Steady-state error analysis in Simulink - Mini Project: Build & Apply

Steady-state error analysis

📖 Scenario: You are working as a control systems engineer. You want to analyze how well a control system performs by checking its steady-state error. This error tells you how close the system output gets to the desired input after a long time.In this project, you will create a simple Simulink model of a control system, set up parameters, run the simulation, and then calculate the steady-state error from the simulation results.

🎯 Goal: Build a Simulink model with a step input and a unity feedback control system. Configure the simulation parameters. Run the simulation and calculate the steady-state error by comparing the final output value to the input value.

📋 What You'll Learn

Create a Simulink model with a Step block as input

Add a Transfer Function block representing the system

Add a Sum block to create unity feedback

Configure simulation stop time

Run the simulation and extract output data

Calculate steady-state error as the difference between input and output at the end

💡 Why This Matters

🌍 Real World

Control engineers use steady-state error analysis to ensure systems like robots, vehicles, or industrial machines perform accurately and reliably.

💼 Career

Understanding steady-state error and how to simulate it in Simulink is essential for roles in control system design, automation, and testing.

1

Create the Simulink model with Step input and Transfer Function

Open Simulink and create a new model. Add a Step block and a Transfer Function block. Connect the output of the Step block to the input of the Transfer Function block. Set the Step block's Step time to 0, Initial value to 0, and Final value to 1. Set the Transfer Function block's numerator to [1] and denominator to [1 2 1].

Simulink

% Create a new Simulink model with Step and Transfer Function blocks connected
% Set Step block parameters: Step time=0, Initial value=0, Final value=1
% Set Transfer Function numerator=[1], denominator=[1 2 1]

Hint

Use add_block to add blocks and set_param to set their parameters. Connect blocks with add_line.

2

Add unity feedback using Sum block and connect output

Add a Sum block to the model. Connect the output of the Transfer Function block to the positive input of the Sum block. Connect the output of the Sum block to a Scope block to visualize the error. Connect the output of the Sum block back to the negative input of the Sum block to create unity feedback.

Simulink

% Add Sum block and Scope block
% Connect Transfer Function output to Sum positive input
% Connect Sum output to Scope
% Connect Sum negative input to Sum output for unity feedback
# Your code here

Hint

Use add_block to add Sum and Scope blocks. Set Sum block inputs to '+-'. Connect lines carefully to create feedback.

3

Configure simulation stop time and run simulation

Set the simulation stop time to 10 seconds. Run the simulation using sim command and save the output to a variable called simOut. Use the model name 'steady_state_error_model' in the sim command.

Simulink

% Set simulation stop time to 10 seconds
% Run simulation and save output to simOut
# Your code here

Hint

Use set_param to set the stop time. Use sim with the model name to run the simulation and save output.

4

Calculate and display the steady-state error

Extract the simulation output data from simOut. Calculate the steady-state error as the difference between the final input value (which is 1) and the final output value of the system. Print the steady-state error using disp with the message 'Steady-state error: ' followed by the error value.

Simulink

% Extract output data from simOut
% Calculate steady-state error as 1 minus final output value
% Display steady-state error
# Your code here

Hint

Use simOut.get('yout') to get output data. The final output value is the last element of y.signals.values. Calculate error as 1 minus this value. Use disp to print.

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