Nonlinear phenomena in a high–power heating unit with pulse modulated control

Yuriy Alexsandrovich Gol'Tsov,Vasiliy Grigorievich Rubanov,Alexander Stepanovich Kizhuk,S Bratan,S Roshchupkin,S Leonov,S Gorbatyuk

doi:10.1051/matecconf/201712901031

Yuriy Alexsandrovich Gol'Tsov, Vasiliy Grigorievich Rubanov + Show 5 more

Open Access

https://doi.org/10.1051/matecconf/201712901031

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Abstract

In this paper we describe the transitions from regular periodic mode to quasiperiodicity that can be observed in a pulse–width modulated control system for a high–power heating unit. The behavior of such a system can be described by a set of two coupled nonautonomous differential equations with discontinuous right–hand sides. We reduce the investigation of this system to the studying of a two–dimensional piecewise–smooth map. We demonstrate how a closed invariant curve associated with quasiperiodic dynamics can arise from a stable periodic motion through a Neimark-Sacker bifurcation. The paper also considers a variety of interesting nonlinear phenomena, including phase-locking modes, multistablilty and hysteretic transitions.

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]
In order to eliminate these regimes and to obtain a fast response, an accurate control, and a higher efficiency we have developed a heating unit control system [3, 4] based on a high–frequency switching power electronics converter with pulse–width modulation [5]
We reduce the investigation of this system to studying the dynamics of a two–dimensional piecewise–smooth mapping

Summary

Introduction

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]. With real conditions of operation smaller or larger changes of parameters always take place Such variations often lead to the loss of stability of the normal operation regime and to the appearance of complex dynamical behaviors, including subharmonic, quasiperiodic or chaotic oscillations [6,7,8]. The appearance of such oscillatory modes leads to the reduction of the control accuracy by several orders, and to the sudden breakdown of the technological equipment. The behavior of such a system may be represented by a two–dimensional piecewise–smooth set of nonautonomous differential equations.

Continuous – time model

Discrete time map

Bifurcation analysis

Conclusions