First Peak Undershoot 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 Undershoot is a straight way difference between the magnitude of the lowest peak of time response and the magnitude of its steady state.ⓘ First Peak Undershoot [M_u]

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Formula

✖

First Peak Undershoot

Formula

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

Example

`"0.531802"=e^(-(2*"0.1"*pi)/(sqrt(1-("0.1")^2)))`

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First Peak Undershoot Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Peak Undershoot - Peak Undershoot is a straight way difference between the magnitude of the lowest 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_u = e^(-(2*ζ*pi)/(sqrt(1-ζ^2))) --> e^(-(2*0.1*pi)/(sqrt(1-0.1^2)))

Evaluating ... ...

M_u = 0.53180208294426

STEP 3: Convert Result to Output's Unit

0.53180208294426 --> No Conversion Required

FINAL ANSWER

0.53180208294426 ≈ 0.531802 <-- Peak Undershoot

(Calculation completed in 00.004 seconds)

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Credits

Created by alokohri

Thapar institute of engineering and technology (TIET), Patiala

alokohri has created this Calculator and 2 more calculators!

Verified by Rachita C

BMS College Of Engineering (BMSCE), Banglore

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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 Undershoot Formula

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

What causes undershoot?

Undershoot occurs when the transient value of the system is lower than the steady state value of the system.

What is undershoot?

Undershoot is the amount by which a system's response to an abrupt change in input falls short of that desired.

How to Calculate First Peak Undershoot?

First Peak Undershoot calculator uses Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2))) to calculate the Peak Undershoot, The First Peak Undershoot formula is defined as maximum deviation less than the steady state value in the 2nd order system response when n is equal to 2. Peak Undershoot is denoted by M_u symbol.

How to calculate First Peak Undershoot using this online calculator? To use this online calculator for First Peak Undershoot, enter Damping Ratio (ζ) and hit the calculate button. Here is how the First Peak Undershoot calculation can be explained with given input values -> 0.531802 = e^(-(2*0.1*pi)/(sqrt(1-0.1^2))).

FAQ

What is First Peak Undershoot?

The First Peak Undershoot formula is defined as maximum deviation less than the steady state value in the 2nd order system response when n is equal to 2 and is represented as M_u = e^(-(2*ζ*pi)/(sqrt(1-ζ^2))) or Peak Undershoot = e^(-(2*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 First Peak Undershoot?

The First Peak Undershoot formula is defined as maximum deviation less than the steady state value in the 2nd order system response when n is equal to 2 is calculated using Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2))). To calculate First Peak Undershoot, 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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