Corresponding author: Balonin Nikolay A., Doctor of Engineering, Associate Professor, State University of Airspace Instrumentation, St.-Petersburg, 190000, Russian Federation,
Phone: (812) 494-70-44 (office), +7 (911) 213-59-07 (mobile); e-mail: korbendfs@mail.ru

Received on April 24, 2014
Accepted September 24, 2014

For multi-connected process of scintillation of the single crystal growth, a synthesis of modal controller was carried out. Modal control is defined as the control, which solves the problem of selection of the dynamic system's eigenspace. The spectrum selection for the multi-connected systems results in an unpleasant problem of manipulation of a big number of eigenvalues, which significantly complicates the process of studying their influence on the behavior of a dynamic system. The main problem of a practical modal synthesis consists in an excessive number of the parameters affecting the systems with different properties. The synthesis was carried out on the basis of the modal dominance measures, which reduce the choice of many eigenvalues to selection of one or more parameters describing the spectrum compression. Modal dominance measures give a formal assessment of the eigenvalues' mobility and allow us to control quantitatively the spectrum change trends during the synthesis. It was demonstrated that an analytical solution to the problem was possible both with a single and iterative shifting of the eigenvalues, one after another, when it was possible to estimate the modal dominance measure of each eigenvalue and the rate of the modal controller feedback gain matrix with a single spectrum change. The parameters of the transition process in a closed system of the single crystal growth control show that the synthesized system meets the requirements for a quality control. It is known that in the production conditions the growth process is exposed to the transient conditions of the thermal perturbations, which may result in inhomogeneous distribution of the activator within the length of the crystal. This process impairs the single crystal's quality. A closed system with a synthesized regulator has a quick dominant eigenvalue in the channel of the single crystal diameter control, which allows the closed system to respond to such a perturbation and reduce its impact on the crystal's quality. The synthesis emphasizes the main idea that adaptation of the eigenspace in the dynamic systems is justified. It should only be carried out with the involvement of the analysis at the first stage of the synthesis procedure.

Keywords: modal control, modal dominance, single crystal growth control

For citation:
Balonin N. A., Suzdal V. S., Kozmin Yu. S., Tonkoshkur V. N. Modal Control Synthesis in Single Crystal Growth Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2015, vol. 16, no. 7, pp. 443—448.
DOI: 10.17587/mau.16.443-448

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