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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]
MATLAB function for computing settling time, rise time, and other step response characteristics; Settling Time Calculator This page was last ...
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."
Figure 3: Step-response of a linear two-pole feedback amplifier; time is in units of 1/ρ, that is, in terms of the time constants of A OL; curves are plotted for three values of mu = μ, which is controlled by β. Figure 3 shows the time response to a unit step input for three values of the parameter μ.
Two examples show the spectra of linear chirps with finite rise-times. The first is for a chirp with time-bandwidth of 250, where the rise and fall times are 4% of the total pulse duration and the second is for a chirp with time-bandwidth of 25, where the rise and fall times are 10% of the total.
These equations show that a series RL circuit has a time constant, usually denoted τ = L / R being the time it takes the voltage across the component to either fall (across the inductor) or rise (across the resistor) to within 1 / e of its final value. That is, τ is the time it takes V L to reach V( 1 / e ) and V R to ...
Graphs of dynamic amplification factors vs non-dimensional rise time (t r /T) exist for standard loading functions (for an explanation of rise time, see time history analysis below). Hence the DAF for a given loading can be read from the graph, the static deflection can be easily calculated for simple structures and the dynamic deflection found.
Given the control plant, desired specifications can be achieved using compensators. I, P, PI, PD, and PID, are optimizing controllers which are used to improve system parameters (such as reducing steady state error, reducing resonant peak, improving system response by reducing rise time). All these operations can be done by compensators as well ...