Synthesis of modal control of multidimensional crystallization process by van der woude

Authors

  • Юрий Семенович Козьмин Institute for Scintillation Materials, NAS of Ukraine Lenina 60, Kharkov, 61001, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2014.23384

Keywords:

optimization, modal control, single crystal, crystallization, parameterization, synthesis of regulators, multilinked process

Abstract

Using the systems of non-adaptive control, in particular, modal for high-quality control over linear dynamic objects is discussed and some results of our research in this area are given in the paper.

The primary objective of the study is to solve the problem of modal control synthesis for a multidimensional object based on the Van der Woyd’s generalized approach, as well as on using the knowledge in the field of control, obtained from different sources, for the process of growing single crystals using the Czochralski method on the “GROWTH”-type setups. Using modern methods and tools for analyzing the properties of linear controllable systems leads to the need of using modal controllability of the system and solving the problem of synthesis of modal control over the multidimensional object.

In the paper, generalization of the Van der Woyd’s theorem in terms of band matrices for the case of MIMO-system modal control is given in the form of the algorithm, difference vectors of coefficients of specified and initial characteristic polynomials with respect to the growing process as the control object are described and parameterized. Using the graphical representation of the transfer characteristics of the object and closed-loop system in trajectory areas for analysis allows to obtain important information about the high-quality system control.

It is proposed to use this method for increasing the dynamic quality of control over inertial objects, which is the process of growing crystals in order to increase the efficiency of control systems for modern growth setups in conditions of producing these crystals.

The research results can be applied by specialists in the field of modal control over material, energy and information flows in control systems for modern technological processes, integrated into the technical environment of these processes

Author Biography

Юрий Семенович Козьмин, Institute for Scintillation Materials, NAS of Ukraine Lenina 60, Kharkov, 61001

Laboratory of control systems

References

  1. Wonham, W. M. On Pole Assignment in Multi-Input Controllable Linear Systems [Text] / W. M. Wonham // IEEE Trans. Automat. Control. – 1967. – Vol. AC-12, № 6. – P. 660–667.
  2. Simon, D. D. A Theory of Modal Control [Text] / D. D. Simon, S. K. Mitter // Inform. Contr. – 1968. – Vol. 13. – P. 316–353.
  3. Kalman, R. E. Controllability of linear dynamical systems [Text] / R. E. Kalman, Y. C. Ho, K. S. Narendra // Contrib. Differ. Equations. – 1962. – Vol. 1(2). – P. 189–213.
  4. Ackermann, J. Der Entwurf Linearer Regelungssysteme im Zustandsraum [Text] / J. Ackermann // Regelungestechnik und Prozessedaten verarbeitung. – 1972. – Vol. 7. – P. 297–300.
  5. Van der Woude, J. W. A note on pole placement by static output feedback for single input systems [Text] / J. W. Van der Woude // Systems & Control Letters. – 1988. – Vol. 11. – P. 285–287.
  6. Буков, В. Н. Решение матричных уравнений методом канонизации [Текст] / В. Н. Буков, В. Н. Рябченко, В. В. Косъянчук, Е. Ю. Зыбин // Вестник Киевского ун-та. Сер. Физ.-матем. Науки. – 2002. – Вып. 1. – С. 19–28.
  7. Мисриханов, М. Ш. Ленточные критерии управляемости и наблюдаемости линейных динамических систем [Текст] / М. Ш. Мисриханов // А и Т. – 2005. – № 2. – С. 93–104.
  8. Мисриханов, М. Ш. Анализ и синтез линейных динамических систем на основе ленточных формул [Текст] / М. Ш. Мисриханов, В. Н. Рябченко // Вестник ИГЭУ. – 2009. – № 2. – С. 81–84.
  9. Мисриханов, М. Ш. Метод синтеза стабилизирующего управления динамической системой на основе развития идеи Ван дер Воуда [Текст] / М. Ш. Мисриханов, В. Н. Рябченко // Повышение эффективности работы энергосистем. Труды ИГЭУ. Системы управления и автоматизации. – 2009. – Вып. IX. – C. 383–399.
  10. Горилецкий, В. И. Рост кристаллов [Текст]: монография / В. И. Горилецкий, Б. В. Гринев, Б. Г. Заславский и др. – Х.: АКТА,
  11. – 535 с.
  12. Wonham, W. (1967). On pole assignment in multi-input controllable linear systems. IEEE Trans. Automat. Control, Vol. 12, 660–667.
  13. Simon, D., Mitter, S. (1968). A theory of modal control. Inform. Control, Vol. 13, 316–353.
  14. Kalman, R., Ho, Y., Narendra, K. (1962). Controllability of linear dynamical systems Contrib. Differ. Equations, Vol. 1 (2), 189–213.
  15. Ackermann, J. (1972). Der entwurf linearer regelungssysteme im zustandsraum. Regelungestechnik und Prozessedaten verarbeitung, Vol. 7, 297–300.
  16. Van der Woude, J. (1988). A note on pole placement by static output feedback for single input systems. Systems & Control Letters, Vol. 11, 285–287.
  17. Bukov, V., Ryabchenko, V., Kosyanchuk, V., Zibin, Ye. (2002). Resheniye matrichnikh uravneniy metodom kanonizatsii. Vestnik Kievskogo universiteta. Seriya : Phiz.-mathem. Nauki, Issue 1, 19–28.
  18. Misrikhanov, M. (2005). Lentochnie kriterii upravlyayemosti i nabludayemosti lineynikh dinamicheskikh system. А & Т, 2, 93–104.
  19. Misrikhanov, M., Ryabchenko, V. (2009). Analiz i cintez lineynikh dinamicheskikh sistem na osnove lentochnikh formul. Vestnik IGEU, 2, 81–84.
  20. Misrikhanov, M., Ryabchenko, V. (2009). Metod sinteza stabiliziruyushego upravleniya dinamicheskoy sistemoy na osnove razvitiya idei Van der Vouda. Trudi IGEU. Sistemi upravleniya i avtomatizatsii, Issue IX, 383–399.
  21. Goriletsky, V., Grinev, B., Zaslavsky, B. (2002). Rost kristallov. Kharkov: AKTA, 535.

Downloads

Published

2014-04-14

How to Cite

Козьмин, Ю. С. (2014). Synthesis of modal control of multidimensional crystallization process by van der woude. Eastern-European Journal of Enterprise Technologies, 2(2(68), 68–72. https://doi.org/10.15587/1729-4061.2014.23384

Issue

Vol. 2 No. 2(68) (2014): Information technology. Industry control systems

Section

Industry control systems

License

Copyright (c) 2014 Юрий Семенович Козьмин

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.