Relay feedback systems—Established approaches and new perspectives for application

Abstract

Relay feedback systems belong, since long, to the rather classical topics of control theory and engineering. While they were first used as robust and simple switching elements in automatic control systems, over time, they have experienced different periods of renewed interest with regards to both theoretical analysis and applications. Examples include the automatic tuning of simple feedback controllers, delta-sigma modulators for analog-digital converters, robust relay-based controls, nonlinear systems analysis and identification, among others. One of the remarkable features of using relays in feedback is the appearance of stable limit cycles. The structural and parametric conditions for the stable limit cycles, their prediction, and controllability of magnitude and frequency have already been solved, to a large part, in previous researches, driven by both theoretical curiosity and application requirements. This brief tutorial paper summarizes the basic principles of relay feedback systems, discusses several characteristics that are interesting from an application perspective, and addresses some issues related to its further use for system identification. A case-specific study for estimating the unknown backlash, hidden within two-mass systems, is demonstrated along with an experimental example, based on provoking the controllable drifting limit cycles by the non-ideal relay in the velocity feedback loop.