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Control Notes

Last modified: Jun, 2014

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.