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, 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
ϕk = (((2*K)+1)*pi)/(P-Z) --> (((2*18)+1)*pi)/(13-6)
Evaluating ... ...
ϕk = 16.6055611689746
STEP 3: Convert Result to Output's Unit
16.6055611689746 Radian -->951.42857142875 Degree (Check conversion here)
951.42857142875 Degree <-- Angle of Asymptotes
(Calculation completed in 00.000 seconds)
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< 16 Control Systems Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Angle of Asymptotes
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))
Damping Ratio or Damping Factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Damped Natural Frequency
Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Frequency
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

< 19 Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Damping Ratio given Percentage Overshoot
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt((pi^2)+ln(Percentage Overshoot/100)^2)
Angle of Asymptotes
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Percentage Overshoot
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive Feedback Gain
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
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
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-Bandwidth Product
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Damped Natural Frequency
Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Steady State Error for Type Zero System
Steady State Error = Coefficient Value/(1+Position Error Constant)
Steady State Error for Type 2 System
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System
Transfer Function = Output of System/Input of System
Damping Ratio
Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Gain with Feedback = 1/Feedback Factor
Q-Factor
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)
ϕk = (((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 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) & 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 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, 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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