Step response analysis in Simulink - Step-by-Step Execution

Concept Flow - Step response analysis

Start Simulation

↓

Apply Step Input

↓

System Responds

↓

Measure Output Over Time

↓

Plot Step Response

↓

Analyze Characteristics

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End

The process starts by applying a step input to the system, then measuring and plotting the output over time to analyze system behavior.

Execution Sample

Simulink

step(sys)
info = stepinfo(sys);
disp(info);

This code plots the step response of a system and calculates key response characteristics.

Execution Table

Step	Action	Input	Output	Result
1	Apply step input	Step from 0 to 1 at t=0	System starts at 0	Initial condition set
2	System response begins	Step input = 1	Output rises	Output increases towards steady state
3	Output approaches steady state	Step input = 1	Output near final value	Settling begins
4	Output settles	Step input = 1	Output stable at final value	Steady state reached
5	Calculate step info	Output data	Rise time, Settling time, Overshoot	Step response characteristics computed
6	Display results	Step info	Printed characteristics	Analysis complete

💡 Step response fully analyzed after output settles and characteristics are computed

Variable Tracker

Variable	Start	After Step Input	During Response	At Steady State	Final
Input	0	1	1	1	1
Output	0	0	Rising	Near 1	1
Time	0	0+	Increasing	Stable	End

Key Moments - 3 Insights

Why does the output not jump instantly to the step input value?

Because the system has dynamics like inertia or delay, the output changes gradually as shown in rows 2 and 3 of the execution table.

What does settling time mean in the step response?

Settling time is when the output stays within a small range around the final value, as shown in row 4 where output stabilizes.

Why do we calculate step response characteristics?

To understand system behavior like speed and stability, which helps in design and control, as shown in rows 5 and 6.

Visual Quiz - 3 Questions

Look at the execution table, what is the output value at step 3?

A Output is rising towards steady state

B Output is zero

C Output is stable at final value

D Output is decreasing

💡 Hint

Check the 'Output' column at step 3 in the execution table.

At which step does the output reach steady state according to the execution table?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look for when the output is described as stable at final value.

If the system had no delay, how would the output change at step 2?

A Output would remain zero

B Output would jump instantly to 1

C Output would rise slowly

D Output would decrease

💡 Hint

Consider the 'Output' behavior at step 2 and how delay affects it.

Concept Snapshot

Step response analysis:
- Apply a step input to the system
- Measure output over time
- Plot output vs time
- Calculate characteristics: rise time, settling time, overshoot
- Use to understand system dynamics and stability

Full Transcript

Step response analysis involves applying a sudden change (step input) to a system and observing how the output changes over time. The system output starts at zero and rises gradually due to system dynamics until it reaches a steady value. Key characteristics like rise time and settling time are calculated to understand how quickly and stably the system responds. This process helps in designing and tuning control systems.

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