## **Lab 12** | Pulse Width Modulation (PWM) and Actuator Control

### Design of Autonomous Systems  
### CSCI 6907/4907 - Section 86  
### Prof. **Sibin Mohan**  
### Spring '25 | SEH 4040

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## **Objectives**

- Understand the fundamentals of **Pulse Width Modulation (PWM)**  
- Learn how to control **servo motors** and **DC motors** using PWM  
- Gain hands-on experience generating PWM signals to control actuators in an autonomous rover

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## **1. Introduction**

PWM is a method of **controlling power** delivered to electrical components using digital signals.  
It is essential for:

- **Speed control** in motors  
- **Brightness control** in LEDs  
- **Precise positioning** in servo motors

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## **2. What is PWM?**

PWM switches a digital signal ON and OFF at a fast rate.  
By adjusting the **ON time**, we control the **average power** delivered.

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### Example:

- Signal toggles between **3.3V (HIGH)** and **0V (LOW)**  
- 50% duty cycle ≈ 1.65V average output

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## **3. Duty Cycle and Control**

| Duty Cycle | Signal Behavior | Effect on Device      |
|------------|------------------|------------------------|
| 0%         | Always OFF       | No power               |
| 50%        | Half ON/OFF      | Medium power/speed     |
| 100%       | Always ON        | Max power/speed        |

**Duty cycle** = % of one cycle that signal is HIGH

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## **4. PWM vs Analog Voltage**

PWM is not true analog but **mimics** analog output:

- **Capacitors** can smooth PWM signals to get a near-analog voltage  
- Useful for controlling devices that require variable voltages

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## **5. Controlling Servo Motors**

Servo motors respond to **pulse width**, not just duty cycle.

| Pulse Width | Approx. Angle |
|-------------|----------------|
| 1.0 ms      | 0°             |
| 1.5 ms      | 90°            |
| 2.0 ms      | 180°           |

**Period:** 20ms (50Hz signal)  
**Formula**:
```python
duty = 2 + (angle / 18)
```

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## **6. Controlling DC Motors**

Use **PWM for speed** and **GPIO for direction** via a motor driver (L298N, TB6612, etc.)

Example:
```python
pwm.ChangeDutyCycle(75)  # 75% speed
```

- Use **≥1kHz** PWM to reduce motor whine

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## **7. Real-World Applications**

| Application     | Frequency | Duty Cycle Range | Notes                            |
|------------------|-----------|------------------|----------------------------------|
| Servo Motors     | 50Hz      | ~5–10%           | Pulse widths: ~1–2ms             |
| DC Motor Speed   | ≥1kHz     | 0–100%           | Fast switching = smoother motion |
| LED Brightness   | ~500Hz    | 0–100%           | Higher freq = less flicker       |

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## **8. Simulator**

Explore and visualize PWM with these tools:

- 🎛️ [PWM Visualizer](https://pwm-visualizer.vercel.app/)  
- 📈 [Desmos: PWM Curve](https://www.desmos.com/calculator/hnhb191rn9)

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## **9. Summary**

- PWM lets digital systems simulate analog control  
- You can tune **speed, brightness, or angle** with duty cycle  
- Both **servo** and **DC motors** rely on PWM in autonomous systems  
- Understanding PWM = deeper hardware-level control