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Анотація
This article is devoted to the development of a new method of synthesis a regulators’ transfer functions matrix of an optimal multivariable open-loop control system. The regulator is designed to maximize an accuracy of a nonlinear multivariable control object transition from one steady state to another. It is assumed that disturbances act on the control object and sensors measuring data has inertia and noise. Both disturbances and noises are an additive combination of regular and random components. Random components belong to a class of interconnected stationary processes with rational spectral density matrices. A substantiated method differs from the known one by the fact that during formulation and solution of the problem somebody uses a new block diagram of the control system, which takes into account the results of metrological certification of a sensor dynamics. Synthesis of the regulator is carried out in the frequency domain by the Wiener-Kolmogorov method. A new algorithm, which is obtained as a result of synthesis problem solution, allows you to find the matrix of regulator transfer functions , which provides a minimum of corresponding quadratic quality criteria’s. The first of them is equal to the sum of certain way weighted squared deviations regular repetition errors of the object path and control signals. The second criterion is equal to the sum of the weighted variance of the random error components and the control signals. To execute the proposed algorithm it is necessary to perform the operations of Wiener factorization and separation of rational matrices. The corresponding functions are contained in the freely distributed software package SciLab.
Ключові слова:
Оптимальный, управление, объект, матрица, факторизация, дисперсия, стохастический
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Як цитувати
Блохин, Л., Осадчий, С., & Зозуля, В. (2017). АНАЛИТИЧЕСКОЕ КОНСТРУИРОВАНИЕ РАЗОМКНУТЫХ СИСТЕМ СТОХАСТИЧЕСКОГО УПРАВЛЕНИЯ МНОГОМЕРНЫМ НЕЛИНЕЙНЫМ ОБЪЕКТОМ. Automation of Technological and Business Processes, 8(3). https://doi.org/10.15673/atbp.v8i3.570
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Розділ
ПИТАННЯ ТЕОРІЇ, МЕТОДИ ТА АЛГОРИТМИ ЕФЕКТИВНОГО АВТОМАТИЧНОГО УПРАВЛІННЯ ОБ’ЄКТАМИ ХІМІКО-ТЕХНОЛОГІЧНОГО ТИПУ
Посилання
References
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/ S. I. Osadchy, V. A. Zozulya, A. S. Timoshenko // Proceedings of the 7th IEEE International Conference on Intelligent
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[3] Blokhin L.N., Zhytetskyy L.S. Nelyneynye optymalʹnye systemy skhastycheskoy stabylyzatsyy // Kybernetyka y
vychyslytelʹnaya tekhnyka. – 2003. – Vyp. 139.-S.12-23.
[4] Osadchiy S.I. Kombinirovannyiy metod sinteza optimalnyih sistem stabilizatsii mnogomernyih podvizhnyih ob'ektov pri
statsionarnyih sluchaynyih vozdeystviyah / S.I. Osadchiy, V.A. Zozulya. // Mezhdunarodnyiy nauchnotehnicheskiy
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[5] Blokhin L.N. Tekhnolohyy konstruyrovanyya sovremennykh konkurentosposobnykh kompleksov upravlenyya
stokhastycheskym dvyzhenyem obʺektov / Osadchyy S.Y., Dydyk O.K., Rudyuk H.Y. - Kyrovohrad: Yzdatelʹ Lysenko
V.F., 2015. – 284 s. ISBN 978-617-7197-30-9
[6] Optymalʹni ta robastni systemy keruvannya tekhnolohichnymy obʺyektamy : monohrafiya / N.M. Lutsʹka, A.P. Ladanyuk
- K.: Vydavnytstvo Lira-K, 2015. – 288s.
[7] Osadchiy S.I. Structural Identification of Unmanned Supercavitation Vehicle Based on Incomplete Experimental Data /
S.I. Osadchiy, V.M. Kalich, O.K. Didyk // Proceedings of the 2013 IEEE 2nd
International Conference ―Actual Problems
of Unmanned Air Vehicles Developments‖, Kyiv, 2013, pp. 93-95
[8] Blokhin L.M., Safronova I.YU. Novyy metod strukturnoyi identyfikatsiyi modeley dynamiky rukhomykh obʺyektiv v
shtatnykh rezhymakh funktsionuvannya// Vesnik PNTS TAU. -2003, -Vyp. 6 – S.60-62.
[9] Gantmaher F.R. Teoriya matrits/ F.R.Gantmaher -4-e izd.- M.: Nauka, 1988.- 552s.
[10]Azarskov V.N. Metodologiya konstruirovaniya optimalnyih sistem stohasticheskoy stabilizatsii: Monografiya / V.N.
Azarskov, L.N. Blohin, L.S. Zhitetskiy / Pod red. Blohina L.N. – K.: Knizhnoe izdatelstvo NAU, 2006. – 440s.
[11]Davis M.C. Factoring the spectral matrix// IEEE Trans. Automat. Cointr. – 1963.- AC-8, N 4. – p. 296-305.
[1] Osadchy S. I. The dynamic characteristics of the mechanism with parallel kinematic structure based on experimental data
/ S. I. Osadchy, V. A. Zozulya, A. S. Timoshenko // Proceedings of the 7th IEEE International Conference on Intelligent
Data Acquisition and Advanced Computing Systems (IDAACS’2013), Berlin, Germany, 2013, vol. 2, pp. 905-911.
[2] Feldbaum A.A. Osnovyi teorii optimalnyih avtomaticheskih sistem/ Feldbaum A.A. – M.: Nauka, 1966. – 623s.
[3] Blokhin L.N., Zhytetskyy L.S. Nelyneynye optymalʹnye systemy skhastycheskoy stabylyzatsyy // Kybernetyka y
vychyslytelʹnaya tekhnyka. – 2003. – Vyp. 139.-S.12-23.
[4] Osadchiy S.I. Kombinirovannyiy metod sinteza optimalnyih sistem stabilizatsii mnogomernyih podvizhnyih ob'ektov pri
statsionarnyih sluchaynyih vozdeystviyah / S.I. Osadchiy, V.A. Zozulya. // Mezhdunarodnyiy nauchnotehnicheskiy
zhurnal «Problemyi upravleniya i informatiki». – 2013. - #3. – S. 40-49.
[5] Blokhin L.N. Tekhnolohyy konstruyrovanyya sovremennykh konkurentosposobnykh kompleksov upravlenyya
stokhastycheskym dvyzhenyem obʺektov / Osadchyy S.Y., Dydyk O.K., Rudyuk H.Y. - Kyrovohrad: Yzdatelʹ Lysenko
V.F., 2015. – 284 s. ISBN 978-617-7197-30-9
[6] Optymalʹni ta robastni systemy keruvannya tekhnolohichnymy obʺyektamy : monohrafiya / N.M. Lutsʹka, A.P. Ladanyuk
- K.: Vydavnytstvo Lira-K, 2015. – 288s.
[7] Osadchiy S.I. Structural Identification of Unmanned Supercavitation Vehicle Based on Incomplete Experimental Data /
S.I. Osadchiy, V.M. Kalich, O.K. Didyk // Proceedings of the 2013 IEEE 2nd
International Conference ―Actual Problems
of Unmanned Air Vehicles Developments‖, Kyiv, 2013, pp. 93-95
[8] Blokhin L.M., Safronova I.YU. Novyy metod strukturnoyi identyfikatsiyi modeley dynamiky rukhomykh obʺyektiv v
shtatnykh rezhymakh funktsionuvannya// Vesnik PNTS TAU. -2003, -Vyp. 6 – S.60-62.
[9] Gantmaher F.R. Teoriya matrits/ F.R.Gantmaher -4-e izd.- M.: Nauka, 1988.- 552s.
[10]Azarskov V.N. Metodologiya konstruirovaniya optimalnyih sistem stohasticheskoy stabilizatsii: Monografiya / V.N.
Azarskov, L.N. Blohin, L.S. Zhitetskiy / Pod red. Blohina L.N. – K.: Knizhnoe izdatelstvo NAU, 2006. – 440s.
[11]Davis M.C. Factoring the spectral matrix// IEEE Trans. Automat. Cointr. – 1963.- AC-8, N 4. – p. 296-305.