Abstract
The dynamic modes and bifurcations in a pulse control system of a heating unit, the condition of which is described through differential equations with discontinuous right–hand sides, have been studied. It has been shown that the system under research can demonstrate a great variety of nonlinear phenomena and bifurcation transitions, such as quasiperiodicity, multistable behaviour, chaotization of oscillations through a classical period–doubling bifurcations cascade and border–collision bifurcation.
Highlights
The technology of monocrystals growth is a controlled crystallization process, during which the quality of a growing crystal is determined by the accuracy of controlling phase transition conditions [1, 2]
The improvement of the energy performance together with the simplification of the production facility control is achieved by applying a field transistors converter as a key element with using fractional control laws of pulse–width modulation, which improves the system’s quality [5]
We reduce the investigation of this system to studying the dynamics of a two–dimensional piecewise–smooth map
Summary
The technology of monocrystals growth is a controlled crystallization process, during which the quality of a growing crystal is determined by the accuracy of controlling phase transition conditions [1, 2]. At the variations of the controlled objects’ parameters in nonlinear pulse systems, as well as under the external disturbances, the complicated nonlinear phenomena can occur, including high–frequency oscillations, multiple of the modulation frequency, and quasiperiodic or chaotic modes [6,7,8]. The appearance of such oscillatory modes leads to the reduction of the control accuracy, and to sudden breakdown of the technological equipment.
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