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%
✖Number of poles is the number of finite open loop poles for constructing the root locus.ⓘ Number of poles [P]			+10% -10%
✖Number of zeros is the number of finite open loop zeros for construction of 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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Credits

Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Calculator and 1000+ more calculators!

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, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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- Number of poles is the number of finite open loop poles for constructing the root locus.
Number of zeros- Number of zeros is the number of finite open loop zeros for construction of root locus.

STEP 1: Convert Input(s) to Base Unit

Parameter for root locus: 20 --> No Conversion Required
Number of poles: 100 --> No Conversion Required
Number of zeros: 50 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ_k = ((2*k+1)*pi)/(P-Z) --> ((2*20+1)*pi)/(100-50)

Evaluating ... ...

ϕ_k = 2.57610597594363

STEP 3: Convert Result to Output's Unit

2.57610597594363 Radian -->147.600000000028 Degree (Check conversion here)

FINAL ANSWER

147.600000000028 Degree <-- Angle of Asymptotes

(Calculation completed in 00.002 seconds)

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< 2 Root locus Calculators

Angle of asymptotes

angle_of_asymptotes = ((2*Parameter for root locus+1)*pi)/(Number of poles-Number of zeros) Go

Number of Asymptotes

number_of_asymptotes = Number of poles-Number of zeros Go

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 do you mean by angle of asymptotes?

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 and 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) and Number of zeros (Z) and hit the calculate button. Here is how the Angle of asymptotes calculation can be explained with given input values -> 147.6 = ((2*20+1)*pi)/(100-50).

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, Number of poles is the number of finite open loop poles for constructing the root locus and Number of zeros is the number of finite open loop zeros for construction of 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) and Number of zeros (Z). With our tool, you need to enter the respective value for Parameter for root locus, Number of poles and Number of zeros and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angle of Asymptotes?

In this formula, Angle of Asymptotes uses Parameter for root locus, Number of poles and Number of zeros. We can use 2 other way(s) to calculate the same, which is/are as follows -

number_of_asymptotes = Number of poles-Number of zeros
angle_of_asymptotes = ((2*Parameter for root locus+1)*pi)/(Number of poles-Number of zeros)

Where is the Angle of asymptotes calculator used?

Among many, Angle of asymptotes calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}

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