## Steady State Error for Type 2 System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Steady State Error = Coefficient Value/Acceleration error constant
ess = A/Ka
This formula uses 3 Variables
Variables Used
Steady State Error - Steady State Error means a System whose open loop transfer function has no pole at origin.
Coefficient Value - Coefficient value will be used to calculate the system errors.
Acceleration error constant - Acceleration error constant:- A control system has steady state error constants for changes in position, velocity and acceleration, these constants are called as static error constants.
STEP 1: Convert Input(s) to Base Unit
Coefficient Value: 2 --> No Conversion Required
Acceleration error constant: 20 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ess = A/Ka --> 2/20
Evaluating ... ...
ess = 0.1
STEP 3: Convert Result to Output's Unit
0.1 --> No Conversion Required
(Calculation completed in 00.000 seconds)
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## < 10+ Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

## Bandwidth Frequency given Damping Ratio

Formula
"f"_{"b"} = "f"*((sqrt(1-(2*("ζ"^2))))+sqrt(("ζ"^4)-(4*("ζ"^2))+2))

Example
"54.96966Hz"="23Hz"*((sqrt(1-(2*("0.1"^2))))+sqrt(("0.1"^4)-(4*("0.1"^2))+2))

Calculator
LaTeX
Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Angle of Asymptotes

## Angle of Asymptotes

Formula
"ϕ"_{"k"} = (((2*"K")+1)*pi)/("P"-"Z")

Example
"951.4286°"=(((2*"18")+1)*pi)/("13"-"6")

Calculator
LaTeX
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Damping Ratio or Damping Factor

## Damping Ratio or Damping Factor

Formula
"ζ" = "c"/(2*sqrt("M"*"K"_{"spring"}))

Example
"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))

Calculator
LaTeX
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-bandwidth Product

## Gain-bandwidth Product

Formula
"G.B" = "modulus"("A"_{"M"})*"BW"

Example
"56.16Hz"="modulus"("0.78")*"72b/s"

Calculator
LaTeX
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid-band)*Amplifier Bandwidth
Damped Natural Frequency

## Damped Natural Frequency

Formula
"ω"_{"d"} = "f"*(sqrt(1-("ζ")^2))

Example
"22.88471Hz"="23Hz"*(sqrt(1-("0.1")^2))

Calculator
LaTeX
Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak

## Resonant Peak

Formula
"M"_{"r"} = 1/((2*"ζ")*sqrt(1-("ζ")^2))

Example
"5.025189"=1/((2*"0.1")*sqrt(1-("0.1")^2))

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

## Resonant Frequency

Formula
"ω"_{"r"} = "f"*sqrt(1-2*("ζ")^2)

Example
"22.76884Hz"="23Hz"*sqrt(1-2*("0.1")^2)

Calculator
LaTeX
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Number of Asymptotes

## Number of Asymptotes

Formula
"N"_{"a"} = "P"-"Z"

Example
"7"="13"-"6"

Calculator
LaTeX
Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System

## Transfer Function for Closed and Open Loop System

Formula
"G"_{"s"} = "C"_{"s"}/"R"_{"s"}

Example
"0.458333"="22"/"48"

Calculator
LaTeX
Transfer Function = Output of System/Input of System
Closed-loop Gain

## Closed-loop Gain

Formula
"A"_{"f"} = 1/"β"

Example
"0.25"=1/"4"

Calculator
LaTeX
Gain-with-feedback = 1/Feedback Factor

## Steady State Error for Type 2 System Formula

Steady State Error = Coefficient Value/Acceleration error constant
ess = A/Ka

## What is Transient Response?

t is a part of the time response that reaches 0 (zero) when the time becomes very large. In the graph analysis containing poles and zeroes, the poles lying on the left half of the s-plane gives the transient response. We can also say that it is a part of the response where output continuously increases or decreases. The transient response is also known as the temporary part of the response.

## How to Calculate Steady State Error for Type 2 System?

Steady State Error for Type 2 System calculator uses Steady State Error = Coefficient Value/Acceleration error constant to calculate the Steady State Error, Steady State error for Type 2 system means a System whose open loop transfer function has two pole at origin is called as Type 2 system. Steady State Error is denoted by ess symbol.

How to calculate Steady State Error for Type 2 System using this online calculator? To use this online calculator for Steady State Error for Type 2 System, enter Coefficient Value (A) & Acceleration error constant (Ka) and hit the calculate button. Here is how the Steady State Error for Type 2 System calculation can be explained with given input values -> 0.1 = 2/20.

### FAQ

What is Steady State Error for Type 2 System?
Steady State error for Type 2 system means a System whose open loop transfer function has two pole at origin is called as Type 2 system and is represented as ess = A/Ka or Steady State Error = Coefficient Value/Acceleration error constant. Coefficient value will be used to calculate the system errors & Acceleration error constant:- A control system has steady state error constants for changes in position, velocity and acceleration, these constants are called as static error constants.
How to calculate Steady State Error for Type 2 System?
Steady State error for Type 2 system means a System whose open loop transfer function has two pole at origin is called as Type 2 system is calculated using Steady State Error = Coefficient Value/Acceleration error constant. To calculate Steady State Error for Type 2 System, you need Coefficient Value (A) & Acceleration error constant (Ka). With our tool, you need to enter the respective value for Coefficient Value & Acceleration error constant 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 Steady State Error?
In this formula, Steady State Error uses Coefficient Value & Acceleration error constant. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Steady State Error = Coefficient Value/(1+Position error constant)
• Steady State Error = Coefficient Value/Velocity error constant Let Others Know