Feedback loop in Simulink - Step-by-Step Execution

Concept Flow - Feedback loop in Simulink

Start Simulation

↓

Input Signal

↓

Process Block

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Output Signal

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Feedback Path

↓

Sum Block (Add Feedback to Input)

Back to Process Block↓

End or Continue Loop

↩Back to Process Block

The simulation starts with an input signal that goes through a process block. The output is fed back through a feedback path and summed with the input, creating a loop that continues during simulation.

Execution Sample

Simulink

% Simulink model steps (conceptual)
Input -> Sum (+ feedback) -> Process -> Output -> Feedback -> Sum

This shows the flow of signals in a feedback loop where output is fed back and combined with input.

Execution Table

Step	Block	Input Signal	Feedback Signal	Sum Output	Process Output	Next Feedback
1	Sum	1.0	0.0	1.0	1.5	1.5
2	Sum	1.0	1.5	2.5	3.75	3.75
3	Sum	1.0	3.75	4.75	7.125	7.125
4	Sum	1.0	7.125	8.125	12.1875	12.1875
5	Sum	1.0	12.1875	13.1875	19.78125	19.78125
6	Sum	1.0	19.78125	20.78125	31.171875	31.171875
7	Sum	1.0	31.171875	32.171875	46.7578125	46.7578125
8	Sum	1.0	46.7578125	47.7578125	70.13671875	70.13671875
9	Sum	1.0	70.13671875	71.13671875	106.705078125	106.705078125
10	Sum	1.0	106.705078125	107.705078125	161.5576171875	161.5576171875
11	Sum	1.0	161.5576171875	162.5576171875	244.33642578125	244.33642578125
12	Sum	1.0	244.33642578125	245.33642578125	366.004638671875	366.004638671875
13	Sum	1.0	366.004638671875	367.004638671875	549.5069580078125	549.5069580078125
14	Sum	1.0	549.5069580078125	550.5069580078125	824.2604370117188	824.2604370117188
15	Sum	1.0	824.2604370117188	825.2604370117188	1237.8906555175781	1237.8906555175781
16	Sum	1.0	1237.8906555175781	1238.8906555175781	1858.3359832763672	1858.3359832763672
17	Sum	1.0	1858.3359832763672	1859.3359832763672	2788.0039749145508	2788.0039749145508
18	Sum	1.0	2788.0039749145508	2789.0039749145508	4182.005962371826	4182.005962371826
19	Sum	1.0	4182.005962371826	4183.005962371826	6274.508943557739	6274.508943557739
20	Sum	1.0	6274.508943557739	6275.508943557739	9413.263415336609	9413.263415336609
Exit	Sum	1.0	9413.263415336609	Condition met or max steps reached	-	-

💡 Simulation stops after 20 steps or when output grows beyond threshold.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 10	After 15	After 20
Input Signal	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
Feedback Signal	0.0	1.5	3.75	7.125	12.1875	19.78125	161.5576171875	824.2604370117188	9413.263415336609
Sum Output	-	1.0	2.5	4.75	8.125	13.1875	107.705078125	825.2604370117188	6275.508943557739
Process Output	-	1.5	3.75	7.125	12.1875	19.78125	161.5576171875	1237.8906555175781	9413.263415336609

Key Moments - 3 Insights

Why does the feedback signal start at 0 in the first step?

At step 1 in the execution_table, the feedback signal is 0 because the loop has not yet produced any output to feed back.

Why does the output grow so quickly after several steps?

The process output multiplies the sum output by 1.5 each step, so the feedback loop causes exponential growth as seen from step 3 onward in the execution_table.

What causes the simulation to stop after 20 steps?

The exit_note in the execution_table shows the simulation stops either after 20 steps or when the output grows beyond a set threshold to prevent infinite looping.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the value of the Sum Output?

A 4.75

B 7.125

C 3.75

D 2.5

💡 Hint

Check the 'Sum Output' column at row with Step 3 in the execution_table.

At which step does the Feedback Signal first exceed 1000?

A Step 10

B Step 20

C Step 15

D Step 5

💡 Hint

Look at the 'Feedback Signal' values in variable_tracker after each step.

If the process block multiplier changed from 1.5 to 1.0, how would the Process Output change at step 2?

A It would be 1.5

B It would be 2.5

C It would be 1.0

D It would be 3.75

💡 Hint

Process Output = Sum Output * multiplier; check step 2 Sum Output in execution_table.

Concept Snapshot

Feedback loop in Simulink:
- Output feeds back to input via Sum block
- Sum block adds input and feedback
- Process block transforms sum output
- Loop repeats each simulation step
- Can cause output to grow or stabilize
- Used for control and dynamic systems

Full Transcript

In a Simulink feedback loop, the simulation starts with an input signal that goes into a Sum block. This Sum block adds the input signal and the feedback signal from the previous output. The combined signal then passes through a Process block, which modifies it (for example, multiplying by 1.5). The output of the Process block is then fed back as the feedback signal for the next step. This loop continues for each simulation step, causing the output to change over time. The feedback signal starts at zero because there is no previous output at the first step. As the simulation runs, the output can grow quickly due to repeated multiplication. The simulation stops after a set number of steps or when the output reaches a threshold to avoid infinite loops. This feedback mechanism is common in control systems and dynamic simulations.

Practice

1. What is the main purpose of a feedback loop in Simulink?

easy

A. To use the output to control the input and stabilize the system

B. To create random signals for testing

C. To display the output only without affecting input

D. To disconnect blocks automatically

Solution

1. Step 1: Understand feedback loop concept

   A feedback loop uses the output signal to influence the input, helping control system behavior.

2. Step 2: Identify the purpose in Simulink

   In Simulink, feedback loops stabilize or regulate system outputs by adjusting inputs based on output values.

3. Final Answer:

   To use the output to control the input and stabilize the system -> Option A

4. Quick Check:

   Feedback loop = control input from output [OK]

Hint: Feedback loops control input using output signals [OK]

Common Mistakes:

• Thinking feedback loops only display output
• Confusing feedback with feedforward
• Assuming feedback loops generate random signals

2. Which block is commonly used in Simulink to combine signals for creating a feedback path?

easy

A. Sum block

B. Gain block

C. Scope block

D. Constant block

Solution

1. Step 1: Identify blocks that combine signals

   The Sum block adds or subtracts multiple input signals, combining them into one output.

2. Step 2: Understand feedback path creation

   Feedback loops require combining signals, which the Sum block does, unlike Gain or Scope blocks.

3. Final Answer:

   Sum block -> Option A

4. Quick Check:

   Sum block combines signals [OK]

Hint: Sum block adds signals for feedback paths [OK]

Common Mistakes:

• Choosing Gain block which scales but does not combine
• Selecting Scope block which only displays signals
• Confusing Constant block with signal combiner

3. Consider a feedback loop in Simulink with a Gain block of 2 and an Integrator block. If the input is a constant 1, what is the expected behavior of the output over time?

medium

A. Output will oscillate without settling

B. Output will remain constant at 1

C. Output will increase linearly over time

D. Output will decrease exponentially

Solution

1. Step 1: Analyze Gain and Integrator effect

   The Gain block multiplies input by 2, and the Integrator accumulates this value over time.

2. Step 2: Predict output behavior

   Since input is constant 1, output = integral of 2*1 = 2*t, which increases linearly over time.

3. Final Answer:

   Output will increase linearly over time -> Option C

4. Quick Check:

   Integrator accumulates scaled input linearly [OK]

Hint: Integrator sums input; gain scales it, causing linear growth [OK]

Common Mistakes:

• Assuming output stays constant with integrator
• Thinking output oscillates without a feedback oscillator
• Confusing exponential decrease with integration

4. You created a feedback loop in Simulink but the model simulation fails with an algebraic loop error. What is the most likely cause?

medium

A. Using a Sum block instead of a Gain block

B. Missing delay or memory block in the feedback path

C. Incorrect block parameter values in Gain block

D. Not connecting the output to a Scope block

Solution

1. Step 1: Understand algebraic loop error

   An algebraic loop occurs when output depends directly on itself without delay, causing simulation failure.

2. Step 2: Identify cause in feedback loops

   Feedback loops need a delay or memory block to break direct dependency; missing this causes algebraic loops.

3. Final Answer:

   Missing delay or memory block in the feedback path -> Option B

4. Quick Check:

   Algebraic loop = no delay in feedback [OK]

Hint: Add delay block to break algebraic loops [OK]

Common Mistakes:

• Blaming Sum block for algebraic loop
• Ignoring need for delay in feedback
• Thinking Scope block affects algebraic loops

5. You want to design a feedback loop in Simulink that stabilizes a system output at a target value. Which combination of blocks should you use?

hard

A. Gain block for input scaling, Integrator block for output, and Constant block for feedback

B. Constant block for input, Scope block for output, and Gain block for scaling

C. Sum block to add signals, Constant block for feedback, and Scope block to display

D. Sum block to compare output and target, Gain block for feedback strength, and Integrator block to accumulate error

Solution

1. Step 1: Identify blocks for feedback control

   Sum block compares output with target to find error; Gain block adjusts feedback strength; Integrator accumulates error over time.

2. Step 2: Understand how these stabilize output

   Accumulated error helps correct system output gradually, stabilizing it at the target value.

3. Final Answer:

   Sum block to compare output and target, Gain block for feedback strength, and Integrator block to accumulate error -> Option D

4. Quick Check:

   Sum + Gain + Integrator = stable feedback control [OK]

Hint: Use Sum, Gain, and Integrator for stable feedback loops [OK]

Common Mistakes:

• Using Scope or Constant blocks instead of error calculation
• Missing Integrator to accumulate error
• Confusing feedback with feedforward blocks