Disturbance rejection in Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding disturbance rejection in control systems

Which of the following best describes the main goal of disturbance rejection in a control system?

A To ignore disturbances and focus only on the reference input

B To minimize the effect of external disturbances on the system output

C To increase the speed of the system response regardless of disturbances

D To maximize the input signal amplitude to overcome disturbances

💡 Hint

Think about what happens when unexpected changes affect the system output.

Disturbance rejection aims to reduce the impact of external disturbances so the system output stays close to the desired value.

❓ Predict Output

intermediate

Simulink disturbance rejection block output

Given a Simulink model with a disturbance input added to the plant output, what will be the output if the disturbance rejection controller perfectly cancels the disturbance?

Simulink

disturbance = 5;
plant_output = 10;
controller_output = plant_output - disturbance;
system_output = plant_output + disturbance - controller_output;

A 15

B 0

C 5

D 10

💡 Hint

Calculate the system output step by step considering the controller cancels disturbance.

The controller output cancels the disturbance, so the system output equals the original plant output.

❓ data_output

advanced

Analyzing disturbance rejection performance data

You have disturbance rejection data from a Simulink simulation showing output values over time with and without disturbance rejection. Which data set shows better disturbance rejection?

Simulink

time = [0,1,2,3,4];
output_with_disturbance = [10, 15, 20, 25, 30];
output_with_rejection = [10, 11, 12, 13, 14];

A Both are equal

B output_with_disturbance

C output_with_rejection

D Cannot determine from data

💡 Hint

Look for which output stays closer to the initial value despite disturbance.

The output with rejection changes less over time, showing better disturbance rejection.

🔧 Debug

advanced

Identify the error in disturbance rejection Simulink model setup

In a Simulink model, the disturbance signal is added after the controller block instead of before the plant. What is the likely effect on disturbance rejection?

A The controller cannot reject the disturbance effectively

B The disturbance is perfectly canceled

C The system output ignores the disturbance

D The disturbance is amplified by the controller

💡 Hint

Consider where the disturbance enters the system relative to the controller.

If disturbance is added after the controller, the controller cannot sense or cancel it, reducing rejection effectiveness.

🚀 Application

expert

Designing a disturbance rejection strategy in Simulink

You want to design a Simulink model that rejects a sinusoidal disturbance at 1 Hz. Which approach is best to achieve this?

A Add a notch filter tuned to 1 Hz in the feedback loop

B Increase the controller gain without filtering

C Add a low-pass filter with cutoff at 10 Hz before the plant

D Ignore the disturbance and rely on feedforward control

💡 Hint

Think about how to target a specific frequency disturbance.

A notch filter tuned to the disturbance frequency can effectively reduce that disturbance in the feedback loop.

Practice

1. What is the main goal of disturbance rejection in a Simulink control system?

easy

A. To keep the system output stable despite external changes

B. To increase the system's input signal strength

C. To remove all feedback loops from the system

D. To make the system run faster without delays

Solution

1. Step 1: Understand disturbance rejection purpose

   Disturbance rejection aims to keep the system output steady even when outside changes happen.

2. Step 2: Compare options to this goal

   Only To keep the system output stable despite external changes matches this goal by focusing on output stability despite disturbances.

3. Final Answer:

   To keep the system output stable despite external changes -> Option A

4. Quick Check:

   Disturbance rejection = output stability [OK]

Hint: Disturbance rejection means steady output despite changes [OK]

Common Mistakes:

• Confusing disturbance rejection with increasing input
• Thinking disturbance rejection removes feedback loops
• Assuming it speeds up the system only

2. Which Simulink block is commonly used to reduce the effect of disturbances in a control system?

easy

A. PID Controller block

B. Gain block

C. Scope block

D. Mux block

Solution

1. Step 1: Identify blocks that affect disturbance

   PID Controller blocks adjust system response to reduce disturbance effects.

2. Step 2: Eliminate unrelated blocks

   Gain changes signal strength, Scope shows signals, Mux combines signals but doesn't reduce disturbances.

3. Final Answer:

   PID Controller block -> Option A

4. Quick Check:

   PID Controller reduces disturbances [OK]

Hint: PID blocks help control disturbances in Simulink [OK]

Common Mistakes:

• Choosing Scope block which only displays signals
• Confusing Gain block with disturbance rejection
• Selecting Mux block which combines signals

3. Given this Simulink feedback loop with a disturbance input, what will happen if the PID controller gains are set too low?

Disturbance --> + --> System --> Output
               ^                 |
               |-----------------|
               PID Controller

medium

A. The system output will oscillate rapidly

B. The system output will closely follow the disturbance

C. The system output will reject the disturbance completely

D. The system output will be zero regardless of disturbance

Solution

1. Step 1: Understand low PID gains effect

   Low PID gains mean weak correction to disturbances, so system output follows disturbance closely.

2. Step 2: Analyze other options

   Complete rejection needs strong gains, oscillation usually comes from too high gains, zero output is unrealistic here.

3. Final Answer:

   The system output will closely follow the disturbance -> Option B

4. Quick Check:

   Low gains = poor disturbance rejection [OK]

Hint: Low PID gains mean weak disturbance correction [OK]

Common Mistakes:

• Assuming low gains cause oscillations
• Thinking output will be zero regardless
• Believing disturbance is fully rejected with low gains

4. You have a Simulink model with a disturbance rejection loop, but the output still shows large fluctuations. Which of these is the most likely error?

medium

A. The feedback loop is missing the disturbance input

B. The system has no input signal

C. The Scope block is not connected properly

D. The PID controller gains are set too high causing instability

Solution

1. Step 1: Identify cause of large output fluctuations

   High PID gains can cause the system to become unstable and oscillate, causing large fluctuations.

2. Step 2: Check other options

   Missing disturbance input means no disturbance effect, Scope connection affects display only, no input signal means no output but not fluctuations.

3. Final Answer:

   The PID controller gains are set too high causing instability -> Option D

4. Quick Check:

   High gains cause instability and fluctuations [OK]

Hint: Too high PID gains cause unstable output [OK]

Common Mistakes:

• Blaming Scope block for output fluctuations
• Ignoring PID gain settings
• Assuming missing disturbance input causes fluctuations

5. You want to design a Simulink model that rejects a sudden step disturbance affecting the system output. Which combination of blocks and settings is best to achieve fast disturbance rejection with minimal overshoot?

hard

A. Use a Scope block to monitor output and manually adjust input

B. Use only a Gain block with high gain and no feedback loop

C. Use a PID Controller block with tuned proportional and derivative gains, plus a feedback loop including the disturbance input

D. Use a Mux block to combine disturbance and input signals without control

Solution

1. Step 1: Identify blocks for disturbance rejection

   PID Controller with tuned gains helps react quickly and reduce overshoot; feedback loop is needed to correct disturbances.

2. Step 2: Evaluate other options

   Gain block alone cannot reject disturbances well; Scope only monitors signals; Mux combines signals but does not control.

3. Final Answer:

   Use a PID Controller block with tuned proportional and derivative gains, plus a feedback loop including the disturbance input -> Option C

4. Quick Check:

   PID + feedback = fast, minimal overshoot rejection [OK]

Hint: Combine PID with feedback loop for best disturbance rejection [OK]

Common Mistakes:

• Relying on Gain block without feedback
• Using Scope as control instead of monitoring
• Ignoring feedback loop importance