Error signal computation in Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of error signal calculation block

Given a Simulink model where the error signal is computed as the difference between a reference input and a feedback signal, what is the output of the error signal block if the reference input is a constant 5 and the feedback signal is a sine wave with amplitude 3 at time t=0?

Simulink

Reference input: 5
Feedback signal at t=0: 3 * sin(0) = 0
Error signal = Reference input - Feedback signal

A 3

B 5

C -3

D 0

💡 Hint

Remember error signal = reference input minus feedback signal.

At time t=0, sine wave value is 0, so error = 5 - 0 = 5.

❓ data_output

intermediate

Error signal array from sampled signals

If the reference signal is [2, 4, 6, 8] and the feedback signal is [1, 3, 5, 7], what is the error signal array computed as reference minus feedback?

Simulink

reference = [2, 4, 6, 8]
feedback = [1, 3, 5, 7]
error = reference - feedback

A [1, 1, 1, 1]

B [-1, -1, -1, -1]

C [3, 7, 11, 15]

D [2, 4, 6, 8]

💡 Hint

Subtract each feedback element from the corresponding reference element.

Element-wise subtraction: 2-1=1, 4-3=1, 6-5=1, 8-7=1.

❓ visualization

advanced

Plot of error signal over time

You have a reference signal as a constant 10 and a feedback signal as a decaying exponential 10 * exp(-t) for t from 0 to 5 seconds sampled every 1 second. Which plot correctly shows the error signal computed as reference minus feedback?

Simulink

import numpy as np
import matplotlib.pyplot as plt

t = np.arange(0, 6, 1)
reference = 10
feedback = 10 * np.exp(-t)
error = reference - feedback

plt.plot(t, error, marker='o')
plt.xlabel('Time (s)')
plt.ylabel('Error Signal')
plt.title('Error Signal over Time')
plt.grid(True)
plt.show()

A A flat line at 10 across all times

B A plot starting at 10 and decreasing to 0 at t=5

C A plot starting at 0 and increasing to about 9.9 at t=5

D A plot starting at 0 and decreasing to -10 at t=5

💡 Hint

Error = 10 - 10*exp(-t), which starts at 0 and grows as exp(-t) decays.

At t=0, error=10-10=0; at t=5, error approaches 10-10*exp(-5) ≈ 9.93.

🧠 Conceptual

advanced

Effect of delay in feedback on error signal

In a control system, if the feedback signal is delayed by 2 seconds compared to the reference signal, how does this delay affect the error signal computation?

A The error signal will reflect the difference between the current reference and the delayed feedback, causing a phase lag in error response.

B The error signal will be zero because delay cancels out the difference.

C The error signal will be the sum of reference and feedback signals.

D The error signal will be unaffected by the delay.

💡 Hint

Think about how delay shifts the feedback signal in time.

Delay causes feedback to be out of sync, so error reflects difference with older feedback, causing lag.

🔧 Debug

expert

Identify error in error signal computation block

A Simulink model computes error signal as 'feedback - reference' instead of 'reference - feedback'. What is the impact on the error signal and system behavior?

A The model will produce a runtime error due to invalid operation.

B The error signal magnitude is doubled, causing instability.

C The error signal remains correct because subtraction order does not matter.

D The error signal sign is inverted, potentially causing the controller to react in the opposite direction.

💡 Hint

Consider what happens if you swap the order of subtraction in error calculation.

Swapping reference and feedback in subtraction inverts error sign, which can cause wrong control actions.

Practice

1. What does the error signal represent in Simulink models?

easy

A. The multiplication of input and output signals

B. The sum of all output signals

C. The delay between input and output

D. The difference between the desired and actual output values

Solution

1. Step 1: Understand the definition of error signal and match to options

   The error signal is defined as the difference between what is desired (reference) and what is actually produced (output). The difference between the desired and actual output values correctly states this difference, while others describe unrelated operations.

2. Final Answer:

   The difference between the desired and actual output values -> Option D

3. Quick Check:

   Error signal = desired - actual [OK]

Hint: Error signal = desired value minus actual output [OK]

Common Mistakes:

• Confusing error with sum or product of signals
• Thinking error is a delay or time difference
• Mixing input and output signals

2. Which Simulink block is commonly used to compute the error signal?

easy

A. Gain block to multiply signals

B. Integrator block to accumulate signals

C. Sum block with configuration to subtract output from reference

D. Scope block to display signals

Solution

1. Step 1: Identify block for error calculation and eliminate others

   The Sum block can be configured to subtract one input from another, which matches error signal computation. Gain multiplies, Integrator accumulates, Scope only displays signals, so they do not compute error.

2. Final Answer:

   Sum block with configuration to subtract output from reference -> Option C

3. Quick Check:

   Sum block subtracts signals for error [OK]

Hint: Use Sum block set to subtract for error calculation [OK]

Common Mistakes:

• Choosing Gain block which multiplies instead of subtracts
• Confusing Scope as a computation block
• Using Integrator which accumulates rather than subtracts

3. Given the following Simulink signals: Reference = [5, 7, 9], Output = [3, 7, 10]. What is the error signal computed as Reference - Output?

medium

A. [2, 0, -1]

B. [8, 14, 19]

C. [-2, 0, 1]

D. [3, 7, 10]

Solution

1. Step 1: Subtract output values from reference values element-wise

   Calculate 5-3=2, 7-7=0, 9-10=-1. The resulting error signal is [2, 0, -1].

2. Final Answer:

   [2, 0, -1] -> Option A

3. Quick Check:

   Error = Reference - Output = [2, 0, -1] [OK]

Hint: Subtract output from reference element-wise for error [OK]

Common Mistakes:

• Adding instead of subtracting signals
• Mixing order: output - reference instead of reference - output
• Copying output values as error

4. A Simulink model uses a Sum block to compute error as Reference + Output. What is the issue with this setup?

medium

A. Reference and Output cannot be inputs to the same block

B. The error signal should be Reference minus Output, not their sum

C. Output should be subtracted from Reference using a Gain block

D. Sum block cannot add signals

Solution

1. Step 1: Understand correct error signal formula and identify setup issue

   Error signal is Reference minus Output, so adding them is incorrect. Sum block configured to add will produce wrong error values, leading to incorrect control or training.

2. Final Answer:

   The error signal should be Reference minus Output, not their sum -> Option B

3. Quick Check:

   Error = Reference - Output, not Reference + Output [OK]

Hint: Sum block must subtract output from reference for error [OK]

Common Mistakes:

• Configuring Sum block to add instead of subtract
• Using Gain block unnecessarily for subtraction
• Assuming inputs cannot be connected to same block

5. In a control system modeled in Simulink, the error signal is computed as Reference - Output. If the Reference signal is constant at 10 and the Output signal fluctuates as [8, 12, 9, 11], what is the correct error signal sequence, and why is this important for system performance?

hard

A. [2, -2, 1, -1]; it shows how far output deviates from desired value to adjust control

B. [18, 22, 19, 21]; it sums signals to increase output

C. [10, 10, 10, 10]; constant error means system is stable

D. [-2, 2, -1, 1]; error is output minus reference for feedback

Solution

1. Step 1: Calculate error signal and understand its importance

   Subtract each output value from 10: 10-8=2, 10-12=-2, 10-9=1, 10-11=-1, resulting in [2, -2, 1, -1]. The error shows how much the output deviates from desired value, guiding adjustments to improve system performance.

2. Final Answer:

   [2, -2, 1, -1]; it shows how far output deviates from desired value to adjust control -> Option A

3. Quick Check:

   Error = Reference - Output; deviation guides control [OK]

Hint: Error = desired minus actual; guides system corrections [OK]

Common Mistakes:

• Adding signals instead of subtracting
• Reversing subtraction order
• Ignoring error's role in control adjustment