Steady State Error for Type 1 System Calculator

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Fundamental Parameters

Second Order System

✖Coefficient value will be used to calculate the system errors.ⓘ Coefficient Value [A]			+10% -10%
✖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.ⓘ Velocity Error Constant [K_v]			+10% -10%

✖Steady State Error means a System whose open loop transfer function has no pole at origin.ⓘ Steady State Error for Type 1 System [e_ss]

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Formula

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Steady State Error for Type 1 System

Formula

`"e"_{"ss"} = "A"/"K"_{"v"}`

Example

`"0.064516"="2"/"31"`

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Steady State Error for Type 1 System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Steady State Error = Coefficient Value/Velocity Error Constant
e_ss = A/K_v
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

e_ss = A/K_v --> 2/31

Evaluating ... ...

e_ss = 0.0645161290322581

STEP 3: Convert Result to Output's Unit

0.0645161290322581 --> No Conversion Required

FINAL ANSWER

0.0645161290322581 ≈ 0.064516 <-- Steady State Error

(Calculation completed in 00.004 seconds)

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Credits

Created by Jaffer Ahmad Khan

College Of Engineering, Pune (COEP), Pune

Jaffer Ahmad Khan has created this Calculator and 10+ more calculators!

Verified by Parminder Singh

Chandigarh University (CU), Punjab

Parminder Singh has verified this Calculator and 600+ more calculators!

< 19 Fundamental Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Damping Ratio given Percentage Overshoot

Go Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Closed Loop Negative Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Positive Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1-(Feedback Factor*Open Loop Gain of an OP-AMP))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Damping Ratio given Critical Damping

Go Damping Ratio = Actual Damping/Critical Damping

Closed Loop Gain

Go Closed-Loop Gain = 1/Feedback Factor

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

< 3 Steady State Error Calculators

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

< 25 Control System Design Calculators

Time Response in Overdamped Case

Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))

Time Response of Critically Damped System

Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

Steady State Error for Type 1 System Formula

Steady State Error = Coefficient Value/Velocity Error Constant
e_ss = A/K_v

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 e_ss 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 (K_v) 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 e_ss = A/K_v 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 (K_v). 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 6 other way(s) to calculate the same, which is/are as follows -

Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error = Coefficient Value/Acceleration Error Constant

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