Stability analysis using Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Stability Criteria in Simulink

Which of the following best describes the primary method Simulink uses to analyze system stability?

A Simulink uses symbolic algebra to solve characteristic equations analytically.

B Simulink applies frequency-domain Bode plots directly to the block diagram without simulation.

C Simulink uses time-domain simulation to observe if system outputs settle to a steady value.

D Simulink automatically linearizes the system and checks eigenvalues without simulation.

💡 Hint

Think about how Simulink simulates system behavior over time to check stability.

Simulink primarily uses time-domain simulations to observe if the system output settles or diverges, indicating stability or instability.

❓ Predict Output

intermediate

Output of a Step Response Simulation

Given a Simulink model of a system with transfer function H(s) = 1/(s+2), what is the expected steady-state output value after a unit step input?

A 0.5

B 1

C 2

D 0

💡 Hint

Use the final value theorem or steady-state gain of the transfer function.

The steady-state output for a unit step input is the DC gain of the system: H(0) = 1/2 = 0.5.

❓ data_output

advanced

Eigenvalues from Linearized Simulink Model

You linearize a Simulink model at an operating point and obtain the state-space matrix A. Which option correctly shows the eigenvalues of matrix A?

Matrix A = [[-1, 2], [-3, 4]]

A Eigenvalues are approximately 1.5 ± 2.69i

B Eigenvalues are approximately 0 and 3

C Eigenvalues are approximately -1.0 and 4.0

D Eigenvalues are approximately 1.0 and 2.0

💡 Hint

Calculate eigenvalues by solving det(A - λI) = 0.

The eigenvalues of A are approximately 1.5 ± 2.69i (complex conjugates), indicating oscillatory behavior.

❓ visualization

advanced

Interpreting a Root Locus Plot from Simulink Linear Analysis

Given a root locus plot generated from a Simulink linearized model, which statement correctly describes system stability as gain increases?

A Root locus plot does not provide information about stability changes.

B System remains stable for all gains since poles stay in the left half-plane.

C System is unstable at zero gain but stabilizes as gain increases.

D System becomes unstable when poles cross into the right half-plane as gain increases.

💡 Hint

Recall that poles in the right half-plane indicate instability.

Root locus shows how poles move with gain; crossing into right half-plane means instability.

🔧 Debug

expert

Diagnosing Simulation Divergence in Stability Analysis

A Simulink model simulation diverges with outputs growing without bound. Which is the most likely cause?

A The simulation step size is too small causing numerical overflow.

B The system has at least one pole with positive real part causing instability.

C The input signal is zero leading to no system response.

D The model uses a discrete solver for a continuous system which always stabilizes.

💡 Hint

Think about what causes outputs to grow indefinitely in a dynamic system.

Positive real part poles cause exponential growth, leading to simulation divergence.

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