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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
The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio by = () A general form is T s = − ln ( tolerance fraction × 1 − ζ 2 ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}}\times {\sqrt {1-\zeta ^{2}}})}{{\text ...
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.
The overshoot is the maximum swing above final value, and clearly increases with μ. Likewise, the undershoot is the minimum swing below final value, again increasing with μ. The settling time is the time for departures from final value to sink below some specified level, say 10% of final value.
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 Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
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In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, [citation needed] a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs ...