Time of Peak Overshoot in Second Order System Calculator

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Second Order System

Fundamental Parameters

✖Kth value a sequence of numbers where each number is the sum of the k preceding numbers. Kth value of a formula to find different values of the formula.ⓘ Kth Value [k]			+10% -10%
✖Damped natural frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency.ⓘ Damped Natural Frequency [ω_d]			+10% -10%

✖Time of peak overshoot is the different value of time where peak overshoot occurs.ⓘ Time of Peak Overshoot in Second Order System [T_po]

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Formula

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Time of Peak Overshoot in Second Order System

Formula

`"T"_{"po"} = ((2*"k"-1)*pi)/"ω"_{"d"}`

Example

`"1.235766s"=((2*"5"-1)*pi)/"22.88Hz"`

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Time of Peak Overshoot in Second Order System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
T_po = ((2*k-1)*pi)/ω_d
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Time of Peak Overshoot - (Measured in Second) - Time of peak overshoot is the different value of time where peak overshoot occurs.
Kth Value - Kth value a sequence of numbers where each number is the sum of the k preceding numbers. Kth value of a formula to find different values of the formula.
Damped Natural Frequency - (Measured in Hertz) - Damped natural frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency.

STEP 1: Convert Input(s) to Base Unit

Kth Value: 5 --> No Conversion Required
Damped Natural Frequency: 22.88 Hertz --> 22.88 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_po = ((2*k-1)*pi)/ω_d --> ((2*5-1)*pi)/22.88

Evaluating ... ...

T_po = 1.23576634100997

STEP 3: Convert Result to Output's Unit

1.23576634100997 Second --> No Conversion Required

FINAL ANSWER

1.23576634100997 ≈ 1.235766 Second <-- Time of Peak Overshoot

(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 Parminder Singh

Chandigarh University (CU), Punjab

Parminder Singh has verified this Calculator and 600+ more calculators!

< 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

Time of Peak Overshoot in Second Order System Formula

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

What is overshoot?

overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters.

How to Calculate Time of Peak Overshoot in Second Order System?

Time of Peak Overshoot in Second Order System calculator uses Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency to calculate the Time of Peak Overshoot, The Time of Peak Overshoot in second order system formula is defined as the time instance where peak overshoot occurs in the response. Time of Peak Overshoot is denoted by T_po symbol.

How to calculate Time of Peak Overshoot in Second Order System using this online calculator? To use this online calculator for Time of Peak Overshoot in Second Order System, enter Kth Value (k) & Damped Natural Frequency (ω_d) and hit the calculate button. Here is how the Time of Peak Overshoot in Second Order System calculation can be explained with given input values -> 1.235766 = ((2*5-1)*pi)/22.88.

FAQ

What is Time of Peak Overshoot in Second Order System?

The Time of Peak Overshoot in second order system formula is defined as the time instance where peak overshoot occurs in the response and is represented as T_po = ((2*k-1)*pi)/ω_d or Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency. Kth value a sequence of numbers where each number is the sum of the k preceding numbers. Kth value of a formula to find different values of the formula & Damped natural frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency.

How to calculate Time of Peak Overshoot in Second Order System?

The Time of Peak Overshoot in second order system formula is defined as the time instance where peak overshoot occurs in the response is calculated using Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency. To calculate Time of Peak Overshoot in Second Order System, you need Kth Value (k) & Damped Natural Frequency (ω_d). With our tool, you need to enter the respective value for Kth Value & Damped Natural Frequency 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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