PID controller block in Simulink - Step-by-Step Execution

Concept Flow - PID controller block in Simulink

Input Error Signal

↓

Proportional Term (P)

↓

Integral Term (I)

↓

Derivative Term (D)

↓

Sum P + I + D

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Output Control Signal

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System/Plant

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Feedback to Input Error

The PID controller takes the error input, calculates proportional, integral, and derivative terms, sums them, and outputs a control signal to the system, which feeds back to update the error.

Execution Sample

Simulink

error = setpoint - measurement
P = Kp * error
I = I + Ki * error * dt
D = Kd * (error - prev_error) / dt
output = P + I + D

This code calculates the PID output control signal step-by-step from the error input.

Execution Table

Step	error	P	I	D	output	prev_error	Action
1	5.0	10.0	0.5	0.0	10.5	0.0	Calculate P, I, D; output = 10+0.5+0
2	4.0	8.0	0.9	-2.0	6.9	5.0	Update I, D with new error; output = 8+0.9-2
3	3.0	6.0	1.2	-1.0	6.2	4.0	Update I, D; output = 6+1.2-1
4	1.0	2.0	1.3	-3.0	0.3	3.0	Update I, D; output = 2+1.3-3
5	0.0	0.0	1.3	-1.0	0.3	1.0	Error zero, output stabilizes
6	-1.0	-2.0	0.8	-1.0	-2.2	0.0	Negative error, output adjusts
7	-2.0	-4.0	0.0	-1.0	-5.0	-1.0	Integral resets, output changes
8	-3.0	-6.0	-1.5	-1.0	-8.5	-2.0	Integral negative, output decreases
9	-3.0	-6.0	-3.0	0.0	-9.0	-3.0	Derivative zero, output steady
10	-2.0	-4.0	-4.0	3.0	-5.0	-3.0	Derivative positive, output rises
Exit							Simulation ends after 10 steps

💡 Simulation ends after 10 steps to show PID output changes over time

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	After 7	After 8	After 9	After 10
error	5.0	5.0	4.0	3.0	1.0	0.0	-1.0	-2.0	-3.0	-3.0	-2.0
P	0.0	10.0	8.0	6.0	2.0	0.0	-2.0	-4.0	-6.0	-6.0	-4.0
I	0.0	0.5	0.9	1.2	1.3	1.3	0.8	0.0	-1.5	-3.0	-4.0
D	0.0	0.0	-2.0	-1.0	-3.0	-1.0	-1.0	-1.0	-1.0	0.0	3.0
output	0.0	10.5	6.9	6.2	0.3	0.3	-2.2	-5.0	-8.5	-9.0	-5.0
prev_error	0.0	0.0	5.0	4.0	3.0	1.0	0.0	-1.0	-2.0	-3.0	-3.0

Key Moments - 3 Insights

Why does the integral term (I) sometimes decrease even though error is positive?

Because the integral term accumulates error over time and can be affected by previous negative errors, as shown in execution_table rows 7 and 8 where error becomes negative and I decreases.

Why does the derivative term (D) sometimes become zero?

The derivative term depends on the change in error. When error does not change between steps, like in row 9, D becomes zero because (error - prev_error) is zero.

Why does the output control signal sometimes become negative?

Output is sum of P, I, and D. When error is negative and terms combine negatively, output can be negative as in rows 6 to 10, reflecting control action in opposite direction.

Visual Quiz - 3 Questions

Look at the execution table at step 3. What is the value of the integral term (I)?

A 0.9

B 1.2

C 1.3

D 0.5

💡 Hint

Check the 'I' column in execution_table row 3

At which step does the derivative term (D) first become negative?

A Step 1

B Step 4

C Step 2

D Step 5

💡 Hint

Look at the 'D' column in execution_table rows 1 and 2

If the error at step 6 was positive instead of negative, how would the output likely change?

A Output would increase

B Output would decrease

C Output would stay the same

D Output would become zero

💡 Hint

Refer to variable_tracker for error and output values around step 6

Concept Snapshot

PID Controller in Simulink:
- Input: error = setpoint - measurement
- Output = P + I + D terms
- P = Kp * error (reacts to current error)
- I = integral of error over time (removes steady error)
- D = rate of change of error (predicts future error)
- Output controls system to reduce error over time

Full Transcript

The PID controller block in Simulink calculates a control signal based on the difference between a desired setpoint and the current measurement. It computes three parts: proportional (P), integral (I), and derivative (D). The proportional part reacts to the current error, the integral sums past errors to remove steady offset, and the derivative predicts future error trends. The sum of these three parts forms the output control signal that adjusts the system. The execution table shows step-by-step how error changes, how each term is calculated, and how the output evolves. Key moments clarify why integral can decrease, why derivative can be zero, and why output can be negative. The visual quiz tests understanding of these calculations at specific steps. This helps beginners see how the PID controller works dynamically in Simulink.

Practice

1. What is the main purpose of the PID Controller block in Simulink?

easy

A. To display system output without control

B. To generate random signals for testing

C. To store data for later analysis

D. To automatically adjust system output to reach a desired target smoothly

Solution

1. Step 1: Understand the role of PID controller

   The PID controller adjusts the output of a system to reach a target value by using proportional, integral, and derivative actions.

2. Step 2: Identify the correct purpose in Simulink

   Simulink's PID Controller block is designed to automatically control system output to reach the desired setpoint smoothly.

3. Final Answer:

   To automatically adjust system output to reach a desired target smoothly -> Option D

4. Quick Check:

   PID controller purpose = automatic smooth control [OK]

Hint: PID controls output to target smoothly [OK]

Common Mistakes:

• Confusing PID with signal generation
• Thinking PID only displays data
• Assuming PID stores data

2. Which of the following is the correct way to add a PID Controller block in Simulink?

easy

A. Drag the PID Controller block from the Simulink Library Browser into your model

B. Write pid() function in the MATLAB command window

C. Use the plot() function to create a PID block

D. Insert a MATLAB script block and type PID code inside

Solution

1. Step 1: Recall how Simulink blocks are added

   Simulink blocks are added by dragging them from the Library Browser into the model workspace.

2. Step 2: Identify the correct method for PID Controller block

   The PID Controller block is found in the Simulink Library Browser and must be dragged into the model to use it.

3. Final Answer:

   Drag the PID Controller block from the Simulink Library Browser into your model -> Option A

4. Quick Check:

   Adding blocks = drag from Library Browser [OK]

Hint: Add blocks by dragging from Library Browser [OK]

Common Mistakes:

• Trying to create PID block by MATLAB commands
• Using plot() function incorrectly
• Typing PID code inside script block

3. Consider this Simulink PID Controller block configuration: Proportional gain = 2, Integral gain = 1, Derivative gain = 0.5. What is the expected effect on system response?

medium

A. System will become unstable immediately

B. Faster response with some overshoot and reduced steady-state error

C. No change in response because gains are too low

D. Slower response with no overshoot and large steady-state error

Solution

1. Step 1: Analyze the effect of proportional gain

   Proportional gain of 2 increases the speed of response but may cause overshoot.

2. Step 2: Consider integral and derivative gains

   Integral gain of 1 reduces steady-state error by accumulating past errors; derivative gain of 0.5 helps reduce overshoot and smooth response.

3. Final Answer:

   Faster response with some overshoot and reduced steady-state error -> Option B

4. Quick Check:

   PID gains effect = faster, some overshoot, less steady error [OK]

Hint: Higher P speeds up, I reduces steady error, D smooths [OK]

Common Mistakes:

• Ignoring integral effect on steady-state error
• Assuming derivative gain causes instability
• Thinking low gains cause no change

4. You configured a PID Controller block but the system output oscillates wildly. Which of the following is the most likely cause?

medium

A. Derivative gain is set too high causing noise amplification

B. Integral gain is zero, so no oscillations should occur

C. Proportional gain is zero, system cannot oscillate

D. The PID block is disconnected from the model

Solution

1. Step 1: Understand oscillations in PID control

   Oscillations often occur when derivative gain is too high, amplifying noise and causing instability.

2. Step 2: Evaluate other options

   Integral gain zero reduces steady-state correction but does not cause oscillations; proportional gain zero means no control action; disconnected block means no output, not oscillations.

3. Final Answer:

   Derivative gain is set too high causing noise amplification -> Option A

4. Quick Check:

   High derivative gain = oscillations [OK]

Hint: High D gain can cause oscillations [OK]

Common Mistakes:

• Assuming zero integral gain causes oscillations
• Thinking zero proportional gain causes oscillations
• Ignoring block connection status

5. You want to design a PID controller in Simulink for a temperature control system that must avoid overshoot and reach the target temperature quickly. Which tuning strategy should you choose?

hard

A. Use a low proportional gain, moderate integral gain, and high derivative gain

B. Use high proportional gain, zero integral gain, and zero derivative gain

C. Use moderate proportional gain, moderate integral gain, and moderate derivative gain

D. Use zero proportional gain, high integral gain, and zero derivative gain

Solution

1. Step 1: Understand tuning goals

   To avoid overshoot and reach target quickly, proportional gain should be moderate to speed response without causing instability.

2. Step 2: Balance integral and derivative gains

   Integral gain helps eliminate steady-state error moderately; derivative gain helps reduce overshoot and smooth response.

3. Step 3: Evaluate options

   Use moderate proportional gain, moderate integral gain, and moderate derivative gain balances all gains moderately, fitting the goal. Use a low proportional gain, moderate integral gain, and high derivative gain's high derivative gain risks noise; Use high proportional gain, zero integral gain, and zero derivative gain lacks integral and derivative control; Use zero proportional gain, high integral gain, and zero derivative gain lacks proportional control, causing slow response.

4. Final Answer:

   Use moderate proportional gain, moderate integral gain, and moderate derivative gain -> Option C

5. Quick Check:

   Balanced PID gains = quick, no overshoot [OK]

Hint: Balance P, I, D for smooth fast control [OK]

Common Mistakes:

• Using too high derivative gain causing noise
• Ignoring integral gain causing steady error
• Setting proportional gain to zero causing slow response