Speed control with PID in Simulink - Step-by-Step Execution

Concept Flow - Speed control with PID

Set desired speed (Setpoint)

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Measure actual speed (Feedback)

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Calculate error = Setpoint - Feedback

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PID Controller: Compute control signal

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Apply control signal to motor

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Motor speed changes

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Loop back: Measure new speed

The system compares desired speed with actual speed, calculates error, uses PID to adjust control signal, and updates motor speed in a loop.

Execution Sample

Simulink

error = setpoint - actual_speed
control_signal = Kp*error + Ki*integral(error) + Kd*derivative(error)
motor_speed = motor_speed + control_signal
actual_speed = measure_speed(motor_speed)

This code calculates the error, applies PID formula to get control signal, updates motor speed, and measures new speed.

Execution Table

Step	Setpoint	Actual Speed	Error	Integral of Error	Derivative of Error	Control Signal	Motor Speed
1	100	0	100	100	100	150	150
2	100	150	-50	50	-150	20	170
3	100	170	-70	-20	-20	10	180
4	100	180	-80	-100	-10	5	185
5	100	185	-85	-185	-5	2	187
Exit	100	187	-87	-272	-2	0	187

💡 Motor speed stabilizes near setpoint, error becomes small, control signal approaches zero

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
Setpoint	100	100	100	100	100	100	100
Actual Speed	0	150	170	180	185	187	187
Error	100	-50	-70	-80	-85	-87	-87
Integral of Error	0	100	50	-20	-100	-185	-272
Derivative of Error	0	100	-150	-20	-10	-5	-2
Control Signal	0	150	20	10	5	2	0
Motor Speed	0	150	170	180	185	187	187

Key Moments - 3 Insights

Why does the error become negative after the first step?

Because the actual speed overshoots the setpoint, making actual_speed > setpoint, so error = setpoint - actual_speed becomes negative (see execution_table step 2).

Why does the control signal decrease over time even if error is still negative?

The integral and derivative terms adjust the control signal to reduce overshoot and stabilize speed, so control signal decreases as error magnitude reduces (see execution_table steps 3 to 5).

Why does motor speed not instantly reach setpoint?

Because the motor responds gradually to control signals and physical limits, so speed changes step-by-step as control signal is applied (see motor speed column in execution_table).

Visual Quiz - 3 Questions

Look at the execution table, what is the error value at step 3?

A -70

B -50

C 100

D -80

💡 Hint

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

At which step does the control signal first drop below 20?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at the 'Control Signal' column in execution_table and find when it goes below 20.

If the setpoint was increased to 120, how would the initial error at step 1 change?

A It would be 100

B It would be 0

C It would be 120

D It would be -120

💡 Hint

Error = setpoint - actual_speed; actual_speed starts at 0, so error equals setpoint at step 1.

Concept Snapshot

Speed control with PID:
- Measure error = desired speed - actual speed
- PID computes control signal from error, integral, derivative
- Control signal adjusts motor speed
- Loop repeats to stabilize speed near setpoint
- Integral reduces steady error, derivative reduces overshoot

Full Transcript

This visual execution shows how a PID controller manages motor speed. We start with a desired speed (setpoint) and measure actual speed. The error is the difference. The PID controller calculates a control signal using proportional, integral, and derivative parts of the error. This signal adjusts the motor speed. Over steps, the motor speed approaches the setpoint, error reduces, and control signal stabilizes near zero. Key points include error sign changes when speed overshoots, control signal adjustments to prevent oscillations, and gradual motor response. The execution table tracks all variables step-by-step for clear understanding.