تعريف أنظمة التحكم الديناميكية الخطية فى صورة فضاء الحالة

المؤلفون

  • محمود نوح زقوط قسم الهندسة الكهربائية والالكترونية، كلية الهندسة، جامعة مصراتة، ليبيا

DOI:

https://doi.org/10.59743/jau.v8i4.1950

الكلمات المفتاحية:

تعريف الأنظمة، الأنظمة الخطية، نموذج فضاء الحالة، تشويش القياس، تقدير المعاملات

الملخص

تزايد الاهتمام بمجال تعريف الأنظمة في المجالات الهندسة على مدار الستين عامًا الماضية، حيث شهدت نشر العديد من البحوث المكثفة حولها. تقدم هذه الدراسة طريقة تعريف للأنظمة الخطية الديناميكية المستمرة ذات المعاملات الثابتة مباشرة من سلسلة بيانات زمنية. يتم تمثيل النظام الخطى في صورة فضاء الحالة، مع فرضية أن جميع متغيرات الحالة قابلة للقياس. أوضحت الدراسة خوارزمية التعريف المقترحة وخطوات اشتقاقها واختبارها باستخدام بيانات خالية من التشويش وبيانات مشوشة، في بيئة محاكاة بالماتلاب. كما أكدت النتائج المتحصل عليها أن الخطوات البسيطة للخوارزمية المقترحة تعطي تقدير فعال وناجح لمصفوفات معاملات النظام.

المراجع

M. Moonen, B. De Moor, L. Vandenberghe, and J. Vandewalle, "On- and Off-Line Identification of Linear State-Space Models," International Journal of Control, vol. 49, no.1, pp. 219-232, 1989. DOI: https://doi.org/10.1080/00207178908559631

D. Park and S-K. Hong, "On-line System Identification using State Observer," Kintex, Gyeonggi-Do, Korea, June 2-5, 2005.

N. K. Sinha and B. Kuszta, Modeling and Identification of Dynamic systems, Van Nostrand Reinhold Company Inc, New York, Cincinnati, Toronto, London, Melbourne, 1983.

S. Ahmed, "Identification from Step Response – The Integral Equation Approach," The Canadian Journal for Chemical Engineering, vol. 94, pp. 2243-2256, 2016. DOI: https://doi.org/10.1002/cjce.22645

Q. G. Wang, X. Guo, and Y. Zhang, "Direct identification of continuous time delay systems from step response," Journal of Process Control, vol 11, pp. 531–542, 2001. DOI: https://doi.org/10.1016/S0959-1524(00)00031-7

Q. Bi, W. Cai, E. L. Lee, Q. G. Wang, C. C. Hang, Y. Zhang, "Robust identification of first-order plus dead-time model from step response," Control Engineering Practice, vol. 7, no. 1, pp. 71–77, 1999. DOI: https://doi.org/10.1016/S0967-0661(98)00166-X

S. Ahmed, B. Huang, and S. L. Shah, "Identification from step responses with transient initial conditions," Journal of Process Control, vol. 18, no. 2, pp. 121–130, 2008. DOI: https://doi.org/10.1016/j.jprocont.2007.07.009

S. Hwang, and S. Lai, "Use of Two-Stage Least-Squares Algorithm for identification of Continuous Systems with Time Delay Based on Pulse Response," Automatica, vol. 40, no. 9, pp. 1561-1568, 2004. DOI: https://doi.org/10.1016/j.automatica.2004.03.017

S. Ahmed, "Continuous-Time Identification Using Sinusoidal Inputs: An Integral Equation Approach," Industrial & Engineering Chemistry Research, vol. 53, pp. 13065−13072, 2014. DOI: https://doi.org/10.1021/ie403162e

X. G. Liu, and J. Lu, "Least squares based iterative identification for a class of multirate systems," Automatica, vol. 46, no. 3, pp.549–554, 2010. DOI: https://doi.org/10.1016/j.automatica.2010.01.007

F. Ding, and T. Chen, "Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 3, pp. 555–566, 2005. DOI: https://doi.org/10.1109/TCSI.2004.842874

J. R. Deller, M. Nayeri, and S. F. Odeh, "Least-squares identification with error bounds for real-time signal processing and control," Proceedings of the IEEE, vol. 81, no. 6, pp. 815–849, 1993. DOI: https://doi.org/10.1109/5.257681

J. Zhou, Y. Zhu, X. R. Li, and Z. You, "Exactly Initialized Recursive Least Squares," In Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2001, pp. 3318–3323.

Y. Zhu, and X. R. Li, "Recursive Least Squares with Linear Constraints," Communications in Information and Systems, vol. 7, no. 3, pp. 287–312, 2007. DOI: https://doi.org/10.4310/CIS.2007.v7.n3.a5

F. Ding, G. Liu, and X. P. Liu, "Partially coupled stochastic gradient identification methods for non-uniformly sampled systems," IEEE Transactions on Automatic Control, vol. 55, no. 8, pp. 1976–1981, 2010. DOI: https://doi.org/10.1109/TAC.2010.2050713

J. Ding, Y. Shi, H.G. Wang, and F. Ding, "A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems," Digital Signal Processing, vol. 20, no. 4, pp. 1238–1249, 2010. DOI: https://doi.org/10.1016/j.dsp.2009.10.023

L. L. Han, and F. Ding, "Multi-innovation stochastic gradient algorithms for multi-input multi-output systems," Digital Signal Processing, vol. 19, no. 4, pp. 545–554, 2009. DOI: https://doi.org/10.1016/j.dsp.2008.12.002

D. Q. Wang, and F. Ding, "Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems," Digital Signal Processing, vol. 20, no. 3, pp. 750–762, 2010. DOI: https://doi.org/10.1016/j.dsp.2009.09.002

Y. J. Liu, Y. S. Xiao, and X. L. Zhao, "Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model," Applied Mathematics and Computation, vol. 215, no. 4, pp. 1477–1483, 2009. DOI: https://doi.org/10.1016/j.amc.2009.07.012

L. Xie, Y.J. Liu, H.Z. Yang, and F. Ding, "Modeling and identification for non-uniformly periodically sampled-data systems," IET Control Theory & Applications, vol. 4, no. 5, pp. 784–794, 2010. DOI: https://doi.org/10.1049/iet-cta.2009.0064

F. Ding, P. X. Liu, and G. Liu, "Multi-innovation least squares identification for linear and pseudo-linear regression models," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no.3, pp. 767–778, 2010. DOI: https://doi.org/10.1109/TSMCB.2009.2028871

Y.J. Liu, L. Xie, and F. Ding, "An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 223, pp. 445–454, 2009. DOI: https://doi.org/10.1243/09596518JSCE686

L. L. Han, J. Sheng, F. Ding, and Y. Shi, "Auxiliary model identification method for multirate multi-input systems based on least squares," Mathematical and Computer Modelling, vol. 50, no. 7–8, pp. 1100–1106, 2009. DOI: https://doi.org/10.1016/j.mcm.2009.06.002

H. Q. Han, L. Xie, F. Ding, and X. G. Liu, "Hierarchical least squares based iterative identification for multivariable systems with moving average noises," Mathematical and Computer Modelling, vol. 51, no. 9–10, pp. 1213–1220, 2010. DOI: https://doi.org/10.1016/j.mcm.2010.01.003

L. L. Xiang, L. B. Xie, and R. F. Ding, "Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model," Mathematical and Computer Modelling, vol. 52, no. 5–6, pp. 918–924, 2010. DOI: https://doi.org/10.1016/j.mcm.2010.05.025

F. Ding, P. X. Liu, and G. Liu, "Gradient based and least-squares based iterative identification methods for OE and OEMA systems," Digital Signal Processing, vol. 20, no. 3, pp. 664–677, 2010. DOI: https://doi.org/10.1016/j.dsp.2009.10.012

Y. J. Liu, D. Q. Wang, and F. Ding, "Least-squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data," Digital Signal Processing, vol. 20, no. 5, pp. 1458–1467, 2010. DOI: https://doi.org/10.1016/j.dsp.2010.01.004

F. Ding, and T. Chen, "On iterative solutions of general coupled matrix equations," SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 2269–2284, 2006. DOI: https://doi.org/10.1137/S0363012904441350

F. Ding, P.X. Liu, and J. Ding, "Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle," Applied Mathematics and Computation, vol. 197, no. 1, pp. 41–50, 2008. DOI: https://doi.org/10.1016/j.amc.2007.07.040

L. Xie, J. Ding, and F. Ding, "Gradient based iterative solutions for general linear matrix equations," Computers & Mathematics with Applications, vol. 58, no. 7, pp. 1441–1448, 2009. DOI: https://doi.org/10.1016/j.camwa.2009.06.047

E. Ikonen and K. Najim, Advanced Process identification and Control. Marcel Dekker, Inc, New Yourk, 2002. DOI: https://doi.org/10.1201/9781482294699

R. A. Ricco, "Identification of Dynamical Systems in State-Space; Gray-Box Approaches," PhD Thesis, University of Minas Gerais (UFMG), Belo Horizonte, Brazil, 2019.

S. Privara, J. Cigler, Z. Vaná, and L. Ferkl, "Incorporation of System Steady State Properties into Subspace Identification Algorithm," International Journal of Modelling, Identification and Control, vol. 16, no. 2, pp.159–167, 2012. DOI: https://doi.org/10.1504/IJMIC.2012.047123

A. Alenany, and H. Shang, "Recursive Subspace Identification with Prior Information Using the Constrained Least Squares Approach," Computers & Chemical Engineering, vol. 54, pp. 174–180, 2013. DOI: https://doi.org/10.1016/j.compchemeng.2013.03.016

Y. Wang, L. Zhang, and Y. Zhao, "Improved Closed-Loop Subspace Identification with Prior Information," International Journal of Systems Science, vol. 49, no. 9, 1821-1835 2018. DOI: https://doi.org/10.1080/00207721.2018.1460409

التنزيلات

منشور

27-12-2023

كيفية الاقتباس

زقوط م. ن. (2023). تعريف أنظمة التحكم الديناميكية الخطية فى صورة فضاء الحالة. مجلة الجامعة الأسمرية, 8(4), 182–195. https://doi.org/10.59743/jau.v8i4.1950