Angle of Asymptotes Calculator

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✖Parameter for root locus is used to calculate the angle of asymptotes for the construction of the root nodes.ⓘ Parameter for Root Locus [K]			+10% -10%
✖The Number of Poles is the number of finite open-loop poles for constructing the root locus.ⓘ Number of Poles [P]			+10% -10%
✖The Number of Zeros is the number of finite open-loop zeros for the construction of the root locus.ⓘ Number of Zeros [Z]			+10% -10%

✖Angle of Asymptotes is the angle at which an asymptote is oriented at from the positive real axis.ⓘ Angle of Asymptotes [ϕ_k]

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Formula

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Angle of Asymptotes

Formula

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

Example

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

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Angle of Asymptotes Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
ϕ_k = (((2*K)+1)*pi)/(P-Z)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Angle of Asymptotes - (Measured in Radian) - Angle of Asymptotes is the angle at which an asymptote is oriented at from the positive real axis.
Parameter for Root Locus - Parameter for root locus is used to calculate the angle of asymptotes for the construction of the root nodes.
Number of Poles - The Number of Poles is the number of finite open-loop poles for constructing the root locus.
Number of Zeros - The Number of Zeros is the number of finite open-loop zeros for the construction of the root locus.

STEP 1: Convert Input(s) to Base Unit

Parameter for Root Locus: 18 --> No Conversion Required
Number of Poles: 13 --> No Conversion Required
Number of Zeros: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ_k = (((2*K)+1)*pi)/(P-Z) --> (((2*18)+1)*pi)/(13-6)

Evaluating ... ...

ϕ_k = 16.6055611689746

STEP 3: Convert Result to Output's Unit

16.6055611689746 Radian -->951.42857142875 Degree (Check conversion here)

FINAL ANSWER

951.42857142875 Degree <-- Angle of Asymptotes

(Calculation completed in 00.000 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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< 16 Control Systems Calculators

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))

Angle of Asymptotes

Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)

Maximum Overshoot

Go Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Damped Natural Frequency

Go Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))

Resonant Peak

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

Resonant Frequency

Go Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

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)

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeros

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Frequency

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 19 Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Frequency*(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)

Angle of Asymptotes

Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)

Percentage Overshoot

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

Closed Loop Positive Feedback Gain

Go Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Negative Feedback Gain

Go Closed-Loop Gain = 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))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Damped Natural Frequency

Go Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))

Resonant Peak

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

Resonant Frequency

Go Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position 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 Zeros

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Damping Ratio

Go Damping Ratio = Actual Damping/Critical Damping

Closed Loop Gain

Go Gain with Feedback = 1/Feedback Factor

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Angle of Asymptotes Formula

Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
ϕ_k = (((2*K)+1)*pi)/(P-Z)

What are asymptotes?

An asymptote of a curve is a line such that the distance between the curve and the line approaches to zero as one or both of the x or y co-ordinates tends to infinity. Asymptotes makes some angle with the real axis and this angle can be called the angle of asymptotes. In the expression to calculate the angle of asymptotes, k=0,1,2,3.....(P-Z-1).
Here, P=number of poles in root locus
Z= number of zeros in root locus

How to Calculate Angle of Asymptotes?

Angle of Asymptotes calculator uses Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros) to calculate the Angle of Asymptotes, Angle of Asymptotes is the angle at which an asymptote is oriented at from the positive real axis. Angle of Asymptotes is denoted by ϕ_k symbol.

How to calculate Angle of Asymptotes using this online calculator? To use this online calculator for Angle of Asymptotes, enter Parameter for Root Locus (K), Number of Poles (P) & Number of Zeros (Z) and hit the calculate button. Here is how the Angle of Asymptotes calculation can be explained with given input values -> 951.4286 = (((2*18)+1)*pi)/(13-6).

FAQ

What is Angle of Asymptotes?

Angle of Asymptotes is the angle at which an asymptote is oriented at from the positive real axis and is represented as ϕ_k = (((2*K)+1)*pi)/(P-Z) or Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros). Parameter for root locus is used to calculate the angle of asymptotes for the construction of the root nodes, The Number of Poles is the number of finite open-loop poles for constructing the root locus & The Number of Zeros is the number of finite open-loop zeros for the construction of the root locus.

How to calculate Angle of Asymptotes?

Angle of Asymptotes is the angle at which an asymptote is oriented at from the positive real axis is calculated using Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros). To calculate Angle of Asymptotes, you need Parameter for Root Locus (K), Number of Poles (P) & Number of Zeros (Z). With our tool, you need to enter the respective value for Parameter for Root Locus, Number of Poles & Number of Zeros 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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