## First Peak Undershoot Solution

STEP 0: Pre-Calculation Summary
Formula Used
Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
Mu = 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
Mu = e^(-(2*ζ*pi)/(sqrt(1-ζ^2))) --> e^(-(2*0.1*pi)/(sqrt(1-0.1^2)))
Evaluating ... ...
Mu = 0.53180208294426
STEP 3: Convert Result to Output's Unit
0.53180208294426 --> No Conversion Required
0.53180208294426 0.531802 <-- Peak Undershoot
(Calculation completed in 00.004 seconds)
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## Credits

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Thapar institute of engineering and technology (TIET), Patiala
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## < 17 Second Order System Calculators

Time Response in Overdamped Case
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
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
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
Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Time Response in Undamped Case
Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
First Peak Undershoot
Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## < 16 Second Order System Calculators

Time Response in Overdamped Case
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
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)
Rise Time given Damping Ratio
Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Time Response in Undamped Case
Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
First Peak Undershoot
Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## < 25 Control System Design Calculators

Time Response in Overdamped Case
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
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
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
Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Percentage Overshoot
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Time Response in Undamped Case
Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
First Peak Undershoot
Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Gain-Bandwidth Product
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Steady State Error for Type Zero System
Steady State Error = Coefficient Value/(1+Position of Error Constant)
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Steady State Error for Type 2 System
Steady State Error = Coefficient Value/Acceleration Error Constant
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Steady State Error for Type 1 System
Steady State Error = Coefficient Value/Velocity Error Constant
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeroes
Peak Time
Peak Time = pi/Damped Natural Frequency
Q-Factor
Q Factor = 1/(2*Damping Ratio)
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## First Peak Undershoot Formula

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