Estimating Industrial Process Stability by Whitney's Singularity Theory When Choosing a Sufficient Time-Sampling Frequency of the Control Signal
- 作者: Rabotnikov M.A1, Stafeichuk B.G1, Shumikhin A.G1
-
隶属关系:
- Perm National Research Polytechnic University
- 期: 编号 6 (2022)
- 页面: 35-41
- 栏目: Control of Technical Systems and Industrial Processes
- URL: https://journal-vniispk.ru/1819-3161/article/view/351149
- DOI: https://doi.org/10.25728/pu.2022.6.4
- ID: 351149
如何引用文章
全文:
详细
In this paper, we estimate the stability of continuous-type automated industrial processes and choose a sufficient time-sampling frequency of the control signal using Whitney’s singularity theory. The proposed stability analysis approach is based on constructing typical bifurcations for the historical data of a technological object under different time-sampling frequencies of its control signal. The singularity equation serves for obtaining the equation of the equilibrium state curves of the system and a sufficient time-sampling frequency of the control signal corresponding to the vertex of the resulting curve. As an illustrative example, the developed method is applied to the control system of the mass balance stripping section in the purification process of a styrene distillation column of the ethylbenzene, styrene, and polystyrene plants. Based on the quantitative analysis results, we construct a bifurcation and determine a sufficient time-sampling frequency of the control signal to ensure system stability.
作者简介
M. Rabotnikov
Perm National Research Polytechnic University
编辑信件的主要联系方式.
Email: rabotnikovma@gmail.com
Perm, Russia
B. Stafeichuk
Perm National Research Polytechnic University
Email: bgstaf@mail.ru
Perm, Russia
A. Shumikhin
Perm National Research Polytechnic University
Email: shumichin@gmail.com
Perm, Russia
参考
- Зиненко А.В. Теория катастроф и ценовая динамика // Экономика и математические методы. – 2018. – T. 54, № 4. – С. 116–123. [Zinenko, A.V. Catastrophe Theory and Price Dynamics // Economic and Mathematical methods. – 2018. – Vol. 54, no. 4. – P. 116–123. (In Russian)]
- Неделько Н.С. Использование теории катастроф к анализу поведения экономических систем // Вестник МГТУ. – 2010. – T. 13, № 1. – С. 223–227. [Nedelko, N.S. Catastrophe Theory and Analysis of Economic Systems Behavior // Vestnik of MSTU. – 2010. – Vol. 13, no. 1. – P. 223–227. (In Russian)]
- Schmitt, N., Tramontana, F., Westerhoff, F. Nonlinear Asset-price Dynamics and Stabilization Policies // Nonlinear Dynamics. – 2020. – No. 102. – P. 1045–1070.
- Мужиков Г.П., Гилев М.А. Анализ динамических систем с использованием элементов теории бифуркаций // Современные тенденции развития и перспективы внедрения инновационных технологий в машиностроении, образовании и экономике. – 2017. – T. 3, № 1 (2). – С. 35–37. [Muzhikov, G.P., Gilev, M.A. Analysis of Dynamic Systems Using Elements of the Theory of Bifurcations // Economic and Mathematical Methods. – 2017. – Vol. 3, no. 1 (2). – P. 35–37. (In Russian)]
- Qin, L., Qin, H., Xing, J. Energy Flow Characteristics of Friction-Induced Nonlinear Vibrations in a Water-Lubricated Bearing-Shaft Coupled System // Acta Mechanica Sinica. – 2021. – No. 37. – P. 679–704.
- Skorobogatov, S.M. Catastrophes and Serviceability of Reinforced Concrete Structures (Classification and Elements of Theory). – Ekaterinburg: Ural'skii gosudarstvennyi universitet putei soobshcheniya, 2020. – 532 p.
- Hassard, B., Kazarinov, D., Wan, Y. Theory and Applications of Hopf Bifurcation. – Cambridge: Cambridge University Press, 1982. – 320 p.
- Острейковский В.А. Анализ устойчивости и управляемости динамических систем методами теории катастроф. Учебное пособие. – М.: Высшая Школа, 2005. – 560 с. [Ostreikovskii, V.A. Analiz ustoichivosti i upravlyaemosti dinamicheskikh sistem metodami teorii katastrof. Uchebnoe posobie. – Moscow: Vysshaya Shkola, 2005. – 560 s. (In Russian)]
- Черешко А.А., Шундерюк М.М. Границы применимости алгоритмов усовершенствованного управления с прогнозирующей моделью в условиях неопределенности объекта управления // Проблемы управления. – 2020. – № 1. – С. 17–23. [Chereshko, A.A., Shunderyuk, M.M. Applicability Limits of Model-Based Predictive Control Algorithms Under Uncertain Control Object Dynamics // Control Sciences. – 2020. – No. 1. – P. 17–23. (In Russian)]
- Бахтадзе Н.Н., Лотоцкий В.А. Современные методы управления производственными процессами // Проблемы упраления. – 2009. – № 3. – С. 56–63. [Bakhtadze, N.N., Lototskii, V.A. Contemporary Methods of Production Process Control // Control Sciences. – 2009. – No. 3. – P. 56–63. (In Russian)]
- Арнольд В.И. Теория катастроф. – М.: Наука. Гл. ред. физ.-мат. лит., 1990. – 128с. [Arnold, V.I. Catastrophe Theory. – Moscow: Nauka. Gl. red. fiz.-mat. lit., 1990. – 128 s. (In Russian)]
- Iooss, G., Joseph, D. Elementary Stability and Bifurcation Theory. – New York: Springer, 2014. – 286 p.
- Москаленко А.В., Тетуев Р.К., Махортых С.А. О состоянии исследований бифуркационных феноменов памяти и запаздывания // Препринты ИПМ им. М.В. Келдыша. – 2019. – № 109. – С. 1–44. [Moskalenko, A.V., Tetuev, R.K., Makhortyk, S.A. On Studies of Bifurcation Phenomena such as Memory and Delay // Preprinty IPM im. M.V. Keldysha. – 2019. – No. 109. – P. 1–44. (In Russian)]
- Работников М.А. Стратегия реализации управления материальным балансом исчерпывающей части ректификационной колонны получения стирола // Химия. Экология. Урбанистика.: материалы Всерос. науч.-практ. конф. – Пермь, 2021. – Т. 4. – С. 242–246. [Rabotnikov, M.A. Strategy of Material Balance Control Implementation of the Styrene Rectifying Column Bottom // Chemistry. Ecology. Urbanism.: Proceedings of the All-Russian Scientific and Practical Conference. – Perm, 2021. – Vol. 4 – P. 242–246. (In Russian)]
补充文件
