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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
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.
Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations, for example, in the case of a mass-spring-damper system we know that ¨ = ˙ (). Even assuming that a "complete" model is used in designing the controller, all the parameters ...
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]
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
Berry, Michael V. (1995), "The Riemann–Siegel expansion for the zeta function: high orders and remainders", Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences , 450 (1939): 439–462, doi : 10.1098/rspa.1995.0093 , ISSN 0962-8444 , MR 1349513 , Zbl 0842.11030
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The equation relates values of the Riemann zeta function at the points s and 1 − s, in particular relating even positive integers with odd negative integers. Owing to the zeros of the sine function, the functional equation implies that ζ ( s ) has a simple zero at each even negative integer s = −2 n , known as the trivial zeros of ζ ( s ) .