Stability analysis using Simulink - Mini Project: Build & Apply

Stability analysis using Simulink

📖 Scenario: You are working as a control engineer. You want to check if a simple feedback control system is stable using Simulink. Stability means the system output settles to a steady value over time.

🎯 Goal: Build a Simulink model of a feedback control system, configure a gain parameter, run the simulation, and observe the output to analyze stability.

📋 What You'll Learn

Create a Simulink model with a transfer function block representing the system

Add a gain block to set the feedback gain

Connect blocks to form a feedback loop

Run the simulation and plot the system output

💡 Why This Matters

🌍 Real World

Control engineers use Simulink to design and test control systems before building physical devices.

💼 Career

Understanding stability analysis in Simulink is essential for roles in control system design, automation, and robotics.

1

Create the Simulink model with a transfer function

Open Simulink and create a new model. Add a Transfer Fcn block from the Continuous library. Set the numerator to [1] and denominator to [1 2 1] to represent the system. Name the block Plant.

Simulink

% Add a Transfer Fcn block named Plant with numerator [1] and denominator [1 2 1]
% Your code here

Hint

Use add_block to add the Transfer Fcn block and set_param to set numerator and denominator.

2

Add a gain block for feedback

Add a Gain block from the Math Operations library. Name it FeedbackGain. Set its gain value to 5.

Simulink

% Add a Gain block named FeedbackGain with gain 5
% Your code here

Hint

Use add_block and set_param to add and configure the Gain block.

3

Connect blocks to form feedback loop

Connect the output of Plant to the input of FeedbackGain. Then connect the output of FeedbackGain back to the negative input of a Sum block. Add a Step input block connected to the positive input of the Sum block. Connect the output of the Sum block to the input of Plant. Name the Sum block Sum.

Simulink

% Add Sum and Step blocks and connect all blocks to form feedback loop
% Your code here

Hint

Use add_block to add Sum and Step blocks. Use add_line to connect blocks in the feedback loop.

4

Run simulation and plot output

Run the simulation for 10 seconds using sim. Get the output signal from the Plant block. Plot the output signal versus time to observe if it settles, indicating stability.

Simulink

% Run simulation for 10 seconds and plot Plant output
% Your code here

Hint

Use set_param to set stop time, sim to run, and plot to visualize output.

Practice

1. What does stability analysis in Simulink primarily check for in a system?

easy

A. Whether the system output settles to a steady value over time

B. The color scheme of the Simulink blocks

C. The speed of the computer running Simulink

D. The number of blocks used in the model

Solution

1. Step 1: Understand stability concept

   Stability means the system output does not grow uncontrollably but settles to a steady value.

2. Step 2: Relate to Simulink analysis

   Simulink stability analysis checks if outputs stabilize after simulation with inputs like Step.

3. Final Answer:

   Whether the system output settles to a steady value over time -> Option A

4. Quick Check:

   Stability = output settles [OK]

Hint: Stability means output settles, not grows [OK]

Common Mistakes:

• Confusing stability with simulation speed
• Thinking stability depends on block colors
• Assuming stability is about model size

2. Which Simulink block is commonly used to provide a sudden change input for stability testing?

easy

A. Integrator

B. Gain

C. Scope

D. Step

Solution

1. Step 1: Identify input blocks for testing

   The Step block provides a sudden change from one value to another, ideal for testing system response.

2. Step 2: Confirm block purpose

   Integrator accumulates signals, Gain multiplies, Scope displays output; only Step creates sudden input change.

3. Final Answer:

   Step -> Option D

4. Quick Check:

   Step block = sudden input [OK]

Hint: Step block creates sudden input change [OK]

Common Mistakes:

• Using Scope as input block
• Confusing Integrator with input source
• Thinking Gain creates input changes

3. Given a Simulink model with a Step input and a Scope showing output, what does an output graph that grows without bound indicate?

medium

A. The simulation stopped early

B. The system is stable

C. The system is unstable

D. The Step input is not working

Solution

1. Step 1: Analyze output behavior

   If the output graph grows without bound, it means the system output is increasing endlessly over time.

2. Step 2: Interpret stability meaning

   A stable system output settles or stays bounded; unbounded growth means instability.

3. Final Answer:

   The system is unstable -> Option C

4. Quick Check:

   Unbounded output = unstable system [OK]

Hint: Output grows endlessly means unstable system [OK]

Common Mistakes:

• Assuming growing output means stable
• Thinking simulation error caused growth
• Confusing input failure with output behavior

4. You run a Simulink simulation for stability but the Scope shows a flat line at zero despite a Step input. What is the likely error?

medium

A. The Step block is not connected to the system input

B. The Scope block is missing

C. The simulation time is too long

D. The system is perfectly stable

Solution

1. Step 1: Check signal connections

   If the Scope shows zero output despite Step input, the input may not be connected to the system properly.

2. Step 2: Rule out other causes

   Scope presence is confirmed; simulation time too long would show output; perfect stability would not cause zero output if input changes.

3. Final Answer:

   The Step block is not connected to the system input -> Option A

4. Quick Check:

   No input connection = zero output [OK]

Hint: Check if Step input is connected to system [OK]

Common Mistakes:

• Assuming zero output means perfect stability
• Ignoring block connections
• Thinking simulation time affects output zero

5. You want to analyze the stability of a feedback control system in Simulink. Which combination of blocks and steps will best help you determine if the system is stable?

hard

A. Use only a Gain block and check its value without simulation

B. Use a Step input block, connect it to the system input, add a Scope to observe output, and simulate to see if output settles

C. Add multiple Scope blocks without any input and run simulation

D. Use a Constant block as input and ignore output behavior

Solution

1. Step 1: Set up input and output blocks

   Use a Step block to provide a sudden input change and a Scope block to observe system output over time.

2. Step 2: Run simulation and analyze output

   Simulate the model and check if the output settles to a steady value, indicating stability.

3. Step 3: Confirm feedback system setup

   Ensure feedback connections are correct to reflect real system behavior during simulation.

4. Final Answer:

   Use a Step input block, connect it to the system input, add a Scope to observe output, and simulate to see if output settles -> Option B

5. Quick Check:

   Step + Scope + simulate = check stability [OK]

Hint: Step input + Scope output + simulate to check stability [OK]

Common Mistakes:

• Ignoring input type and output observation
• Not simulating the model
• Using constant input without checking output