To Fundamentals of the Hysteresis Control with Double Synchronization

Discussion on the hysteresis control with double synchronization (HDS-control) represents one of the most illustrative examples of striking influence of the bifurcation theory on the comprehension of regulator peculiarities. On the one hand, the HDS-regulator provides efficiency, simplicity and stability of energy conversion at the expense of the successful combination of advantages of both hysteresis control and pulse control. On the other hand, it turned out, that the HDS-operating regime can not be explained completely from the control theory only. Simplistically, any system under the HDS-control will inevitably demonstrate nonlinear dynamics; and HDS-operating regime represents various alternations between several operating processes (so-called elementary processes) with equal frequency (the synchronization frequency) and different orders of structural changes caused by four synchronizing surfaces. From the bifurcation theory, the following nontrivial points appear: how many elementary processes and how to treat alternations? Perhaps, due to these circumstances HDS-regulators are practically ignored in industrial applications after 2009 (after quarter-of-a-century accident-free usage of HDS-regulators in the control system of the high-speed railway train ER200 exploited on the railway line Moscow - St. Petersburg from year 1984, Russia). Revival interest in the HDS-dynamics nonlinear picture was initiated by the novel results when accents were shifted from the desired operating performance towards potential nonlinear phenomena. Here we comment briefly HDS-control basis and discuss these accents with attracting both computer simulations and experimental tests.