On the parametric analysis of complex switching relay control systems

In certain applications relay control systems, under specific system conditions, might present a complex switching. These complex switchings result in limit cycles of complex type. In the literature complex limit cycles are treated only for relay control systems using relay elements without dead-zone. In this context, this work follows the method proposed by Tsypkin to derive existence conditions of complex limit cycles for relay control systems using relay elements with dead-zone and go further on the analysis and determination of existence conditions for complex limit cycles in systems with this element and time restrictions. These complex limit cycles are shown experimentally to exist. Additionally, this paper shows how to estimate the shape of these complex switchings according to specific bifurcations occurrence.