Abstract
Many real-world processes exhibit fractional-order dynamics and are described by the non-integer order differential equations. In this paper, we quantify the fitting of the Oustaloup approximation method to the fractional-order state-space system to be obtained in the specified narrow frequency range and order. A novel method of the plant model state estimation using the model predictive control (MPC) technique has been verified on the approximated fractional-order water tanks system. To improve the system tracking and reduce the experimental effort, the Kalman filter (KF) has been connected to the MPC structure. The main objective is to design a control system of the linearized fractional-order system with the tuning of its parameters concerning an additive white noise affecting the output of the system. The presented scheme has been verified using numerical examples, and the results of the prediction of the state are discussed.
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References
Monje, C.A., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional orders systems and controls: fundamentals and applications. Advances in Industrial Control. Springer, Cham (2010). https://doi.org/10.1007/978-1-84996-335-0
Chen, Y., Petráš, I., Xue, D.: Fractional order control - a tutorial. In: Proceedings of ACC 2009. American Control Conference, pp. 1397–1411 (2009)
Torvik, P.J., Bagley, R.L.: On the appearance of the fractional derivative in the behavior of real materials. Trans. ASME 51(4), 294–298 (1984)
Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. Fund. Theory Appl. 47(1), 25–40 (2000)
Miller, K., Ross, B.: An introduction to the fractional calculus and fractional differential equations. Wiley, Hoboken (1993)
Magin, R., L.: Fractional Calculus in Bioengineering. Begell House Publishers, Danbury (2006)
West, B., Bologna, M., Grigolini, P.: Physics of Fractal Operators. Springer, New York (2003). https://doi.org/10.1007/978-0-387-21746-8
Petras, I.: Fractional-Order Nonlinear Systems. Springer, New York (2011)
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
Valério, D., Costa, J.: An Introduction to Fractional Control. IET, London (2013)
Sheng, H., Chen, Y.D., Qiu, T.S.: Fractional Processes and Fractional-order Signal Processing. Springer, London (2012). https://doi.org/10.1007/978-1-4471-2233-3
Tepljakov, A., Petlenkov, E., Belikov, J.: FOMCON: a MATLAB toolbox for fractional-order system identification and control. Int. J. Microelectron. Comput. Sci. 2(2), 51–62 (2011)
Monje, C., Vinagre, B., Feliu, V., Chen, Y.: Tuning and autotuning of fractional order controllers for industry applications. Control Eng. Pract. 16(7), 798–812 (2008)
Hussain, M.: Review of the applications of neural networks in chemical process control–simulation and on–line implementation. Artif. Intell. Eng. 13, 55–68 (1999)
Maciejowski, J.M.: Predictive Control with Constraints, pp. 108–115. Prentice-Hall, Englewood Cliffs (2002)
Jakowluk, W.: Design of a state estimation considering model predictive control strategy for a nonlinear water tanks process. In: Saeed, K., Chaki, R., Janev, V. (eds.) CISIM 2019. LNCS, vol. 11703, pp. 457–468. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-28957-7_38
Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design, 5th ed., Nob Hill Pub., Madison (2012)
Bernardini, D., Bemporad, A.: Stabilizing model predictive control of stochastic constrained linear systems. IEEE Trans. Autom. Control 57, 1468–1480 (2012)
Atkinson, A.C., Donev, A.N., Tobias, R.D.: Optimum Experimental Designs, with SAS, pp. 119–147. Oxford University Press, Oxford (2007)
Schoukens, J., Ljung, L.: Nonlinear system identification. A user-oriented roadmap. IEEE Control Syst. Mag. 39(6), 28–99 (2019)
Rojas, C.R., Agüero, J.C., Welsh, J.S., Goodwin, G.C.: On the equivalence of least costly and traditional experiment design for control. Automatica 44(11), 2706–2715 (2008)
Jakowluk, W.: Plant friendly input design for parameter estimation in an inertial system with respect to D-efficiency constraints. Entropy 16(11), 5822–5837 (2014)
Kumar, A., Nabil, M., Narasimhan, S.: Economical and plant friendly input design for system identification. In: Proceedings 2014 European Control Conference (ECC), Strasbourg, France, pp. 732–737 (2014)
Annergren, M., Larsson, C.A., Hjalmarsson, H., Bombois, X., Wahlberg, B.: Application-oriented input design in system identification: optimal input design for control. IEEE Control Syst. Mag. 37(2), 31–56 (2017)
Jakowluk, W.: Optimal input signal design for fractional-order system identification. Bull. Polish Acad. Sci. Tech. Sci. 67(1), 37–44 (2019)
Jakowluk, W., Świercz, M.: Application-oriented experiment design for model predictive control. Bull. Polish Acad. Sci. Tech. Sci. 68(4), 883–891 (2020)
Acknowledgment
The present study was supported by a grant WZ/WI-IIT/4/2020 from the Bialystok University of Technology and was funded from the resources for research by the Ministry of Science and Higher Education.
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Jakowluk, W., Boersma, S. (2021). Fractional-Order Nonlinear System Identification Using MPC Technique. In: Saeed, K., Dvorský, J. (eds) Computer Information Systems and Industrial Management. CISIM 2021. Lecture Notes in Computer Science(), vol 12883. Springer, Cham. https://doi.org/10.1007/978-3-030-84340-3_31
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