Step response analysis in Simulink - Mini Project: Build & Apply

Step Response Analysis

📖 Scenario: You are working as a control systems engineer. You want to analyze how a system responds to a sudden change in input, called a step input. This helps you understand the system's behavior over time.

🎯 Goal: Build a Simulink model to simulate the step response of a simple system and analyze its output.

📋 What You'll Learn

Create a Simulink model with a Step block and a Transfer Function block

Configure the Step block with a step time of 1 second

Set the Transfer Function block with numerator [1] and denominator [1 1]

Add a Scope block to visualize the output

Run the simulation and observe the step response

💡 Why This Matters

🌍 Real World

Step response analysis is used in engineering to understand how systems like motors, circuits, or mechanical parts react to sudden changes.

💼 Career

Control engineers and data scientists use step response to design and tune systems for stability and performance.

1

Create the basic Simulink model

Open Simulink and create a new model. Add a Step block, a Transfer Function block, and a Scope block to the model.

Simulink

% Add Step, Transfer Function, and Scope blocks to the model
% Your code here

Hint

Use the Simulink Library Browser to find the Step, Transfer Function, and Scope blocks and drag them into your model.

2

Configure the Step and Transfer Function blocks

Set the Step block's Step time parameter to 1. Set the Transfer Function block's numerator to [1] and denominator to [1 1].

Simulink

% Set Step block Step time to 1
% Set Transfer Function numerator to [1]
% Set Transfer Function denominator to [1 1]
% Your code here

Hint

Use the set_param function to set block parameters programmatically or configure them manually in the block dialog.

3

Run the simulation

Run the simulation of the model using the sim command with the model name 'model'. Store the simulation output in a variable called simOut.

Simulink

% Run the simulation and store output in simOut
% Your code here

Hint

Use the sim function with the model name as a string to run the simulation.

4

Display the step response output

Extract the output data from simOut and plot the step response using the plot function. Use simOut.tout for time and simOut.yout{1}.Values.Data for output data.

Simulink

% Plot the step response using simOut data
% Your code here

Hint

Use plot with time and output data arrays to visualize the step response.

Practice

1. What does the step function in Simulink primarily show about a system?

easy

A. The system's output response to a sudden input change

B. The frequency response of the system

C. The system's steady-state error only

D. The system's input signal over time

Solution

1. Step 1: Understand the purpose of the step function

   The step function simulates how a system reacts when a sudden input (step input) is applied.

2. Step 2: Identify what the output represents

   The output shows how the system's output changes over time after the step input, revealing speed and stability.

3. Final Answer:

   The system's output response to a sudden input change -> Option A

4. Quick Check:

   Step response = output after sudden input [OK]

Hint: Step function shows output after sudden input change [OK]

Common Mistakes:

• Confusing step response with frequency response
• Thinking it shows only steady-state error
• Assuming it plots input signal instead of output

2. Which of the following is the correct syntax to plot the step response of a transfer function sys in MATLAB?

easy

A. response.step(sys)

B. plotstep(sys)

C. sys.step()

D. step(sys)

Solution

1. Step 1: Recall MATLAB step response syntax

   The standard MATLAB command to plot step response is step(sys), where sys is the system model.

2. Step 2: Check other options for correctness

   Options B, C, and D are not valid MATLAB commands for step response plotting.

3. Final Answer:

   step(sys) -> Option D

4. Quick Check:

   Use step(sys) to plot response [OK]

Hint: Use step(sys) to plot step response in MATLAB [OK]

Common Mistakes:

• Using incorrect function names like plotstep
• Trying object method calls not supported
• Confusing syntax with other toolboxes

3. Given the following MATLAB code, what is the approximate settling time of the system's step response?

sys = tf([1], [1 3 2]);
info = stepinfo(sys);
settling_time = info.SettlingTime;

medium

A. About 2 seconds

B. About 1 second

C. About 3 seconds

D. About 4 seconds

Solution

1. Step 1: Analyze the transfer function

   The system has poles at -1 and -2, so it is stable and expected to settle quickly.

2. Step 2: Use stepinfo to find settling time

   The stepinfo function calculates settling time, which for this system is approximately 2 seconds.

3. Final Answer:

   About 2 seconds -> Option A

4. Quick Check:

   Settling time from stepinfo ≈ 2 sec [OK]

Hint: Use stepinfo(sys).SettlingTime for settling time [OK]

Common Mistakes:

• Confusing settling time with rise time
• Ignoring system poles location
• Assuming default values without calculation

4. Identify the error in the following MATLAB code for plotting step response:

sys = tf([1 2], [1 4 5]);
step(sys)
title('Step Response')
xlabel('Time')
ylabel('Output')

medium

A. Missing semicolon after tf definition

B. No error; code runs correctly

C. The transfer function numerator and denominator are reversed

D. Step function should be called as step_response(sys)

Solution

1. Step 1: Check transfer function syntax

   The numerator and denominator vectors are correctly placed in tf([1 2], [1 4 5]).

2. Step 2: Verify step function and plot commands

   The step(sys) command is correct, and titles and labels are properly set.

3. Final Answer:

   No error; code runs correctly -> Option B

4. Quick Check:

   Code syntax is correct and runs [OK]

Hint: Check tf and step syntax carefully [OK]

Common Mistakes:

• Thinking numerator and denominator are swapped
• Expecting semicolon is mandatory (optional)
• Using incorrect step function names

5. You want to compare the step responses of two systems sys1 = tf([1], [1 2 1]) and sys2 = tf([2], [1 3 2]). Which MATLAB code snippet correctly plots both responses on the same graph for comparison?

hard

A. step(sys1); step(sys2);

B. plot(step(sys1), step(sys2));

C. step([sys1 sys2]);

D. step(sys1 + sys2);

Solution

1. Step 1: Understand how to plot multiple step responses

   Using step([sys1 sys2]) plots both systems' step responses on the same figure for easy comparison.

2. Step 2: Evaluate other options

   step(sys1); step(sys2); overwrites the first plot without hold on; plot(step(sys1), step(sys2)); is invalid syntax; step(sys1 + sys2); plots sum system, not comparison.

3. Final Answer:

   step([sys1 sys2]) -> Option C

4. Quick Check:

   Use step([sys1 sys2]) for combined plot [OK]

Hint: Use step([sys1 sys2]) to plot both responses together [OK]

Common Mistakes:

• Trying to add systems instead of plotting separately
• Using plot() on step outputs incorrectly
• Forgetting hold on/off when plotting separately