Setting time when tolerance is 5 percent Solution

STEP 0: Pre-Calculation Summary
Formula Used
Setting Time = 3/(Damping Ratio*Damped natural frequency)
ts = 3/(ζ*ωd)
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: 12 Hertz --> 12 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ts = 3/(ζ*ωd) --> 3/(0.1*12)
Evaluating ... ...
ts = 2.5
STEP 3: Convert Result to Output's Unit
2.5 Second --> No Conversion Required
FINAL ANSWER
2.5 Second <-- Setting Time
(Calculation completed in 00.007 seconds)

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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10+ Control Systems Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)) Go
Angle of asymptotes
Angle of Asymptotes = ((2*Parameter for Root Locus+1)*pi)/(Number of Poles-Number of Zeros) Go
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped natural frequency)/(sqrt(1-(Damping Ratio)^2))) Go
Damping ratio or Damping factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) Go
Number of oscillations
Number of Oscillations = (Setting Time*Damped natural frequency)/(2*pi) Go
Damped natural frequency
Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2)) Go
Resonant frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2) Go
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros Go
Delay time
Delay Time = (1+(0.7*Damping Ratio))/Frequency Go
Peak time
Peak Time = pi/Damped natural frequency Go

10+ Second Order Systems Calculators

Time response in overdamped case
Time response for second order system = 1-((e^(-(Overdamping ratio-(sqrt((Overdamping ratio^2)-1)))*(Frequency*Time Period of Oscillations))/(2*sqrt((Overdamping ratio^2)-1)*(Overdamping ratio-sqrt((Overdamping ratio^2)-1))))) Go
Time response of critically damped system
Time response for second order system = 1-e^(-(Frequency*Time Period of Oscillations))*(1+(Frequency*Time Period of Oscillations)) Go
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped natural frequency)/(sqrt(1-(Damping Ratio)^2))) Go
Time response in undamped case
Time response for second order system = 1-cos(Frequency*Time Period of Oscillations) Go
Number of oscillations
Number of Oscillations = (Setting Time*Damped natural frequency)/(2*pi) Go
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped natural frequency Go
Setting time when tolerance is 2 percent
Setting Time = 4/(Damping Ratio*Damped natural frequency) Go
Setting time when tolerance is 5 percent
Setting Time = 3/(Damping Ratio*Damped natural frequency) Go
Delay time
Delay Time = (1+(0.7*Damping Ratio))/Frequency Go
Peak time
Peak Time = pi/Damped natural frequency Go

Setting time when tolerance is 5 percent Formula

Setting Time = 3/(Damping Ratio*Damped natural frequency)
ts = 3/(ζ*ωd)

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 ts 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 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 -> 2.5 = 3/(0.1*12).

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 ts = 3/(ζ*ωd) 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 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 2 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)
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