## Steady State Error for Type 1 System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Steady State Error = Coefficient Value/Velocity error constant
ess = A/Kv
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.
Velocity error constant - Velocity 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
Velocity error constant: 31 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ess = A/Kv --> 2/31
Evaluating ... ...
ess = 0.0645161290322581
STEP 3: Convert Result to Output's Unit
0.0645161290322581 --> 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 1 System Formula

Steady State Error = Coefficient Value/Velocity error constant
ess = A/Kv

## What are the basic concepts of Routh Hurwitz criteria?

1. The Routh criteria do not provide the exact locations of the roots of the characteristic equation that lie on the right-half of the s-plane. It is because the system becomes unstable if any one of the root approaches towards the right-half of the s-plane.

2. It does not tell whether the roots are real or complex. The real roots are in the form of real numbers. The complex roots are represented with iota and includes the imaginary part.

3. It works for only a linear system.

4. It is valid if the characteristic equation is algebraic. It means that the criteria are not valid if any of the coefficients of the characteristic equation is exponential or complex.

## How to Calculate Steady State Error for Type 1 System?

Steady State Error for Type 1 System calculator uses Steady State Error = Coefficient Value/Velocity error constant to calculate the Steady State Error, Steady State error for Type 1 system means a System whose open loop transfer function has one pole at origin is called as Type 1 system. Steady State Error is denoted by ess symbol.

How to calculate Steady State Error for Type 1 System using this online calculator? To use this online calculator for Steady State Error for Type 1 System, enter Coefficient Value (A) & Velocity error constant (Kv) and hit the calculate button. Here is how the Steady State Error for Type 1 System calculation can be explained with given input values -> 0.064516 = 2/31.

### FAQ

What is Steady State Error for Type 1 System?
Steady State error for Type 1 system means a System whose open loop transfer function has one pole at origin is called as Type 1 system and is represented as ess = A/Kv or Steady State Error = Coefficient Value/Velocity error constant. Coefficient value will be used to calculate the system errors & Velocity 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 1 System?
Steady State error for Type 1 system means a System whose open loop transfer function has one pole at origin is called as Type 1 system is calculated using Steady State Error = Coefficient Value/Velocity error constant. To calculate Steady State Error for Type 1 System, you need Coefficient Value (A) & Velocity error constant (Kv). With our tool, you need to enter the respective value for Coefficient Value & Velocity 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 & Velocity 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/Acceleration error constant
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