Frequency-domain analysis of self-excited oscillations for a class of multivariable relay systems

This paper investigates certain complex oscillatory phenomena taking place in multivariable relay control systems. A frequency based approach is applied, by making use of such tools of frequency-domain analysis as the Locus of a Perturbed Relay System (LPRS) and transfer properties analysis via the equivalent gain concept. As the novelty, we provide mathematical models and methods of analysis applicable to complex oscillatory modes not dealt with in the existing literature. A thoroughly discussed analysis and simulation example is outlined to validate the presented results.