Number 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%

✖The Number of Asymptotes is the number of root locus branches starting at finite open loop poles and ending at infinite open loop zeros.ⓘ Number of Asymptotes [N_a]

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Formula

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Number of Asymptotes

Formula

`"N"_{"a"} = "N"-"M"`

Example

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

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Number of Asymptotes Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Asymptotes = Number of Poles-Number of Zeroes
N_a = N-M
This formula uses 3 Variables

Variables Used

Number of Asymptotes - The Number of Asymptotes is the number of root locus branches starting at finite open loop poles and ending at infinite open loop zeros.
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

N_a = N-M --> 13-6

Evaluating ... ...

N_a = 7

STEP 3: Convert Result to Output's Unit

7 --> No Conversion Required

FINAL ANSWER

7 <-- Number of Asymptotes

(Calculation completed in 00.004 seconds)

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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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< 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 Negative 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 Positive 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)

Number of Asymptotes Formula

Number of Asymptotes = Number of Poles-Number of Zeroes
N_a = N-M

How many asymptotes can a function have?

A function can have at most two different horizontal asymptotes. A graph can approach a horizontal asymptote in many different ways; see Figure 8 in §1.6 of the text for graphical illustrations. In particular, a graph can, and often does, cross a horizontal asymptote.

How to Calculate Number of Asymptotes?

Number of Asymptotes calculator uses Number of Asymptotes = Number of Poles-Number of Zeroes to calculate the Number of Asymptotes, Number of Asymptotes is the number of root locus branches starting at finite open loop poles and ending at infinite open loop zeros. Number of Asymptotes is denoted by N_a symbol.

How to calculate Number of Asymptotes using this online calculator? To use this online calculator for Number of Asymptotes, enter Number of Poles (N) & Number of Zeroes (M) and hit the calculate button. Here is how the Number of Asymptotes calculation can be explained with given input values -> 7 = 13-6.

FAQ

What is Number of Asymptotes?

Number of Asymptotes is the number of root locus branches starting at finite open loop poles and ending at infinite open loop zeros and is represented as N_a = N-M or Number of Asymptotes = 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 Number of Asymptotes?

Number of Asymptotes is the number of root locus branches starting at finite open loop poles and ending at infinite open loop zeros is calculated using Number of Asymptotes = Number of Poles-Number of Zeroes. To calculate Number 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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