2. 2.0 2.1 2.2 Jenkins, Alejandro (2013). "Self-oscillation". Physics Reports. 525 (2): 167–222. arXiv:1109.6640. Bibcode:2013PhR...525..167J. doi:10.1016/j.physrep.2012.10.007.
  3. Maxwell, J. Clerk (1867). "On Governors". Proceedings of the Royal Society of London. 16: 270–283. JSTOR 112510.

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Category:Oscillators

类别: 振荡器

Category:Oscillation

类别: 震荡

Category:Amplifiers

类别: 放大器

Category:Systems theory

范畴: 系统论

Category:Dynamical systems

类别: 动力系统

Category:Nonlinear systems

类别: 非线性系统

Category:Mechanical vibrations

类别: 机械振动

Category:Concepts in physics

分类: 物理概念

Category:Ordinary differential equations

类别: 常微分方程

Category:Feedback

分类: 反馈


This page was moved from wikipedia:en:Self-oscillation. Its edit history can be viewed at 自振荡/edithistory