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Tay, Mareels and Moore (1998) defined settling time as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value." [ 2 ] Mathematical detail
A circuit is designed to minimize rise time while containing distortion of the signal within acceptable limits. Overshoot represents a distortion of the signal. In circuit design, the goals of minimizing overshoot and of decreasing circuit rise time can conflict. The magnitude of overshoot depends on time through a phenomenon called "damping."
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
The settling time is the time for departures from final value to sink below some specified level, say 10% of final value. The dependence of settling time upon μ is not obvious, and the approximation of a two-pole system probably is not accurate enough to make any real-world conclusions about feedback dependence of settling time.
For applications in control theory, according to Levine (1996, p. 158), rise time is defined as "the time required for the response to rise from x% to y% of its final value", with 0% to 100% rise time common for underdamped second order systems, 5% to 95% for critically damped and 10% to 90% for overdamped ones. [6]
The dead time θ is the amount of time between when the step change occurred and when the output first changed. The time constant (τ p) is the amount of time it takes for the output to reach 63.2% of the new steady-state value after the step change. One downside to using this method is that it can take a while to reach a new steady-state value ...
= where is the relaxation time of the particle (the time constant in the exponential decay of the particle velocity due to drag), is the fluid velocity of the flow well away from the obstacle, and is the characteristic dimension of the obstacle (typically its diameter) or a characteristic length scale in the flow (like boundary layer thickness ...
The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. [2] [3]: 14