Servo motor control with PWM in Raspberry Pi - Time & Space Complexity

Time Complexity: Servo motor control with PWM

O(n)

Understanding Time Complexity

When controlling a servo motor with PWM on a Raspberry Pi, it's important to understand how the program's running time changes as we adjust parameters like the number of position commands.

We want to know how the time needed grows when we send more commands to the servo.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import RPi.GPIO as GPIO
import time

GPIO.setmode(GPIO.BOARD)
GPIO.setup(12, GPIO.OUT)
pwm = GPIO.PWM(12, 50)  # 50Hz frequency
pwm.start(0)

positions = [2.5, 7.5, 12.5]  # duty cycles for servo positions

for pos in positions:
    pwm.ChangeDutyCycle(pos)
    time.sleep(0.5)  # wait for servo to reach position

pwm.stop()
GPIO.cleanup()

This code moves a servo motor to different positions by changing the PWM duty cycle in a loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through the list of positions to send PWM signals.
• How many times: Once for each position in the list.

How Execution Grows With Input

Each new position adds one more PWM signal change and wait time.

Input Size (n)	Approx. Operations
3	3 PWM changes and waits
10	10 PWM changes and waits
100	100 PWM changes and waits

Pattern observation: The total time grows directly with the number of positions sent.

Final Time Complexity

Time Complexity: O(n)

This means the time to control the servo grows linearly with the number of position commands.

Common Mistake

[X] Wrong: "Changing the PWM duty cycle once controls all positions instantly."

[OK] Correct: Each position requires a separate PWM change and wait time; the servo needs time to move physically to each position.

Interview Connect

Understanding how loops affect timing in hardware control shows you can connect software logic with real-world device behavior, a valuable skill in many projects.

Self-Check

"What if we removed the wait time after each PWM change? How would the time complexity change?"