Bang-Bang Control
On/Off control - simplest form
if (error > 0) ON else OFF
Behavior: Oscillates around setpoint. Heater is either 100% ON or 100% OFF. Simple but causes overshoot and constant cycling.
P Control (Proportional)
Output proportional to error
u(t) = Kp × e(t)
Behavior: Smooth response but never reaches setpoint exactly. Has steady-state error (offset) because output decreases as error decreases.
PI Control (Proportional-Integral)
Eliminates steady-state error
u(t) = Kp×e + Ki×∫e dt
Behavior: Integral term accumulates error over time, eliminating offset. May overshoot and takes longer to settle.
PD Control (Proportional-Derivative)
Anticipates future error
u(t) = Kp×e + Kd×de/dt
Behavior: Derivative predicts error change, reducing overshoot and improving response. Still has steady-state offset like P control.
Full PID Control
Combined: fast response, no offset, minimal overshoot
u(t) = Kp×e + Ki×∫e dt + Kd×de/dt
Behavior: The gold standard of control. P provides quick response, I eliminates offset, D reduces overshoot. Well-tuned PID reaches setpoint quickly with minimal oscillation.
Control Method Comparison
| Method | Speed | Accuracy | Overshoot | Complexity |
|---|---|---|---|---|
| Bang-Bang | ⚡ Fast | ❌ Poor | �� High | ��� Simple |
| P Only | ⚡ Fast | ⚠️ Offset | 📉 Low | ✅ Simple |
| PI | 🐢 Slower | ✅ Good | 📈 Medium | ⚠️ Medium |
| PD | ⚡ Fast | ⚠️ Offset | 📉 Low | ⚠️ Medium |
| Full PID | ⚡ Fast | ✅ Excellent | 📉 Minimal | ❌ Complex |