Incremental root locus and pid tuning

Abstract

This work discusses the Incremental Root Locus property and one application of it to PID controllers tuning. It is shown that using that property it is easy do determine the departure angle from the real axis, which is a not a trivial task using the classical root locus rules. As an application, a procedure for tuning PID controllers in two steps is shown. Firstly it is necessary to perform a step response test using a proportional controller in order to stabilize the system. In a second step the PID design is performed by a zero-pole canceling. The controller obtained is a two-degree-of-freedom PID controller. Simulations carried out indicate that the controller associated with the setpoint tracking exhibits an almost first-order response whereas the one associated with the disturbance rejection exhibits a more oscillatory response. As illustrations, a real application for a position servo control system and some design projects tested by simulation were done.