Self-oscillation

In linear systems, self-oscillation appears as an instability associated with a negative damping term, which causes small perturbations to grow exponentially in amplitude.

The study of self-oscillators dates back to the early 1830s, with the work of Robert Willis and George Biddell Airy on the mechanism by which the vocal cords produce the human voice.

[2] In the second edition of his treatise on The Theory of Sound, published in 1896, Lord Rayleigh considered various instances of mechanical and acoustic self-oscillations (which he called "maintained vibration") and offered a simple mathematical model for them.

[1] Interest in the subject of self-oscillation was also stimulated by the work of Heinrich Hertz, starting in 1887, in which he used a spark-gap transmitter to generate radio waves that he showed correspond to electrical oscillations with frequencies of hundreds of millions of cycles per second.

[3] The term "self-oscillation" (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.

[1] 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.

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.

Schematic representation of a self-oscillation as a positive feedback loop. The oscillator V produces a feedback signal B . The controller at R uses this signal to modulate the external power S that acts on the oscillator. If the power is modulated in phase with the oscillator's velocity, a negative damping is established and the oscillation grows until limited by nonlinearities.