Table 1: The PID terms and their effect on a control system.
Term |
Math Function |
Effect on Control System |
P Proportional |
$${K}_{P}\text{}{V}_{error}$$ |
Typically the main drive in a control loop, K_{P} reduces a large part of the overall error. |
I Integral |
$${K}_{I}{\displaystyle \int {V}_{error}}dt$$ |
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 |
$${k}_{D}\frac{d{V}_{error}}{dt}$$ |
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. |