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]

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✖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

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First Peak Undershoot

Formula

M u = e^{- \frac{2 \cdot ζ \cdot π}{\sqrt{1 - ζ^{2}}}}

Example

0.531802 = e^{- \frac{2 \cdot 0.1 \cdot π}{\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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Created by alokohri

Thapar institute of engineering and technology (TIET), Patiala

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BMS College Of Engineering (BMSCE), Banglore

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< 5 Second Order System 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)))

Number of Oscillations

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

Delay Time

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

< 5 Second Order System Calculators

First Peak Overshoot

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

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

Setting Time when Tolerance is 2 Percent

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

Peak Time

Go Peak Time = pi/Damped Natural Frequency

< 5 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)))

Number of Oscillations

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

Delay Time

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

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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