Setting Time when Tolerance is 5 Percent Calculator

↳

Electronics

Chemical Engineering

Civil

Electrical

Electronics and Instrumentation

Materials Science

Mechanical

Production Engineering

⤿

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%
✖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%

✖Setting time is the time required for a response to become steady.ⓘ Setting Time when Tolerance is 5 Percent [t_s]

⎘ Copy

👎

Formula

✖

Setting Time when Tolerance is 5 Percent

Formula

`"t"_{"s"} = 3/("ζ"*"ω"_{"d"})`

Example

`"1.311189s"=3/("0.1"*"22.88Hz")`

Calculator

LaTeX

Reset

👍

Download Electronics Formula PDF PDF Image

Setting Time when Tolerance is 5 Percent Solution

STEP 0: Pre-Calculation Summary

Formula Used

Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
t_s = 3/(ζ*ω_d)
This formula uses 3 Variables

Variables Used

Setting Time - (Measured in Second) - Setting time is the time required for a response to become steady.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
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

Damping Ratio: 0.1 --> 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_s = 3/(ζ*ω_d) --> 3/(0.1*22.88)

Evaluating ... ...

t_s = 1.31118881118881

STEP 3: Convert Result to Output's Unit

1.31118881118881 Second --> No Conversion Required

FINAL ANSWER

1.31118881118881 ≈ 1.311189 Second <-- Setting Time

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electronics » Control System » Second Order System » Setting Time when Tolerance is 5 Percent

Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

Verified by Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Calculator and 1100+ 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

Setting Time when Tolerance is 5 Percent Formula

Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
t_s = 3/(ζ*ω_d)

What is setting time?

It is the time required for the response to reach the steady state and stay within the specified tolerance bands around the final value. In general, the tolerance bands are 2% and 5%. The settling time is denoted by ts.
The settling time for 5% tolerance band is -
ts=3/δωn

How to Calculate Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 Percent calculator uses Setting Time = 3/(Damping Ratio*Damped Natural Frequency) to calculate the Setting Time, Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value. Setting Time is denoted by t_s symbol.

How to calculate Setting Time when Tolerance is 5 Percent using this online calculator? To use this online calculator for Setting Time when Tolerance is 5 Percent, enter Damping Ratio (ζ) & Damped Natural Frequency (ω_d) and hit the calculate button. Here is how the Setting Time when Tolerance is 5 Percent calculation can be explained with given input values -> 1.311189 = 3/(0.1*22.88).

FAQ

What is Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value and is represented as t_s = 3/(ζ*ω_d) or Setting Time = 3/(Damping Ratio*Damped Natural Frequency). Damping Ratio in control system is defined as the ratio with which any signal gets decayed & 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 Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value is calculated using Setting Time = 3/(Damping Ratio*Damped Natural Frequency). To calculate Setting Time when Tolerance is 5 Percent, you need Damping Ratio (ζ) & Damped Natural Frequency (ω_d). With our tool, you need to enter the respective value for Damping Ratio & Damped Natural Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Setting Time?

In this formula, Setting Time uses Damping Ratio & Damped Natural Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search