Delay of a System, Its Natural Period of Oscillation and Performance of the Controlled System: An Approach from Control Theory

The delay of a system is directly related to other of its most important intrinsic temporal and frequency characteristics: the natural period of oscillation. Although this link is well known since the middle of the last century and is used in practice by control engineers, it is notable that it has not received enough attention in the academic world.

This article is devoted to exploring the connection of these two parameters with each other, the relationship of both with the temporal response of the controlled system, and its impact on the calibration rules of the controllers.

Also, a proof of the relationship between delay and natural period of oscillation is provided, based on the behaviour of first-order systems with pure delay, using basic tools of linear control as root locus and polynomial algebra.

Even though this development is carried out from the control theory approach, it is also of interest to control technicians and engineers as it explains the basic behaviour of most industrial processes.