Oscillations in a relay control system with hysteresis and time dead zone Original Research Article

We describe the results of a study of dynamic modes and bifurcations in a relay system with hysteresis. An electric drive with a dc motor powered by a static electric power converter in which the motor torque is stabilized by a relay control system is taken as an example. The behavior of such a system is described by a four-dimensional piecewise-smooth set of autonomous differential equations. A two-position relay element in the system is considered to have a time dead zone and hysteresis. In actual converters with relay control, time dead zones are indispensable. Among other things, such zones are necessary to limit the switching frequency of the converter and to secure a minimum interval between the “on” and “off” pulses. Typical bifurcation mechanisms for the complication of oscillations and the dependence of the mode characteristics upon the hysteresis value of the relay element and upon the electric drive parameters are analyzed in detail.