Development of methods for identification of mathematical models for the technological objects with uncertainties
DOI:
https://doi.org/10.31548/energiya2019.04.056Abstract
Abstract. In the practical implementation of robust control methods for technological objects, a problem arose along with the identification of the mathematical model of the object, the identification of uncertainties. This raises several questions: the choice of the structure of uncertainties; calculation of the range of uncertainty.
The aim of the work is to develop generalized methods for identifying mathematical models of technological objects oriented to robust control. This will allow the efficient use of robust control systems and will lead to increased energy efficiency of the system as a whole.
Two methods for identifying mathematical models with interval uncertainties are proposed: empirical simple and with using randomization. The methodology is based on phased procedures, including the experiment, the identification of parameters in the nominal mode, as well as the identification of the interval uncertainty of the parameters of the mathematical model. The use of randomization methods, in particular bootstrap and jackknife at the stage of identification of the nominal model and interval uncertainty, allows to reducing the number and time of experiments, as well as increasing the accuracy of the estimates obtained. The advantages of both methods are the simplicity and intuitiveness of the obtained solutions.
Key words: mathematical model, identification, uncertainty, technological objectReferences
Lutska, N.M., Ladaniuk, A.P. (2015). Optymalni ta robastni systemy keruvannia tekhnolohichnymy ob'iektamy [Optimal and robust control systems for technological objects]. Kyiv, Ukraine: Lira-K, 288.
Ljung L. System Identification: Theory for the User, Second Ed. (1999). Prentice Hall PTR, 609.
Ljung L. and Vicino A. (2005) Special Issue on System Identification. IEEE Trans. Autom. Control, 50 (10). P. 1473.
https://doi.org/10.1109/TAC.2005.856638
Soderstrom T., Van Den Hof P., Wahlberg B. and Weiland S. (2005). Special Issue on Data Based Modelling and System Identification. Automatica, 41 (3), 357-362.
https://doi.org/10.1016/j.automatica.2004.11.004
Sippe G. Douma, Paul M.J. Van den Hof. (2005). Relations between uncertainty structures in identification for robust control. Automatica, 41 (3), 439-457.
https://doi.org/10.1016/j.automatica.2004.11.005
Sippe G. Douma, Paul M.J. Van den Hof. (2002). On the choice of uncertainty structure in identification for robust control. Proceeding of 41st IEEE conference on decision and control Las Vegas, Nevada USA, 4197-4202.
https://doi.org/10.1109/CDC.2002.1185028
Sippe G. Douma, Paul M.J. Van den Hof. (2005). An alternative paradigm for probabilistic uncertainty bounding in prediction error identification. Proceeding of 44st IEEE conference on decision and control, and the European Control Conference 2005. Seville, Spain, 4970-4975.
Chen J., Gu G. (2000). Control Oriented System Identification. Wiley Interscience, 421.
Milanese M, Vicino A. (1991). Optimal estimation theory for dynamic systems with set membership uncertainty: an overview. Automatica, 27(6), 997-1009.
https://doi.org/10.1016/0005-1098(91)90134-N
Mäkilä P M, Partington J R, Gustafsson T K. (1995). Worst-case control-relevant identification // Automatica, 31(12), 1799-1819.
https://doi.org/10.1016/0005-1098(95)00106-3
Jafarian S. Hamed and Häggblom Kurt E. (2011). Frequency-domain uncertainty model identification using a state space model with time-delay compensation. Report 11-1 ABO Academi.
Wang Le-Yi, Zhao Wen-Xiao. (2013). System Identification: New Paradigms, Challenges, and Opportunities. Acta automatica sinica, 39 (7), 933-942.
https://doi.org/10.1016/S1874-1029(13)60062-2
Efron B., Tibshirani R.J. (1993). An introduction to the bootstrap. N.Y.: Chapman & Hall, 436.
https://doi.org/10.1007/978-1-4899-4541-9
Shitikov V.K., Rozenberg G.S. (2013). Randomizatsiya i butstrep: statisticheskiy analiz v biologii i ekologii s ispolzovaniem R [Randomization and bootstrap: statistical analysis in biology and ecology using R]. Tolyatti: Kassandra, 314.
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