Step response analysis in Simulink

Introduction

Step response analysis helps us see how a system reacts when we suddenly change its input. It shows how the system moves from one state to another over time.

Checking how fast a temperature control system reaches the desired temperature after turning on.

Testing how a car's cruise control adjusts speed when you press the accelerator.

Seeing how a water tank level changes when you open a valve suddenly.

Evaluating how an electrical circuit responds when voltage is applied quickly.

Syntax

Simulink

step(sys)
step(sys, t)
[y, t] = step(sys)
stepplot(sys)

sys is the system model you want to analyze.

You can specify time t to see the response over a certain period.

Examples

Shows the step response of the system sys over default time.

Simulink

step(sys)

Plots the step response from 0 to 10 seconds in steps of 0.1 seconds.

Simulink

step(sys, 0:0.1:10)

Returns the output y and time t data of the step response for further analysis.

Simulink

[y, t] = step(sys)

Creates a detailed plot with grid and labels for the step response.

Simulink

stepplot(sys)

Sample Program

This code creates a simple second-order system and plots its step response from 0 to 5 seconds. You can see how the system output changes over time after a sudden input.

Simulink

s = tf('s');
sys = 1/(s^2 + 2*s + 2);
step(sys, 0:0.01:5);
title('Step Response of a Second-Order System');
grid on;

Important Notes

Step response shows how fast and stable a system reacts to sudden changes.

Look for overshoot, settling time, and steady-state value in the plot.

You can use step to get data and analyze it numerically.

Summary

Step response analysis helps understand system behavior after sudden input changes.

Use step function in Simulink or MATLAB to plot or get response data.

Check key features like speed, overshoot, and stability from the response plot.

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