The PID terms and their effect on a control system.

Table 1: The PID terms and their effect on a control system.

Term	Math Function	Effect on Control System
P Proportional	$K_{P} V_{e r r o r}$	Typically the main drive in a control loop, K_P reduces a large part of the overall error.
I Integral	$K_{I} \int V_{e r r o r} d t$	Reduces the final error in a system. Summing even a small error over time produces a drive signal large enough to move the system toward a smaller error.
D Derivative	$k_{D} \frac{d V_{e r r o r}}{d t}$	Counteracts the K_P and K_I terms when the output changes quickly. This helps reduce overshoot and ringing. It has no effect on the final error.