Step response analysis in Simulink - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a step response in system analysis?

A step response shows how a system reacts over time when a sudden change (step input) is applied. It helps us understand system behavior like speed and stability.

beginner

Why do we use step response analysis in Simulink?

We use step response analysis in Simulink to see how a model reacts to a sudden input change. It helps check if the system is stable and how fast it reaches a steady state.

intermediate

What key characteristics can we find from a step response plot?

From a step response plot, we find rise time, settling time, overshoot, and steady-state value. These tell us how quickly and smoothly the system reacts.

beginner

How do you set up a step input in Simulink for step response analysis?

In Simulink, use the Step block to create a sudden change input. Connect it to your system model, then run the simulation to see the output response over time.

intermediate

What does overshoot in a step response indicate?

Overshoot means the output goes above the final steady value before settling down. It shows how much the system temporarily exceeds the target after the step input.

What does a step response show in system analysis?

A The system's power consumption

B How the system reacts to a sudden input change

C The system's noise level

D The system's frequency response

A step response shows how the system output changes over time after a sudden input change.

Which Simulink block is used to create a step input?

A Pulse Generator block

B Sine Wave block

C Constant block

D Step block

The Step block creates a sudden change input for step response analysis.

What does 'overshoot' mean in a step response?

A Output exceeds the final value temporarily

B Output stays constant

C Output goes below zero

D Output never reaches steady state

Overshoot means the output temporarily goes above the final steady value.

Which characteristic tells how fast the system output reaches near the final value?

A Rise time

B Overshoot

C Settling time

D Steady-state error

Settling time is how long the output takes to stay close to the final value.

Why is step response analysis important?

A To check system stability and speed

B To measure system color

C To calculate system weight

D To find system cost

Step response helps us understand if the system is stable and how quickly it reacts.

Explain what a step response is and why it is useful in analyzing systems.

Think about how a system reacts when you suddenly turn something on.

Describe how you would perform a step response analysis in Simulink.

Imagine setting up a test to see how fast a machine reacts when switched on.

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