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Angle of Asymptotes Calculator

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Fundamental Parameters Second Order System

✖The Number of Poles or the number of magnetic poles refers to the magnetic poles (NSNSNS……) that appear on the surface created by cutting the motor perpendicularly to the shaft.ⓘ Number of Poles [N]			+10% -10%
✖The Number of Zeroes is the number of finite open-loop zeros for the construction of the root locus.ⓘ Number of Zeroes [M]			+10% -10%

✖Angle of Asymptotes is the angle formed by asymptotes with the positive real axis.ⓘ Angle of Asymptotes [ϕ_k]

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Angle of Asymptotes Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
ϕ_k = ((2*(modulus(N-M)-1)+1)*pi)/(modulus(N-M))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Angle of Asymptotes - (Measured in Radian) - Angle of Asymptotes is the angle formed by asymptotes with the positive real axis.
Number of Poles - The Number of Poles or the number of magnetic poles refers to the magnetic poles (NSNSNS……) that appear on the surface created by cutting the motor perpendicularly to the shaft.
Number of Zeroes - The Number of Zeroes is the number of finite open-loop zeros for the construction of the root locus.

STEP 1: Convert Input(s) to Base Unit

Number of Poles: 13 --> No Conversion Required
Number of Zeroes: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ_k = ((2*(modulus(N-M)-1)+1)*pi)/(modulus(N-M)) --> ((2*(modulus(13-6)-1)+1)*pi)/(modulus(13-6))

Evaluating ... ...

ϕ_k = 5.83438635666676

STEP 3: Convert Result to Output's Unit

5.83438635666676 Radian --> No Conversion Required

FINAL ANSWER

5.83438635666676 ≈ 5.834386 Radian <-- Angle of Asymptotes

(Calculation completed in 00.020 seconds)

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< Fundamental Parameters Calculators

Angle of Asymptotes

LaTeX 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

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

Closed Loop Negative Feedback Gain

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

Closed Loop Gain

LaTeX Go Closed-Loop Gain = 1/Feedback Factor

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

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

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

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

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

< Modelling Parameters Calculators

Damping Ratio or Damping Factor

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

Damped Natural Frequency

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

Resonant Frequency

LaTeX Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

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

Angle of Asymptotes Formula

LaTeX Go

Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
ϕ_k = ((2*(modulus(N-M)-1)+1)*pi)/(modulus(N-M))

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*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes)) to calculate the Angle of Asymptotes, Angle of Asymptotes is defined as the angle at which an asymptote is oriented at from the positive real axis. It is usually calculated in radians but can be converted into degrees as well. 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 Number of Poles (N) & Number of Zeroes (M) and hit the calculate button. Here is how the Angle of Asymptotes calculation can be explained with given input values -> 5.834386 = ((2*(modulus(13-6)-1)+1)*pi)/(modulus(13-6)).

FAQ

What is Angle of Asymptotes?

Angle of Asymptotes is defined as the angle at which an asymptote is oriented at from the positive real axis. It is usually calculated in radians but can be converted into degrees as well and is represented as ϕ_k = ((2*(modulus(N-M)-1)+1)*pi)/(modulus(N-M)) or Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes)). The Number of Poles or the number of magnetic poles refers to the magnetic poles (NSNSNS……) that appear on the surface created by cutting the motor perpendicularly to the shaft & The Number of Zeroes 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 defined as the angle at which an asymptote is oriented at from the positive real axis. It is usually calculated in radians but can be converted into degrees as well is calculated using Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes)). To calculate Angle of Asymptotes, you need Number of Poles (N) & Number of Zeroes (M). With our tool, you need to enter the respective value for Number of Poles & Number of Zeroes 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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