How PID Control Works
u(t) = Kp·e(t) + Ki·∫e(t)dt + Kd·de(t)/dt
Proportional (P)
Responds to current error with output proportional to error magnitude. Higher Kp = faster response but may cause oscillation.
Output = Kp × error
Integral (I)
Accumulates past errors to eliminate steady-state error. Higher Ki = faster error elimination but may cause overshoot.
Output = Ki × ∫error dt
Derivative (D)
Predicts future error based on rate of change. Higher Kd = reduced oscillation and overshoot but sensitive to noise.
Output = Kd × de/dt
Response Curve
Setpoint
Output
Error
Physical System Animation
Target Position
Actual Position
PID Components
P
I
D
Observation Guide
Tuning Kp (Proportional)
- Increase Kp for faster response
- Too high Kp causes oscillation and instability
- Start with Kp around 1-3 for moderate response
Tuning Ki (Integral)
- Add Ki to eliminate steady-state error
- Too high Ki causes overshoot and slow settling
- Use small Ki values (0.01-0.5) typically
Tuning Kd (Derivative)
- Add Kd to reduce overshoot and oscillation
- High Kd amplifies sensor noise
- Kd = 0.3-1.5 works well for most systems
Test Scenarios
- Click "Step Input" to test step response
- Use "Add Disturbance" to test rejection
- Try "Sine Tracking" for dynamic reference
Pro Tips
- Start with only Kp, add Ki if steady-state error exists
- Add Kd last if you see oscillation or too much overshoot
- Real systems often have limits on actuator output
- PID tuning is iterative - small adjustments work best
- Applications: Temperature control, motor speed, robotics, drones