# Control Notes

## PID

The most widely used controller is probably the proportional-integral-derivative (PID) controller. The system can be understood with the transfer function

$$G(s) = \frac{1}{as^2 + bs + c}$$

The overall properties of P, I and D can be summarized as follows:

P I D
tracking error non-zero, but can be close zero no tracking
disturbance rejection non-zero, but can be close zero no
stability always stable for Kp>0 can be unstable always stable for Kd>0

So I is better for tracking and disturbance rejection, while P and D are more for stability.