Stability analysis using Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a transfer function block in Simulink.

Simulink

sys = tf([1], [1 3 2]);

Drag options to blanks, or click blank then click option'

A[1 5 6]

B[1]

C[2 4 1]

D[3 2 1]

Attempts:

3 left

💡 Hint

Common Mistakes

Using denominator coefficients instead of numerator.

Mixing up the order of coefficients.

The transfer function numerator is set to [1] to define the system.

2fill in blank

medium

Complete the code to plot the step response of the system.

Simulink

step([1]);

Drag options to blanks, or click blank then click option'

Asys_response

Bresponse

Csys

Dsystem

Attempts:

3 left

💡 Hint

Common Mistakes

Using undefined variables like 'sys_response'.

Passing strings instead of system objects.

The step function requires the system variable 'sys' to plot its response.

3fill in blank

hard

Fix the error in the code to compute the poles of the system.

Simulink

poles = [1](sys);

Drag options to blanks, or click blank then click option'

Aeig

Broots

Cpoles

Dpole

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'roots' which works on polynomials but not transfer functions.

Using 'eig' which is for matrices, not transfer functions.

The correct function to find poles of a transfer function in MATLAB is 'pole'.

4fill in blank

hard

Fill both blanks to create a Bode plot and set the frequency range.

Simulink

bode(sys, [1]); xlim([2]);

Drag options to blanks, or click blank then click option'

A[0.1 100]

B[1 1000]

C[0.01 10]

D[10 1000]

Attempts:

3 left

💡 Hint

Common Mistakes

Using mismatched frequency ranges causing inconsistent plots.

Choosing frequency ranges too narrow or too wide.

The frequency range [0.1 100] is used both to specify Bode plot limits and x-axis limits.

5fill in blank

hard

Fill all three blanks to compute the gain margin, phase margin, and crossover frequencies.

Simulink

[GM, PM, [1], [2]] = margin([3]);

Drag options to blanks, or click blank then click option'

AWcg

BWcp

Csys

Dsys_tf

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up the order of output variables.

Using undefined system variables.

The margin function returns gain margin (GM), phase margin (PM), gain crossover frequency (Wcg), and phase crossover frequency (Wcp) for the system 'sys'.

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