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# Control Notes

## PID

**Last modified: Jun, 2014**

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.