Coming to Terms with PID

Abstract

Despite being ubiquitous in industrial control system usage, the PID (Proportional, Integral, Derivative) algorithm is a mystery to many. Since its theoretical analysis was introduced by Minorsky nearly 100 years ago [1], it has been explained primarily by its representation in the Positional form of the equation. This paper will present the PID algorithm as a PVA (Position, Velocity, Acceleration) algorithm, which explains the theory based on the Velocity instead of the Positional form of the equation. PVA is not a new controller but a different representation of the PID from a Velocity instead of Positional view. The paper does not intend to suggest that the implementation of controllers should change from PID to PVA; only that PVA provides a more intuitive way to introduce the theory so that engineers better understand how to configure and tune PID control loops. Despite a long history of teaching the Positional form, and implementation of the Positional (PID) form in control systems, the Velocity (PVA) form offers a way to introduce the algorithm in a more familiar and understandable way to engineering students and practicing engineers.