Percentage Overshoot Solution

STEP 0: Pre-Calculation Summary
Formula Used
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
PO = 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 - Squre root function, 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
PO = 100*(e^((-ζ*pi)/(sqrt(1-(ζ^2))))) --> 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2)))))
Evaluating ... ...
PO = 72.9247614287671
STEP 3: Convert Result to Output's Unit
72.9247614287671 --> No Conversion Required
FINAL ANSWER
72.9247614287671 <-- Percentage Overshoot
(Calculation completed in 00.002 seconds)

Credits

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Indian Institute of Technology,Roorlee (IITR), Roorkee
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10+ Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

Bandwidth Frequency given Damping Ratio

Formula
`"f"_{"b"} = "f"*((sqrt(1-(2*("ζ"^2))))+sqrt(("ζ"^4)-(4*("ζ"^2))+2))`

Example
`"54.96966Hz"="23Hz"*((sqrt(1-(2*("0.1"^2))))+sqrt(("0.1"^4)-(4*("0.1"^2))+2))`

Calculator
LaTeX
Go Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Angle of Asymptotes

Angle of Asymptotes

Formula
`"ϕ"_{"k"} = (((2*"K")+1)*pi)/("P"-"Z")`

Example
`"951.4286°"=(((2*"18")+1)*pi)/("13"-"6")`

Calculator
LaTeX
Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Damping Ratio or Damping Factor

Damping Ratio or Damping Factor

Formula
`"ζ" = "c"/(2*sqrt("M"*"K"_{"spring"}))`

Example
`"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))`

Calculator
LaTeX
Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-bandwidth Product

Gain-bandwidth Product

Formula
`"G.B" = "modulus"("A"_{"M"})*"BW"`

Example
`"56.16Hz"="modulus"("0.78")*"72b/s"`

Calculator
LaTeX
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid-band)*Amplifier Bandwidth
Damped Natural Frequency

Damped Natural Frequency

Formula
`"ω"_{"d"} = "f"*(sqrt(1-("ζ")^2))`

Example
`"22.88471Hz"="23Hz"*(sqrt(1-("0.1")^2))`

Calculator
LaTeX
Go Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak

Resonant Peak

Formula
`"M"_{"r"} = 1/((2*"ζ")*sqrt(1-("ζ")^2))`

Example
`"5.025189"=1/((2*"0.1")*sqrt(1-("0.1")^2))`

Calculator
LaTeX
Go Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency

Resonant Frequency

Formula
`"ω"_{"r"} = "f"*sqrt(1-2*("ζ")^2)`

Example
`"22.76884Hz"="23Hz"*sqrt(1-2*("0.1")^2)`

Calculator
LaTeX
Go Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Number of Asymptotes

Number of Asymptotes

Formula
`"N"_{"a"} = "P"-"Z"`

Example
`"7"="13"-"6"`

Calculator
LaTeX
Go Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System

Transfer Function for Closed and Open Loop System

Formula
`"G"_{"s"} = "C"_{"s"}/"R"_{"s"}`

Example
`"0.458333"="22"/"48"`

Calculator
LaTeX
Go Transfer Function = Output of System/Input of System
Closed-loop Gain

Closed-loop Gain

Formula
`"A"_{"f"} = 1/"β"`

Example
`"0.25"=1/"4"`

Calculator
LaTeX
Go Gain-with-feedback = 1/Feedback Factor

Percentage Overshoot Formula

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