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In control theory, overshoot refers to an output exceeding its final, steady-state value. [13] For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step response minus one.
In control theory, overshoot refers to an output exceeding its final, steady-state value. [2] For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step
However, the unitless damping factor (symbol ζ, zeta) is often a more useful measure, which is related to α by = . The special case of ζ = 1 is called critical damping and represents the case of a circuit that is just on the border of oscillation. It is the minimum damping that can be applied without causing oscillation.
How overshoot may be controlled by appropriate parameter choices is discussed next. Using the equations above, the amount of overshoot can be found by differentiating the step response and finding its maximum value. The result for maximum step response S max is: [3]
The process of determining the equations that govern the model's dynamics is called system identification. This can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its transfer function or matrix.
This equation can be solved exactly for any driving force, using the solutions z(t) that satisfy the unforced equation + + =, and which can be expressed as damped sinusoidal oscillations: z ( t ) = A e − ζ ω 0 t sin ( 1 − ζ 2 ω 0 t + φ ) , {\displaystyle z(t)=Ae^{-\zeta \omega _{0}t}\sin \left({\sqrt {1-\zeta ^{2}}}\omega _{0}t+ ...
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The logarithmic decrement can be obtained e.g. as ln(x 1 /x 3).Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain.. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.