Error signal computation in Simulink - Step-by-Step Execution

Concept Flow - Error signal computation

Input Signal

↓

Reference Signal

↓

Subtract Block

↓

Error Signal Output

The error signal is computed by subtracting the reference signal from the input signal using a subtract block.

Execution Sample

Simulink

error = input_signal - reference_signal

This code calculates the error signal by subtracting the reference signal from the input signal.

Execution Table

Step	Input Signal	Reference Signal	Operation	Error Signal
1	5.0	3.0	5.0 - 3.0	2.0
2	4.5	4.0	4.5 - 4.0	0.5
3	3.0	3.5	3.0 - 3.5	-0.5
4	2.0	2.0	2.0 - 2.0	0.0
5	1.0	1.5	1.0 - 1.5	-0.5
Exit	-	-	No more data	-

💡 All input and reference signal values processed, computation ends.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5
input_signal	5.0	4.5	3.0	2.0	1.0	-
reference_signal	3.0	4.0	3.5	2.0	1.5	-
error	-	2.0	0.5	-0.5	0.0	-0.5

Key Moments - 2 Insights

Why can the error signal be negative?

Because the error is input_signal minus reference_signal, if input is less than reference, the result is negative as shown in steps 3 and 5 in the execution_table.

What happens if input_signal equals reference_signal?

The error signal becomes zero, meaning no difference, as seen in step 4 of the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what is the error signal value?

A 4.5

B 0.5

C -0.5

D 2.0

💡 Hint

Check the 'Error Signal' column in row for step 2 in execution_table.

At which step does the error signal first become negative?

A Step 1

B Step 4

C Step 3

D Step 5

💡 Hint

Look at the 'Error Signal' values in execution_table rows for negative values.

If the reference_signal was always zero, how would the error signal values change?

A Error equals input_signal values

B Error equals zero always

C Error equals negative input_signal

D Error equals reference_signal values

💡 Hint

Error = input_signal - reference_signal, so if reference_signal is zero, error equals input_signal.

Concept Snapshot

Error signal = input_signal - reference_signal
Computed by subtracting reference from input
Negative error means input < reference
Zero error means input = reference
Positive error means input > reference

Full Transcript

In Simulink, error signal computation involves subtracting the reference signal from the input signal. This is done using a subtract block. The error signal shows how far the input is from the reference. If the input is less than the reference, the error is negative. If they are equal, the error is zero. If input is greater, the error is positive. The execution table shows step-by-step values of input, reference, and resulting error. This helps understand how the error changes over time.

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