Steady State Error for Type Zero 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%
✖Position of error constant is a measure of the steady-state error of the system when the input is unit step function.ⓘ Position of Error Constant [K_p]			+10% -10%

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

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Formula

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Steady State Error for Type Zero System

Formula

`"e"_{"ss"} = "A"/(1+"K"_{"p"})`

Example

`"0.060606"="2"/(1+"32")`

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Steady State Error for Type Zero System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Steady State Error = Coefficient Value/(1+Position of Error Constant)
e_ss = A/(1+K_p)
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.
Position of Error Constant - Position of error constant is a measure of the steady-state error of the system when the input is unit step function.

STEP 1: Convert Input(s) to Base Unit

Coefficient Value: 2 --> No Conversion Required
Position of Error Constant: 32 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_ss = A/(1+K_p) --> 2/(1+32)

Evaluating ... ...

e_ss = 0.0606060606060606

STEP 3: Convert Result to Output's Unit

0.0606060606060606 --> No Conversion Required

FINAL ANSWER

0.0606060606060606 ≈ 0.060606 <-- 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 Positive 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 Negative 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 Zero System Formula

Steady State Error = Coefficient Value/(1+Position of Error Constant)
e_ss = A/(1+K_p)

What is steady state error?

Steady-state error is defined as the difference between the desired value and the actual value of a system output in the limit as time goes to infinity (i.e. when the response of the control system has reached steady-state).

How to Calculate Steady State Error for Type Zero System?

Steady State Error for Type Zero System calculator uses Steady State Error = Coefficient Value/(1+Position of Error Constant) to calculate the Steady State Error, Steady State error for Type Zero system means a System whose open loop transfer function has no pole at origin is called as Type 0 system. Steady State Error is denoted by e_ss symbol.

How to calculate Steady State Error for Type Zero System using this online calculator? To use this online calculator for Steady State Error for Type Zero System, enter Coefficient Value (A) & Position of Error Constant (K_p) and hit the calculate button. Here is how the Steady State Error for Type Zero System calculation can be explained with given input values -> 0.060606 = 2/(1+32).

FAQ

What is Steady State Error for Type Zero System?

Steady State error for Type Zero system means a System whose open loop transfer function has no pole at origin is called as Type 0 system and is represented as e_ss = A/(1+K_p) or Steady State Error = Coefficient Value/(1+Position of Error Constant). Coefficient value will be used to calculate the system errors & Position of error constant is a measure of the steady-state error of the system when the input is unit step function.

How to calculate Steady State Error for Type Zero System?

Steady State error for Type Zero system means a System whose open loop transfer function has no pole at origin is called as Type 0 system is calculated using Steady State Error = Coefficient Value/(1+Position of Error Constant). To calculate Steady State Error for Type Zero System, you need Coefficient Value (A) & Position of Error Constant (K_p). With our tool, you need to enter the respective value for Coefficient Value & Position of 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 & Position of Error Constant. We can use 6 other way(s) to calculate the same, which is/are as follows -

Steady State Error = Coefficient Value/Velocity Error Constant
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error = Coefficient Value/Velocity Error Constant
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error = Coefficient Value/Velocity Error Constant
Steady State Error = Coefficient Value/Acceleration Error Constant

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