This article explains proportional integral derivative (PID) control, including the math behind it, with the use case of a linear servo motor.

Proportional integral derivative (PID) control is a common method used to regulate the dynamic behavior of a system. Examples are found in many industrial devices, where it’s employed for ...

Geum-Bae Cho, Pyoung-Ho Kim, A precise control of AC servo motor using neural network PID controller, Current Science, Vol. 89, No. 1 (10 July 2005), pp. 23-29 ...