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?"

Practice

1. What does PWM control in a servo motor connected to a Raspberry Pi?

easy

A. The temperature of the servo motor

B. The angle position of the servo arm

C. The brightness of an LED

D. The speed of the Raspberry Pi processor

Solution

1. Step 1: Understand PWM role in servo control

   PWM (Pulse Width Modulation) sends signals to set the servo arm's angle by changing the pulse width.

2. Step 2: Identify what PWM affects

   It does not control speed, brightness, or temperature but the position of the servo arm.

3. Final Answer:

   The angle position of the servo arm -> Option B

4. Quick Check:

   PWM controls servo angle = D [OK]

Hint: PWM changes pulse width to set servo angle [OK]

Common Mistakes:

• Confusing PWM with speed control
• Thinking PWM controls LED brightness here
• Assuming PWM changes temperature

2. Which of the following is the correct way to start PWM on GPIO pin 18 at 50 Hz in Python using RPi.GPIO?

easy

A. pwm = GPIO.PWM(18, 50); pwm.start(7.5)

B. pwm = GPIO.PWM(50, 18); pwm.start(7.5)

C. pwm = GPIO.PWM(18); pwm.start(50)

D. pwm = GPIO.PWM(7.5, 18); pwm.start(50)

Solution

1. Step 1: Check PWM initialization syntax

   GPIO.PWM(pin, frequency) initializes PWM on the specified pin and frequency.

2. Step 2: Verify correct parameters

   Pin 18 and frequency 50 Hz are correct; start() takes duty cycle like 7.5.

3. Final Answer:

   pwm = GPIO.PWM(18, 50); pwm.start(7.5) -> Option A

4. Quick Check:

   GPIO.PWM(pin, freq) with start(duty) = B [OK]

Hint: Remember GPIO.PWM(pin, freq) then start(duty) [OK]

Common Mistakes:

• Swapping pin and frequency order
• Missing frequency argument
• Passing duty cycle in PWM() instead of start()

3. What will be the output angle of the servo if the duty cycle is set to 12.5% using PWM at 50 Hz?

medium

A. 0 degrees

B. 90 degrees

C. 270 degrees

D. 180 degrees

Solution

1. Step 1: Understand duty cycle to angle mapping

   At 50 Hz, about 2.5% duty cycle corresponds to 0°, 7.5% to 90°, and 12.5% to 180°.

2. Step 2: Match 12.5% duty cycle to angle

   12.5% duty cycle sets the servo to its maximum angle, 180°.

3. Final Answer:

   180 degrees -> Option D

4. Quick Check:

   12.5% duty cycle = 180° [OK]

Hint: Max duty cycle ~12.5% means 180° angle [OK]

Common Mistakes:

• Confusing duty cycle values with angles
• Assuming 12.5% is 90 degrees
• Thinking servo can rotate beyond 180 degrees

4. Given this code snippet, what is the error?

import RPi.GPIO as GPIO
GPIO.setmode(GPIO.BCM)
GPIO.setup(18, GPIO.OUT)
pwm = GPIO.PWM(18, 50)
pwm.start(7.5)
# Missing cleanup

medium

A. GPIO pins are not cleaned up after use

B. PWM frequency is incorrect

C. Duty cycle value is out of range

D. GPIO mode is not set

Solution

1. Step 1: Review code for setup and cleanup

   The code sets mode, pin, and starts PWM correctly but does not call GPIO.cleanup().

2. Step 2: Identify missing cleanup importance

   Not cleaning up GPIO pins can cause warnings or errors on next runs.

3. Final Answer:

   GPIO pins are not cleaned up after use -> Option A

4. Quick Check:

   Missing GPIO.cleanup() = A [OK]

Hint: Always call GPIO.cleanup() after PWM use [OK]

Common Mistakes:

• Ignoring GPIO.cleanup()
• Thinking frequency or duty cycle is wrong here
• Forgetting to set GPIO mode

5. You want to sweep a servo motor from 0° to 180° smoothly using PWM on Raspberry Pi. Which approach is best?

hard

A. Use a fixed duty cycle of 12.5% without delay

B. Set duty cycle to 7.5% and wait for 5 seconds

C. Change duty cycle gradually from 2.5% to 12.5% in small steps with delays

D. Change frequency from 50 Hz to 100 Hz rapidly

Solution

1. Step 1: Understand servo sweeping method

   Sweeping means moving smoothly from 0° to 180°, which requires changing duty cycle gradually.

2. Step 2: Identify correct PWM control

   Duty cycle must change from about 2.5% (0°) to 12.5% (180%) in small steps with short delays for smooth motion.

3. Final Answer:

   Change duty cycle gradually from 2.5% to 12.5% in small steps with delays -> Option C

4. Quick Check:

   Smooth sweep = gradual duty cycle change [OK]

Hint: Sweep by small duty cycle steps with delays [OK]

Common Mistakes:

• Using fixed duty cycle for sweeping
• Changing frequency instead of duty cycle
• Skipping delays causing jerky motion