Percentage Overshoot Solution

STEP 0: Pre-Calculation Summary
Formula Used
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
%o = 100*(e^((-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
Percentage Overshoot - Percentage Overshoot refers to an output exceeding its final, steady-state value.
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
%o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2))))) --> 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2)))))
Evaluating ... ...
%o = 72.9247614287671
STEP 3: Convert Result to Output's Unit
72.9247614287671 --> No Conversion Required
FINAL ANSWER
72.9247614287671 72.92476 <-- Percentage Overshoot
(Calculation completed in 00.004 seconds)

Credits

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Indian Institute of Technology,Roorlee (IITR), Roorkee
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19 Fundamental Parameters Calculators

Angle of Asymptotes
Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
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))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive Feedback Gain
Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))
Closed Loop Negative Feedback Gain
Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
Damping Ratio or Damping Factor
Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
Go Damped Natural Frequency = Natural Frequency of Oscillation*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)
Resonant Peak
Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Transfer Function for Closed and Open Loop System
Go Transfer Function = Output of System/Input of System
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Go Closed-Loop Gain = 1/Feedback Factor
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

25 Control System Design 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))
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

12 Modelling Parameters Calculators

Angle of Asymptotes
Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
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))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Damping Ratio or Damping Factor
Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
Go Damped Natural Frequency = Natural Frequency of Oscillation*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)
Resonant Peak
Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

Percentage Overshoot Formula

Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
%o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2)))))

What is the significance of measuring peak overshoot?

In control theory, signal processing, mathematics, and electronics, overshoot is the manifestation of a function or signal that exceeds its target. It occurs primarily in bandlimited systems, for example, low-pass filters during the step response.

How to Calculate Percentage Overshoot?

Percentage Overshoot calculator uses Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))) to calculate the Percentage Overshoot, Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system. Percentage Overshoot is denoted by %o symbol.

How to calculate Percentage Overshoot using this online calculator? To use this online calculator for Percentage Overshoot, enter Damping Ratio (ζ) and hit the calculate button. Here is how the Percentage Overshoot calculation can be explained with given input values -> 72.92476 = 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2))))).

FAQ

What is Percentage Overshoot?
Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system and is represented as %o = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2))))) or Percentage Overshoot = 100*(e^((-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 Percentage Overshoot?
Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system is calculated using Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))). To calculate Percentage Overshoot, 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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