PID Controllers
PID Controllers, standing for proportional, integral, derivative( We will call them PIDs ), are closed control loop, it helps regulate values.
What are control loops?
Control loops are systems in place to regulate some desired value, they use feedback loops and work off the feedback given.
Ex. The human body
The human body’s tempeture is a closed feedback loop, it attempts to maintain a tempeture of 37 degrees Celsius, too hot, you sweat, too cold, you shiver. This is an example of a control loop.
Formulae
PIDs are defined differently depending if the dataset is discrete, or continuous. You might know that the ideas of calculus are based because the functions you use are continuous. If you are using a continuous dataset the tools of calculus appply, however if not, you have to use the discrete versions of those calculus operators.