Why feedback reduces error and improves stability in Simulink - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a feedback loop in Simulink.

Simulink

feedback_system = feedback([1], 1);

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

AG

BH

CK

DL

Attempts:

3 left

💡 Hint

Common Mistakes

Using the feedback transfer function instead of the forward path.

Confusing the feedback path variable with the forward path.

The feedback function in Simulink uses the forward path transfer function, commonly named G, to create a feedback loop.

2fill in blank

medium

Complete the code to calculate the closed-loop transfer function with unity feedback.

Simulink

closed_loop = [1] / (1 + [2]);

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

AH

BG

CK

DL

Attempts:

3 left

💡 Hint

Common Mistakes

Using the feedback transfer function H instead of G.

Forgetting to add 1 in the denominator.

The closed-loop transfer function with unity feedback is G / (1 + G).

3fill in blank

hard

Fix the error in the code to compute the error signal in a feedback system.

Simulink

error_signal = input_signal - [1];

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

Afeedback_signal

Bdisturbance

Coutput_signal

Dnoise

Attempts:

3 left

💡 Hint

Common Mistakes

Subtracting output signal instead of feedback signal.

Using disturbance or noise in place of feedback signal.

The error signal is the difference between the input and the feedback signal.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each signal to its error if the error {{BLANK_1}} 0.1.

Simulink

error_dict = {signal: error for signal, error in signals.items() if error {{BLANK_2}} 0.1}

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

A>

B<

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of <.

Mixing different comparison operators.

The comprehension filters errors less than 0.1 using the < operator.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each signal name in uppercase to its error if the error {{BLANK_2}} 0.05.

Simulink

filtered_errors = {signal[1]: error for signal, error in signals.items() if error [2] 0.05 and signal[3] 'temp'}

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

A.upper()

B<

C!=

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Using == instead of != to exclude 'temp'.

Using > instead of < for error filtering.

The comprehension converts signal names to uppercase, filters errors less than 0.05, and excludes signals named 'temp'.

Practice

1. In Simulink, why does adding feedback to a system help reduce error?

easy

A. Because feedback removes all noise from the system

B. Because feedback increases the system's input signal strength

C. Because feedback compares the output with the desired input and corrects deviations

D. Because feedback speeds up the system without changing error

Solution

1. Step 1: Understand feedback role in error correction

   Feedback measures the difference between actual output and desired output, called error.

2. Step 2: Feedback reduces error by adjusting system input

   By feeding back the error, the system can adjust inputs to reduce this error over time.

3. Final Answer:

   Because feedback compares the output with the desired input and corrects deviations -> Option C

4. Quick Check:

   Feedback reduces error by comparison [OK]

Hint: Feedback compares output to target to reduce error [OK]

Common Mistakes:

• Thinking feedback increases input strength only
• Assuming feedback removes noise completely
• Believing feedback only speeds system without error change

2. Which of the following is the correct way to represent a feedback loop in Simulink?

easy

A. Using a Constant block as feedback signal

B. Using a Gain block only without any summation

C. Using a Scope block to display output without feedback

D. Using a Sum block to subtract output from input and feeding back the result

Solution

1. Step 1: Identify feedback loop components in Simulink

   A feedback loop requires comparing output and input, typically done with a Sum block.

2. Step 2: Confirm correct feedback representation

   The Sum block subtracts output from input to find error, which is fed back to control the system.

3. Final Answer:

   Using a Sum block to subtract output from input and feeding back the result -> Option D

4. Quick Check:

   Sum block subtracts output for feedback [OK]

Hint: Feedback needs subtraction via Sum block [OK]

Common Mistakes:

• Using Gain block alone without error calculation
• Confusing Scope with feedback mechanism
• Using Constant block as feedback signal incorrectly

3. Consider a Simulink model with a feedback loop where the feedback gain is set too high. What is the likely effect on system stability?

medium

A. The system error reduces smoothly to zero

B. The system becomes unstable and oscillates

C. The system output remains constant regardless of input

D. The system ignores the feedback signal

Solution

1. Step 1: Understand effect of high feedback gain

   High feedback gain amplifies the correction signal, which can cause overshoot and oscillations.

2. Step 2: Connect high gain to system stability

   Excessive gain often leads to instability, causing the system output to oscillate instead of settling.

3. Final Answer:

   The system becomes unstable and oscillates -> Option B

4. Quick Check:

   High gain causes oscillations [OK]

Hint: Too high feedback gain causes oscillations [OK]

Common Mistakes:

• Assuming error always reduces smoothly
• Thinking output stays constant despite feedback
• Believing system ignores feedback at high gain

4. You have a Simulink model with feedback, but the output is not stabilizing and shows growing oscillations. What is the most likely cause?

medium

A. Feedback gain is set too high

B. Feedback gain is set too low

C. Feedback loop is missing the Sum block

D. The input signal is constant

Solution

1. Step 1: Analyze symptoms of growing oscillations

   Growing oscillations indicate instability, often caused by excessive feedback gain.

2. Step 2: Identify cause related to feedback gain

   Too high feedback gain amplifies errors, causing the system to overshoot and oscillate more.

3. Final Answer:

   Feedback gain is set too high -> Option A

4. Quick Check:

   High gain causes instability [OK]

Hint: Growing oscillations mean feedback gain too high [OK]

Common Mistakes:

• Thinking low gain causes oscillations
• Ignoring missing Sum block as cause
• Assuming constant input causes instability

5. You want to design a Simulink feedback system that reduces error quickly but remains stable. Which approach best balances error reduction and stability?

hard

A. Use moderate feedback gain and include a low-pass filter in the feedback path

B. Use maximum feedback gain without any filtering

C. Remove feedback and rely on open-loop control

D. Use zero feedback gain and increase input signal strength

Solution

1. Step 1: Understand trade-off between gain and stability

   High gain reduces error fast but risks instability; moderate gain balances both.

2. Step 2: Use filtering to improve stability

   A low-pass filter smooths feedback signals, reducing oscillations and improving stability.

3. Final Answer:

   Use moderate feedback gain and include a low-pass filter in the feedback path -> Option A

4. Quick Check:

   Moderate gain + filter balances error and stability [OK]

Hint: Moderate gain plus filter keeps system stable [OK]

Common Mistakes:

• Using maximum gain causing instability
• Removing feedback loses error correction
• Zero gain means no feedback effect