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Self-exciting oscillation is a phenomenon in many fields, including engineering, economics and biology. The theory of it has been founded by Aleksandr Andronov.
- 1 Mathematical basis
- 2 Examples in engineering
- 3 Examples in other fields
Self-exciting oscillations are a logical consequence of systems which are described by a closed loop of time-lagged differential equations, i.e. where the change in variable x0 is a function of a variable x1 evaluated at an earlier point in the time evolution of the system, likewise the change in variable x1 is determined by an even earlier value of x2 and so on in this fashion before reaching xn the change of which is determined by the original x0 but at a much earlier time.
Examples in engineering
Railway and automotive wheels
Central heating thermostats
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.
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.
Steering of vehicles when course corrections are delayed
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.
SEIG (Self Excited Induction Generator)
If an asynchronous motor is connected to a capacitor and the shaft turns with above critical speed, an electric hunting occurs which appears as line voltage on the terminals and provides useful function. See Exciter, an open source generator that is built on this principle.
Examples in other fields
Population cycles in biology
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.