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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Formula

✖

First Peak Overshoot

Formula

`"M"_{"o"} = e^(-(pi*"ζ")/(sqrt(1-"ζ"^2)))`

Example

`"0.729248"=e^(-(pi*"0.1")/(sqrt(1-("0.1")^2)))`

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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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Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

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< 17 Second Order System Calculators

Time Response in Overdamped Case

Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))

Time Response of Critically Damped System

Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)

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))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

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

Delay Time

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

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 16 Second Order System Calculators

Time Response in Overdamped Case

Time Response of Critically Damped System

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

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

Delay Time

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

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 25 Control System Design Calculators

Time Response in Overdamped Case

Time Response of Critically Damped System

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))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Percentage Overshoot

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

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

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

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

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

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Delay Time

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

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

First Peak Overshoot Formula

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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