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

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)
ϕk = ((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 ϕk 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 ϕk = ((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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