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First Peak Overshoot Calculator

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Second Order System Fundamental Parameters

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

+10%

-10%

✖Peak Overshoot is a straight way difference between the magnitude of the highest peak of time response and the magnitude of its steady state.ⓘ First Peak Overshoot [M_o]

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First Peak Overshoot Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Peak Overshoot - Peak Overshoot is a straight way difference between the magnitude of the highest peak of time response and the magnitude of its steady state.
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

M_o = e^(-(pi*ζ)/(sqrt(1-ζ^2))) --> e^(-(pi*0.1)/(sqrt(1-0.1^2)))

Evaluating ... ...

M_o = 0.729247614287671

STEP 3: Convert Result to Output's Unit

0.729247614287671 --> No Conversion Required

FINAL ANSWER

0.729247614287671 ≈ 0.729248 <-- Peak Overshoot

(Calculation completed in 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Second Order System Calculators

Bandwidth Frequency given Damping Ratio

LaTeX 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

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

First Peak Overshoot

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

Delay Time

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

< Second Order System Calculators

First Peak Overshoot

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

Rise Time given Damped Natural Frequency

LaTeX Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Delay Time

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

Peak Time

LaTeX Go Peak Time = pi/Damped Natural Frequency

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

LaTeX 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

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

First Peak Overshoot

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

Delay Time

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

First Peak Overshoot Formula

LaTeX Go

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

What does a high overshoot mean?

The definition of maximum overshoot is the maximum peak value when measuring a response curve of the desired response of a system

How to Calculate First Peak Overshoot?

First Peak Overshoot calculator uses Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2))) to calculate the Peak Overshoot, First Peak Overshoot is defined as the deviation of the response at peak time from the final value of response. It is the case when n is any odd integer. Peak Overshoot is denoted by M_o symbol.

How to calculate First Peak Overshoot using this online calculator? To use this online calculator for First Peak Overshoot, enter Damping Ratio (ζ) and hit the calculate button. Here is how the First Peak Overshoot calculation can be explained with given input values -> 0.729248 = e^(-(pi*0.1)/(sqrt(1-0.1^2))).

FAQ

What is First Peak Overshoot?

First Peak Overshoot is defined as the deviation of the response at peak time from the final value of response. It is the case when n is any odd integer and is represented as M_o = e^(-(pi*ζ)/(sqrt(1-ζ^2))) or Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2))). Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

How to calculate First Peak Overshoot?

First Peak Overshoot is defined as the deviation of the response at peak time from the final value of response. It is the case when n is any odd integer is calculated using Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2))). To calculate First Peak 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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