Error signal computation in Simulink

Introduction

We compute error signals to find the difference between what we want and what we get. This helps us improve systems by adjusting them based on the error.

When controlling a robot arm to reach a target position.

When adjusting temperature in a smart thermostat to match the desired setting.

When tuning a car's cruise control to maintain a set speed.

When training a machine learning model to reduce prediction mistakes.

When balancing a drone to keep it stable in the air.

Syntax

Simulink

Error = Reference Signal - Measured Signal

The error is simply the difference between the desired value (reference) and the actual value (measured).

In Simulink, this is often done using a 'Sum' block configured to subtract signals.

Examples

Computing position error for a robot arm.

Simulink

Error = DesiredPosition - ActualPosition

Finding temperature difference for a thermostat control.

Simulink

Error = SetTemperature - CurrentTemperature

Calculating speed error for cruise control.

Simulink

Error = TargetSpeed - VehicleSpeed

Sample Program

This script shows how to compute the error signal by subtracting the measured values from the reference. It simulates a system where the measured value changes over time.

Simulink

/* Simulink model setup steps (conceptual):
1. Use a 'Constant' block for Reference Signal (e.g., 10).
2. Use a 'Step' block for Measured Signal (e.g., starts at 0, steps to 8).
3. Use a 'Sum' block with inputs set to '+-' to compute Error = Reference - Measured.
4. Connect blocks accordingly.
5. Run simulation and observe Error output.
*/

% MATLAB script to simulate error signal computation
ref = 10; % Reference signal
measured = [0 0 0 8 8 8]; % Measured signal over time
error = ref - measured; % Compute error signal

disp('Error signal over time:')
disp(error)

Important Notes

Always check the sign when subtracting signals to get the correct error direction.

In Simulink, the 'Sum' block can handle multiple inputs and signs, making error computation flexible.

Error signals are key for feedback control and system tuning.

Summary

Error signal = Reference - Measured.

It shows how far the system is from the goal.

Used in control systems to improve performance.

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