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Relay feedback systems belong, since long, to rather classical topics of the control theory and engineering. While they were first used as robust and simple switching elements in the automatic control, over time, they experienced different periods of renewed interest regarding both the theoretical analysis and applications. Examples here are the automatic tuning of the simple feedback controllers, delta-sigma modulators for analog-digital converters, robust relaybased controls, nonlinear systems analysis and identification, and others. One of the remarkable features when using relays in feedback is appearance of the stable limit cycles. The structural and parametric conditions for the stable limit cycles, their prediction, and controllability of magnitude and frequency already found answers, to the large part, in the former research, driven by both theoretical curiosity and application requirements. This brief tutorial paper is summarizing the basic principles of relay feedback systems, discuss several characteristics interesting for applications, and address some perspectives of further use for the system identification. A case-specific study of estimating the unknown backlash, hidden within two-mass systems, is demonstrated along with experimental example, based on provoking the controllable drifting limit cycles by the non-ideal relay in the velocity feedback loop.

Relay Feedback Systems — Established Approaches and New Perspectives for Application