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  2. Overshoot (signal) - Wikipedia

    en.wikipedia.org/wiki/Overshoot_(signal)

    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. Also see the definition of overshoot in an electronics context.

  3. Damping - Wikipedia

    en.wikipedia.org/wiki/Damping

    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.

  4. Step response - Wikipedia

    en.wikipedia.org/wiki/Step_response

    As an example of this formula, if Δ = 1/e 4 = 1.8 %, the settling time condition is t S = 8 τ 2. In general, control of overshoot sets the time constant ratio, and settling time t S sets τ 2 . [ 5 ] [ 6 ] [ 7 ]

  5. Ackermann's formula - Wikipedia

    en.wikipedia.org/wiki/Ackermann's_Formula

    Ackermann's formula provides a direct way to calculate the necessary adjustments—specifically, the feedback gains—needed to move the system's poles to the target locations. This method, developed by Jürgen Ackermann , [ 2 ] is particularly useful for systems that don't change over time ( time-invariant systems ), allowing engineers to ...

  6. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.

  7. Riemann–von Mangoldt formula - Wikipedia

    en.wikipedia.org/wiki/Riemann–von_Mangoldt_formula

    In mathematics, the Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann zeta function. The formula states that the number N ( T ) of zeros of the zeta function with imaginary part greater than 0 and less than or equal to T satisfies

  8. Rise time - Wikipedia

    en.wikipedia.org/wiki/Rise_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]

  9. RLC circuit - Wikipedia

    en.wikipedia.org/wiki/RLC_circuit

    The poles of Y(s) are those values of s where Y(s) → ∞. By the quadratic formula, we find =. The poles of Y(s) are identical to the roots s 1 and s 2 of the characteristic polynomial of the differential equation in the section above.