Motor speed control with PWM in Arduino - Time & Space Complexity

Time Complexity: Motor speed control with PWM

O(n)

Understanding Time Complexity

We want to see how the time the program takes changes as we adjust motor speed control using PWM.

How does the program's work grow when we change the input size or speed settings?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const int motorPin = 9;

void setup() {
  pinMode(motorPin, OUTPUT);
}

void loop() {
  for (int speed = 0; speed <= 255; speed++) {
    analogWrite(motorPin, speed);
    delay(10);
  }
}
    

This code gradually increases motor speed from 0 to 255 using PWM signals.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that runs from speed 0 to 255.
• How many times: It runs 256 times each time the loop() function runs.

How Execution Grows With Input

As the speed range increases, the number of loop steps grows directly with it.

Input Size (n)	Approx. Operations
10	10 steps
100	100 steps
255	255 steps

Pattern observation: The work grows in a straight line as the speed steps increase.

Final Time Complexity

Time Complexity: O(n)

This means the time to run grows directly in proportion to the number of speed steps.

Common Mistake

[X] Wrong: "The delay inside the loop does not affect the time complexity."

[OK] Correct: The delay adds fixed time per step, so total time grows with the number of steps, affecting overall time.

Interview Connect

Understanding how loops and delays affect program time helps you explain how embedded systems handle tasks efficiently.

Self-Check

"What if we replaced the for-loop with a while-loop that increments speed by 5 each time? How would the time complexity change?"

Practice

1. What does PWM do in motor speed control on an Arduino?

easy

A. It changes the motor's voltage permanently.

B. It switches power on and off quickly to control speed.

C. It changes the motor's direction.

D. It measures the motor's speed.

Solution

1. Step 1: Understand PWM function

   PWM (Pulse Width Modulation) controls speed by rapidly switching power on and off.

2. Step 2: Compare options

   Only It switches power on and off quickly to control speed. correctly describes PWM's role in speed control, others describe different functions.

3. Final Answer:

   It switches power on and off quickly to control speed. -> Option B

4. Quick Check:

   PWM controls speed by switching power on/off [OK]

Hint: PWM controls speed by fast power switching [OK]

Common Mistakes:

• Thinking PWM changes voltage permanently
• Confusing speed control with direction control
• Believing PWM measures speed

2. Which Arduino function is used to set motor speed with PWM?

easy

A. pinMode(pin, OUTPUT)

B. digitalWrite(pin, value)

C. analogWrite(pin, value)

D. delay(value)

Solution

1. Step 1: Identify PWM function

   analogWrite(pin, value) sets PWM signal on a pin with value 0-255 controlling speed.

2. Step 2: Check other functions

   digitalWrite sets HIGH/LOW only, pinMode sets pin mode, delay pauses code; none control PWM speed.

3. Final Answer:

   analogWrite(pin, value) -> Option C

4. Quick Check:

   Use analogWrite for PWM speed control [OK]

Hint: Use analogWrite to set PWM speed value [OK]

Common Mistakes:

• Using digitalWrite instead of analogWrite
• Confusing pinMode with speed control
• Trying to use delay to control speed

3. What will be the motor speed if the code runs

analogWrite(9, 128);

?

medium

A. Motor runs at full speed

B. Motor is off

C. Motor runs at double speed

D. Motor runs at about half speed

Solution

1. Step 1: Understand PWM value range

   analogWrite value ranges 0 (off) to 255 (full speed). 128 is about half of 255.

2. Step 2: Interpret speed from value

   Value 128 means roughly half the power, so motor runs at about half speed.

3. Final Answer:

   Motor runs at about half speed -> Option D

4. Quick Check:

   128/255 ≈ half speed [OK]

Hint: PWM 128 means about half speed [OK]

Common Mistakes:

• Thinking 128 means full speed
• Assuming motor is off at 128
• Believing speed can be doubled

4. Identify the error in this code snippet for motor speed control:

int speed = 300;
analogWrite(6, speed);

medium

A. Speed value is out of PWM range (0-255).

B. Pin 6 cannot be used for PWM.

C. analogWrite requires three arguments.

D. Variable speed must be declared as float.

Solution

1. Step 1: Check PWM value limits

   analogWrite accepts values from 0 to 255. 300 is outside this range.

2. Step 2: Verify other options

   Pin 6 supports PWM, analogWrite takes two arguments, and int is fine for speed.

3. Final Answer:

   Speed value is out of PWM range (0-255). -> Option A

4. Quick Check:

   PWM value must be 0-255 [OK]

Hint: PWM values must be 0 to 255 only [OK]

Common Mistakes:

• Using values above 255 for PWM
• Thinking analogWrite needs 3 arguments
• Believing PWM pins are limited incorrectly

5. You want to smoothly increase motor speed from 0 to full over 5 seconds using PWM on pin 10. Which code snippet achieves this?

hard

A. for(int speed=0; speed<=255; speed++) { analogWrite(10, speed); delay(20); }

B. analogWrite(10, 255); delay(5000); analogWrite(10, 0);

C. for(int speed=255; speed>=0; speed--) { analogWrite(10, speed); delay(20); }

D. digitalWrite(10, HIGH); delay(5000); digitalWrite(10, LOW);

Solution

1. Step 1: Understand smooth speed increase

   Gradually increasing PWM value from 0 to 255 in small steps with delay creates smooth speed change.

2. Step 2: Analyze code snippets

   for(int speed=0; speed<=255; speed++) { analogWrite(10, speed); delay(20); } uses a for loop from 0 to 255 with delay(20)ms, totaling about 5 seconds. Others either jump speed or use digitalWrite which is not PWM.

3. Final Answer:

   for(int speed=0; speed<=255; speed++) { analogWrite(10, speed); delay(20); } -> Option A

4. Quick Check:

   Gradual PWM increase with delay = smooth speed [OK]

Hint: Use for loop with analogWrite and delay for smooth speed [OK]

Common Mistakes:

• Using digitalWrite instead of analogWrite
• Jumping speed without gradual steps
• Not using delay to slow speed change