Delay Time 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%
✖The natural frequency of oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.ⓘ Natural Frequency of Oscillation [ω_n]			+10% -10%

✖Delay Time is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.ⓘ Delay Time [t_d]

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Formula

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Delay Time

Formula

`"t"_{"d"} = (1+(0.7*"ζ"))/"ω"_{"n"}`

Example

`"0.046522s"=(1+(0.7*"0.1"))/"23Hz"`

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Delay Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
t_d = (1+(0.7*ζ))/ω_n
This formula uses 3 Variables

Variables Used

Delay Time - (Measured in Second) - Delay Time is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Natural Frequency of Oscillation - (Measured in Hertz) - The natural frequency of oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.

STEP 1: Convert Input(s) to Base Unit

Damping Ratio: 0.1 --> No Conversion Required
Natural Frequency of Oscillation: 23 Hertz --> 23 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_d = (1+(0.7*ζ))/ω_n --> (1+(0.7*0.1))/23

Evaluating ... ...

t_d = 0.0465217391304348

STEP 3: Convert Result to Output's Unit

0.0465217391304348 Second --> No Conversion Required

FINAL ANSWER

0.0465217391304348 ≈ 0.046522 Second <-- Delay Time

(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

Delay Time Formula

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

How do you measure delay time?

The delay time is obtained by measuring a phase difference ϑ between the signals at the input and output transducers of the delay line with frequencies under test. The delay time is more precisely obtained by measuring the ϑ at a constant frequency within the bandwidth of the delay line.

How to Calculate Delay Time?

Delay Time calculator uses Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation to calculate the Delay Time, Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp . Delay Time is denoted by t_d symbol.

How to calculate Delay Time using this online calculator? To use this online calculator for Delay Time, enter Damping Ratio (ζ) & Natural Frequency of Oscillation (ω_n) and hit the calculate button. Here is how the Delay Time calculation can be explained with given input values -> 0.046522 = (1+(0.7*0.1))/23.

FAQ

What is Delay Time?

Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp and is represented as t_d = (1+(0.7*ζ))/ω_n or Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation. Damping Ratio in control system is defined as the ratio with which any signal gets decayed & The natural frequency of oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.

How to calculate Delay Time?

Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp is calculated using Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation. To calculate Delay Time, you need Damping Ratio (ζ) & Natural Frequency of Oscillation (ω_n). With our tool, you need to enter the respective value for Damping Ratio & Natural Frequency of Oscillation 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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