Steady-state error analysis in Simulink - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is steady-state error in control systems?

Steady-state error is the difference between the desired output and the actual output of a system when it has settled and is no longer changing.

beginner

How does Simulink help in steady-state error analysis?

Simulink allows you to model control systems and simulate their response to inputs, making it easy to observe and measure steady-state error.

intermediate

What is the role of the system type in steady-state error?

System type, defined by the number of integrators in the open-loop transfer function, determines how well a system can eliminate steady-state error for different input types.

beginner

Which input types are commonly used to test steady-state error?

Common input types are step, ramp, and parabolic inputs, each testing the system's ability to track constant, linearly changing, and accelerating signals.

intermediate

How can you reduce steady-state error in a control system?

You can reduce steady-state error by increasing system type (adding integrators), tuning controller gains, or using feedback to improve accuracy.

What does steady-state error measure in a control system?

A Difference between desired and actual output after settling

B Time taken to reach maximum output

C Speed of the system response

D Initial output value

Steady-state error is the difference between the desired output and the actual output once the system has settled.

Which system type has zero steady-state error for a step input?

A Type 3

B Type 0

C Type 2

D Type 1

Type 1 systems have one integrator and can eliminate steady-state error for step inputs.

In Simulink, how do you observe steady-state error?

A By simulating the system and comparing output to input after settling

B By counting the number of blocks

C By measuring the system's speed

D By checking the initial output

Simulate the system and compare the output to the input after the response settles to find steady-state error.

Which input type tests a system's ability to track a linearly increasing signal?

A Step input

B Parabolic input

C Ramp input

D Sinusoidal input

Ramp input increases linearly over time, testing the system's tracking of linear changes.

What effect does adding an integrator have on steady-state error?

A Has no effect

B Reduces or eliminates steady-state error

C Increases steady-state error

D Slows down the system response

Adding an integrator increases system type and helps reduce or eliminate steady-state error.

Explain what steady-state error is and why it matters in control systems.

Think about the difference between what you want and what you get after the system settles.

Describe how you would use Simulink to analyze steady-state error for a step input.

Consider how to compare the system output to the input after the response stabilizes.

Practice

1. What does steady-state error in a Simulink control system represent?

easy

A. The initial delay before the system starts responding

B. The maximum output value during system response

C. The difference between the desired input and the actual output after the system settles

D. The time taken for the system to reach half of its final value

Solution

1. Step 1: Understand steady-state error meaning

   Steady-state error measures how close the system output is to the input after settling.

2. Step 2: Compare options with definition

   Only The difference between the desired input and the actual output after the system settles correctly describes this difference after settling.

3. Final Answer:

   The difference between the desired input and the actual output after the system settles -> Option C

4. Quick Check:

   Steady-state error = final input - final output [OK]

Hint: Steady-state error = input minus output after settling [OK]

Common Mistakes:

• Confusing steady-state error with response time
• Thinking it measures initial delay
• Mixing it with peak output value

2. Which Simulink block is commonly used to measure steady-state error in a control system?

easy

A. Gain block

B. Sum block

C. Scope block

D. Integrator block

Solution

1. Step 1: Identify block function

   The Sum block calculates the difference between signals, useful for error measurement.

2. Step 2: Match block to steady-state error

   Steady-state error is the difference between input and output, so Sum block is used.

3. Final Answer:

   Sum block -> Option B

4. Quick Check:

   Sum block calculates error difference [OK]

Hint: Use Sum block to find difference between signals [OK]

Common Mistakes:

• Choosing Scope block which only displays signals
• Selecting Gain block which scales signals
• Confusing Integrator block with error calculation

3. Given this MATLAB code snippet analyzing steady-state error in Simulink:

sys = tf([1], [1 3 2]);
y = step(sys, 10);
steady_error = abs(1 - y(end));
disp(steady_error);

What is the output of steady_error?

medium

A. 0.5

B. 1

C. 0

D. 2

Solution

1. Step 1: Analyze transfer function and step response

   The transfer function G(s) = 1/(s^2 + 3s + 2) has DC gain G(0) = 1/2 = 0.5. Poles at -1 and -2 ensure stability, step response settles at 0.5.

2. Step 2: Calculate steady-state error

   Steady-state error = abs(1 - final output) = |1 - 0.5| = 0.5.

3. Final Answer:

   0.5 -> Option A

4. Quick Check:

   DC gain = 1/2, error = |1 - 0.5| = 0.5 [OK]

Hint: Step response final value = DC gain for unit step [OK]

Common Mistakes:

• Miscalculating DC gain as 1 instead of 1/2
• Confusing transient response with steady-state
• Thinking all stable systems have zero steady-state error

4. You have this Simulink model code snippet to calculate steady-state error:

sys = tf([2], [1 2 1]);
y = step(sys, 10);
steady_error = 1 - y(end);

Why might this code give a wrong steady-state error value?

medium

A. Because the variable y is not defined

B. Because the step function is called with wrong time

C. Because the transfer function numerator is incorrect

D. Because it does not take the absolute value of the error

Solution

1. Step 1: Check error calculation formula

   The code calculates error as 1 - y(end) without absolute value, which can be negative.

2. Step 2: Understand steady-state error definition

   Steady-state error should be absolute difference to represent magnitude correctly.

3. Final Answer:

   Because it does not take the absolute value of the error -> Option D

4. Quick Check:

   Error magnitude needs absolute value [OK]

Hint: Always use absolute value for steady-state error [OK]

Common Mistakes:

• Ignoring sign of error
• Assuming step time affects error calculation
• Misdefining transfer function numerator

5. In a Simulink model, you want to reduce steady-state error for a system with transfer function G(s) = 1/(s+1). Which modification will most effectively reduce steady-state error to a step input?

hard

A. Add an integrator in the forward path

B. Increase the gain of the existing transfer function

C. Add a differentiator in the feedback path

D. Add a delay block before the output

Solution

1. Step 1: Understand steady-state error for type 0 system

   G(s) = 1/(s+1) is type 0, which has nonzero steady-state error to step input.

2. Step 2: Effect of adding integrator

   Adding an integrator (1/s) increases system type to 1, eliminating steady-state error for step inputs.

3. Final Answer:

   Add an integrator in the forward path -> Option A

4. Quick Check:

   Integrator reduces steady-state error to zero for step input [OK]

Hint: Add integrator to eliminate steady-state error for step input [OK]

Common Mistakes:

• Thinking gain increase alone removes steady-state error
• Confusing differentiator effect with error reduction
• Adding delay which does not affect steady-state error