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Percentage Overshoot Calculator

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Fundamental Parameters Second Order System

✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio [ζ]

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-10%

✖Percentage Overshoot refers to an output exceeding its final, steady-state value.ⓘ Percentage Overshoot [%_o]

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Formula

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Percentage Overshoot

Formula

% o = 100 \cdot (e^{\frac{- ζ \cdot π}{\sqrt{1 - (ζ^{2})}}})

Example

72.92476 = 100 \cdot (e^{\frac{- 0.1 \cdot π}{\sqrt{1 - ({0.1}^{2})}}})

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Percentage Overshoot Solution

STEP 0: Pre-Calculation Summary

Formula Used

Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
%_o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2)))))
This formula uses 2 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Percentage Overshoot - Percentage Overshoot refers to an output exceeding its final, steady-state value.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

STEP 1: Convert Input(s) to Base Unit

Damping Ratio: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

%_o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2))))) --> 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2)))))

Evaluating ... ...

%_o = 72.9247614287671

STEP 3: Convert Result to Output's Unit

72.9247614287671 --> No Conversion Required

FINAL ANSWER

72.9247614287671 ≈ 72.92476 <-- Percentage Overshoot

(Calculation completed in 00.004 seconds)

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< Fundamental Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Closed Loop Negative Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Gain

Go Closed-Loop Gain = 1/Feedback Factor

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

< Modelling Parameters Calculators

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Percentage Overshoot Formula

Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
%_o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2)))))

What is the significance of measuring peak overshoot?

In control theory, signal processing, mathematics, and electronics, overshoot is the manifestation of a function or signal that exceeds its target. It occurs primarily in bandlimited systems, for example, low-pass filters during the step response.

How to Calculate Percentage Overshoot?

Percentage Overshoot calculator uses Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))) to calculate the Percentage Overshoot, Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system. Percentage Overshoot is denoted by %_o symbol.

How to calculate Percentage Overshoot using this online calculator? To use this online calculator for Percentage Overshoot, enter Damping Ratio (ζ) and hit the calculate button. Here is how the Percentage Overshoot calculation can be explained with given input values -> 72.92476 = 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2))))).

FAQ

What is Percentage Overshoot?

Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system and is represented as %_o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2))))) or Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))). Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

How to calculate Percentage Overshoot?

Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system is calculated using Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))). To calculate Percentage Overshoot, you need Damping Ratio (ζ). With our tool, you need to enter the respective value for Damping Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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