ntvНаучно-технический вестник информационных технологий, механики и оптикиScientific and Technical Journal of Information Technologies, Mechanics and Optics2226-14942500-0373Университет ИТМО10.17586/2226-1494-2022-22-4-666-673ntv-150Research ArticleАВТОМАТИЧЕСКОЕ УПРАВЛЕНИЕ И РОБОТОТЕХНИКАAUTOMATIC CONTROL AND ROBOTICSКомпенсация внешних возмущений для многоканальных систем с запаздыванием в управленииCompensation of external disturbances for MIMO systems with control delayhttps://orcid.org/0000-0001-6430-1927НгуенХ. Т.NguyenKh. T.

Нгуен Хак Тунг — аспирант

Санкт-Петербург, 197101

Khac T. Nguyen — PhD Student

Saint Petersburg, 197101

nguyenkhactunghvhq1994@gmail.comhttps://orcid.org/0000-0002-8345-7553ВласовС. М.VlasovS. M.

Власов Сергей Михайлович — кандидат технических наук, доцент

sc 55355689600

Санкт-Петербург, 197101

Sergey M. Vlasov — PhD, Associate Professor

sc 55355689600

Saint Petersburg, 197101

smvlasov@itmo.ruhttps://orcid.org/0000-0001-8806-4057ПыркинА. А.PyrkinA. A.

Пыркин Антон Александрович — доктор технических наук, профессор, профессор, декан факультета

sc 26656070700

Санкт-Петербург, 197101

Anton A. Pyrkin — D. Sc., Full Professor, Dean of Faculty

sc 26656070700

Saint Petersburg, 197101

a.pyrkin@gmail.comhttps://orcid.org/0000-0002-1504-5856СкобелеваА. В.SkobelevaA. V.

Скобелева Александра Викторовна — студент

Санкт-Петербург, 197101

Aleksandra V. Skobeleva — Student

Saint Petersburg, 197101

skala.job@gmail.comУниверситет ИТМОРоссияITMO UniversityRussian Federation202214122024224666673Copyright © Нгуен Х.Т., Власов С.М., Пыркин А.А., Скобелева А.В., 20242024Нгуен Х.Т., Власов С.М., Пыркин А.А., Скобелева А.В.Nguyen K.T., Vlasov S.M., Pyrkin A.A., Skobeleva A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ntv.elpub.ru/jour/article/view/150

Предмет исследования. Проблема компенсации внешних возмущающих воздействий для линейных многоканальных объектов с запаздыванием на входе является важной и актуальной. Предложено решение данной проблемы в задачах управления динамическими объектами и в ряде других задач. Метод. Предлагаемый метод основан на принципе внутренней модели, где необходима идентификация параметров возмущения. На первом этапе описана схема выделения возмущения, которое представлено как синусоидальный сигнал с неизвестной частотой, амплитудой и фазой. На втором этапе решена задача идентификации частот синусоидального и мультисинусоидального сигналов. На последнем этапе разработан алгоритм стабилизации и приведения состояния объекта к нулю, осуществленный с помощью обратной связи. Основные результаты. Представлена новая схема компенсации внешних возмущений для линейных многоканальных объектов с запаздыванием на входе. Предложен новый алгоритм идентификации частот мультисинусоидального сигнала. Выполнен анализ возможностей предложенного метода оценивания с использованием компьютерного моделирования в среде MATLAB Simulink. Практическая значимость. Разработанный метод может быть эффективно применен для широкого класса прикладных задач, связанных с управлением роботами, манипуляторами различного назначения.

The problem of compensation of external disturbing influences for MIMO system with input delay is important and relevant. A solution to this problem is proposed in the problems of dynamic objects control and in a number of others. The proposed method is based on the principle of an internal model and requires the identification of perturbation parameters. At the first stage, a scheme for extracting a disturbance is presented which is represented as a sinusoidal signal with an unknown frequency, amplitude, and phase. At the second stage, the problem of identifying the frequencies of a sinusoidal and multisinusoidal signal is solved. In the last stage, an algorithm for stabilizing the state of the object to zero is developed using feedback. A new scheme for compensating external disturbances for a MIMO system with an input delay is proposed. A new algorithm for identifying the frequencies of a multisinusoidal signal is proposed. The analysis of the possibilities of the proposed estimation method using computer simulation in the MATLAB Simulink environment is carried out. The developed method can be effectively applied to a wide class of applied tasks related to the control of robots and robotic manipulators for various purposes.

адаптивное управлениемногоканальные системыидентификациявнутренняя модельзапаздываниеadaptive controlMIMO systemsidentificationinternal modeldelayReferencesBobtsov A., Kremlev A. Adaptive compensation of biased sinusoidal disturbances with unknown frequency // IFAC Proceedings Volumes. 2005. V. 38. N 1. P. 131–136. https://doi.org/10.3182/20050703-6-CZ-1902.00022Bobtsov A., Kremlev A. Adaptive compensation of biased sinusoidal disturbances with unknown frequency. IFAC Proceedings Volumes, 2005, vol. 38, no. 1, pp. 131–136. https://doi.org/10.3182/20050703-6-CZ-1902.00022Nikiforov V.O. Adaptive nonlinear servocompensation of unknown external disturbances // IFAC Proceedings Volumes. 1999. V. 32. N 2. P. 4506–4511. https://doi.org/10.1016/S1474-6670(17)56768-3Nikiforov V.O. Adaptive nonlinear servocompensation of unknown external disturbances. IFAC Proceedings Volumes, 1999, vol. 32, no. 2, pp. 4506–4511. https://doi.org/10.1016/S1474-6670(17)56768-3Bobtsov A., Pyrkin A., Titov A., Kremlev A. Compensation of harmonic disturbance for nonlinear plant with parametric and functional uncertainty // IFAC Proceedings Volumes. 2011. V. 44. N 1. P. 1528–1533. https://doi.org/10.3182/20110828-6-IT-1002.02324Bobtsov A., Pyrkin A., Titov A., Kremlev A. Compensation of harmonic disturbance for nonlinear plant with parametric and functional uncertainty. IFAC Proceedings Volumes, 2011, vol. 44, no. 1, pp. 1528–1533. https://doi.org/10.3182/20110828-6-IT-1002.02324Nikiforov V. Adaptive non-linear tracking with complete compensation of unknown disturbances // European Journal of Control. 1998. V. 4. N 2. P. 132–139. https://doi.org/10.1016/S0947-3580(98)70107-4Nikiforov V. Adaptive non-linear tracking with complete compensation of unknown disturbances. European Journal of Control, 1998, vol. 4, no. 2, pp. 132–139. https://doi.org/10.1016/S0947-3580(98)70107-4Nik iforov V.O. Adaptive servocompensation of input disturbances // IFAC Proceedings Volumes. 1996. V. 29. N 1. P. 5114–5119. https:// doi.org/10.1016/S1474-6670(17)58492-XNikiforov V.O. Adaptive servocompensation of input disturbances. IFAC Proceedings Volumes, 1996, vol. 29, no. 1, pp. 5114–5119. https://doi.org/10.1016/S1474-6670(17)58492-XWang J., Vedyakov A., Vediakova A., Pyrkin A., Bobtsov A., Shavetov S. Output adaptive controller for a class of MIMO systems with input delay and multisinusoidal disturbance // IFAC-PapersOnLine. 2015. V. 48. N 11. P. 892–899. https://doi.org/10.1016/j.ifacol.2015.09.304Wang J., Vedyakov A., Vediakova A., Pyrkin A., Bobtsov A., Shavetov S. Output adaptive controller for a class of MIMO systems with input delay and multisinusoidal disturbance. IFAC-PapersOnLine, 2015, vol. 48, no. 11, pp. 892–899. https://doi.org/10.1016/j.ifacol.2015.09.304Olbrot A. Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays // IEEE Transactions on Automatic Control. 1978. V. 23. N 5. P. 887–890. https://doi.org/10.1109/TAC.1978.1101879Olbrot A. Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays. IEEE Transactions on Automatic Control, 1978, vol. 23, no. 5, pp. 887–890. https://doi.org/10.1109/TAC.1978.1101879Manitius A., Olbrot A. Finite spectrum assignment problem for systems with delays // IEEE Transactions on Automatic Control. 1979. V. 24. N 4. P. 541–552. https://doi.org/10.1109/TAC.1979.1102124Manitius A., Olbrot A. Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 1979, vol. 24, no. 4, pp. 541–552. https://doi.org/10.1109/TAC.1979.1102124Anderson R., Spong M. Bilateral control of teleoperators with time delay // IEEE Transactions on Automatic Control. 1989. V. 34. N 5. P. 494–501. https://doi.org/10.1109/9.24201Anderson R., Spong M. Bilateral control of teleoperators with time delay. IEEE Transactions on Automatic Control, 1989, vol. 34, no. 5, pp. 494–501. https://doi.org/10.1109/9.24201Krstic M., Smyshlyaev A. Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays // Systems and Control Letters. 2008. V. 57. N 9. P. 750–758. https://doi.org/10.1016/j.sysconle.2008.02.005Krstic M., Smyshlyaev A. Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Systems and Control Letters, 2008, vol. 57, no. 9, pp. 750–758. https://doi.org/10.1016/j.sysconle.2008.02.005Bresch-Pietri D., Krstic M. Adaptive trajectory tracking despite unknown input delay and plant parameters // Automatica. 2009. V. 45. N 9. P. 2074–2081. https://doi.org/10.1016/j.automatica.2009.04.027Bresch-Pietri D., Krstic M. Adaptive trajectory tracking despite unknown input delay and plant parameters. Automatica, 2009, vol. 45, no. 9, pp. 2074–2081. https://doi.org/10.1016/j.automatica.2009.04.027Pyrkin A.A., Bobtsov A.A., Nikiforov V.O., Vedyakov A.A., Kolyubin S.A., Borisov O.I. Output control approach for delayed linear systems with adaptive rejection of multiharmonic disturbance // IFAC Proceedings Volumes. 2014. V. 43. N 3. P. 12110–12115. https://doi.org/10.3182/20140824-6-ZA-1003.01787Pyrkin A.A., Bobtsov A.A., Nikiforov V.O., Vedyakov A.A., Kolyubin S.A., Borisov O.I. Output control approach for delayed linear systems with adaptive rejection of multiharmonic disturbance. IFAC Proceedings Volumes, 2014, vol. 43, no. 3, pp. 12110–12115. https://doi.org/10.3182/20140824-6-ZA-1003.01787Пыркин А.А., Бобцов А.А., Никифоров В.О., Колюбин С.А., Ведяков А.А., Борисов О.И., Громов В.С. Компенсация полигармонического возмущения, действующего на состояние и выход линейного объекта с запаздыванием в канале управления // Автоматика и телемеханика. 2015. № 12. С. 43–64.Pyrkin A.A., Bobtsov A.A., Nikiforov V.O., Kolyubin S.A., Vedyakov A.A., Borisov O.I., Gromov V.S. Compensation of polyharmonic disturbance of state and output of a linear plant with delay in the control channel. Automation and Remote Control, 2015, vol. 76, no. 12, pp. 2124–2142. https://doi.org/10.1109/TAC.2016.2614889Pyrkin A.A., Bobtsov A.A., Chepinskiy S.A., Kapitanyuk Y.A. Compensation of unknown multiharmonic disturbance for nonlinear plant with delay in control // IFAC Proceedings Volumes. 2010. V. 43. N 14. P. 481–486. https://doi.org/10.3182/20100901-3-IT-2016.00065Pyrkin A.A., Bobtsov A.A., Chepinskiy S.A., Kapitanyuk Y.A. Compensation of unknown multiharmonic disturbance for nonlinear plant with delay in control. IFAC Proceedings Volumes, 2010, vol. 43, no. 14, pp. 481–486. https://doi.org/10.3182/20100901-3-IT-2016.00065Wang J., Vedyakov A.A., Vediakova A.O., Pyrkin A.A., Bobtsov A.A., Shavetov S.V. Output adaptive controller for a class of MIMO Systems with input delay and multisinusoidal disturbance // IFAC-PapersOnLine. 2015. V. 48. N 11. P. 892–899. https://doi.org/10.1016/j.ifacol.2015.09.304Wang J., Vedyakov A.A., Vediakova A.O., Pyrkin A.A., Bobtsov A.A., Shavetov S.V. Output adaptive controller for a class of MIMO Systems with input delay and multisinusoidal disturbance. IFAC-PapersOnLine, 2015, vol. 48, no. 11, pp. 892–899. https://doi.org/10.1016/j.ifacol.2015.09.304Nikiforov V.O. Adaptive compensation of external disturbances // Control of Complex Systems: Preprint 125 / ed. by A.L. Fradkov, A.A. Stotsky. St. Petersburg: IPME, 1995. P. 34–40.Nikiforov V.O. Adaptive compensation of external disturbances. Control of Complex Systems: Preprint 125. Ed. by A.L. Fradkov, A.A. Stotsky. St. Petersburg, IPME, 1995, pp. 34–40.Johnson C.D. Accommodation of external disturbances in linear regulator and servomechanism problems // IEEE Transactions on Automatic Control. 1971. V. 16. N 6. P. 635–644. https://doi.org/10.1109/TAC.1971.1099830Johnson C.D. Accommodation of external disturbances in linear regulator and servomechanism problems. IEEE Transactions on Automatic Control, 1971, vol. 16, no. 6, pp. 635–644. https://doi.org/10.1109/TAC.1971.1099830Francis D.A., Wonham W.M. The internal model principle for linear multivariable regulators // Applied Mathematics and Optimization. 1975. V. 2. N 2. P. 170–194. https://doi.org/10.1007/BF01447855Francis D.A., Wonham W.M. The internal model principle for linear multivariable regulators. Applied Mathematics and Optimization, 1975, vol. 2, no. 2, pp. 170–194. https://doi.org/10.1007/BF01447855Nikiforov V.O. Adaptive servomechanism controller with an implicit reference model // International Journal of Control. 1997. V. 68. N 2. P. 277–286. https://doi.org/10.1080/002071797223604Nikiforov V.O. Adaptive servomechanism controller with an implicit reference model. International Journal of Control, 1997, vol. 68, no. 2, pp. 277–286. https://doi.org/10.1080/002071797223604Никифоров В.О. Адаптивное и робастное управление с компенсацией внешних возмущений. СПб.: Наука, 2003. 282 с.Nikiforov V.O. Adaptive and Robust Control with Compensation of the External Disturbances. St. Petersburg, Nauka Publ., 2003, 282 p. (in Russian)Никифоров В.О. Наблюдатели внешних детерминированных возмущений I. Объекты с известными параметрами // Автоматика и телемеханика. 2004. № 10. С. 13–24.Nikiforov V.O. Observers of external deterministic disturbances. I. Objects with known parameters. Automation and Remote Control, 2004, vol. 65, no. 10, pp. 1531–1541. https://doi.org/10.1023/B:AURC.0000044264.74470.48Нгуен Х.Т., Власов С.М., Пыркин А.А., Попков И.В. Новый алгоритм идентификации частоты синусоидального сигнала с постоянными параметрами // Научно-технический вестник информационных технологий, механики и оптики. 2022. Т. 22. № 1. С. 18–24. https://doi.org/10.17586/2226-1494-2022-22-1-18-24Nguyen Kh.T., Vlasov S.M., Pyrkin A.A., Popkov I.V. A new algorithm for the identification of sinusoidal signal frequency with constant parameters. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2022, vol. 22, no. 1, pp. 18–24. (in Russian). https://doi.org/10.17586/2226-1494-2022-22-1-18-24Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Performance enhancement of parameter estimators via dynamic regressor extension and mixing // IEEE Transactions on Automatic Control. 2017. V. 62. N 7. P. 3546–3550. https://doi.org/10.1109/TAC.2016.2614889Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Performance enhancement of parameter estimators via dynamic regressor extension and mixing. IEEE Transactions on Automatic Control, 2017, vol. 62, no. 7, pp. 3546–3550. https://doi.org/10.1109/TAC.2016.2614889

The authors declare that there are no conflicts of interest present.