BIFURCATIONS AND CHAOTIC OSCILLATIONS IN AN AUTOMATIC CONTROL RELAY SYSTEM WITH HYSTERESIS

Abstract

The dynamics of relay system with hysteresis is investigated. Systems of this type have a broad range of applications for power control and temperature regulation or in order to obtain highly stabilized electric or magnetic fields. Examples are power supplies for radio-electronics, computer equipment or spacecrafts, test stands for investigations of high- or low-temperature superconductivity, electron microscopes, and nuclear magnetic resonance tomographs. We first describe a general approach to determine stable and unstable periodic orbits for systems with hysteresis. Considering a concrete example of a four-dimensional relay system with hysteresis we hereafter determine the regions of periodic and chaotic oscillations in parameter space. The regularities in the occurrence of periodic motions are studied, and the associated bifurcations are described. The causes of nondeterminate (i.e. chaotic) dynamics are discussed and the influence of an external noise signal is analyzed.