Abstract
The work presented here exploits elimination theory (solving systems of polynomial equations in several variables) [1][2] to perform nonlinear parameter identification. In particular show how this technique can be used to estimate the rotor time constant and the stator resistance values of an induction machine. Although the example here is restricted to an induction machine, parameter estimation is applicable to many practical engineering problems. In [3], L. Ljung has outlined many of the challenges of nonlinear system identification as well as its particular importance for biological systems.
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Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, And Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd edn. Springer, Berlin (1996)
von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, Cambridge (1999)
Ljung, L.: Challenges of Nonlinear Identification. In: Bode Lecture, IEEE Conference on Decision and Control, Maui HI (2003)
Fliess, M., Glad, S.T.: An algebraic approach to linear and nonlinear control. In: Essays on Control: Perspectives in the Theory and Applications, Birkhäuser, pp. 223–267 (1993)
Sira-Ramírez, H., Agrawal, S.K.: Differentially Flat Systems. Marcel-Dekker, New York (2004)
Diop, S.: Differential-algebraic decision methods and some applications to system theory. Theor. Computer Sci. 98, 137–161 (1992)
Ollivier, F.: Le problème de l’identifiabilité structurelle globale: Ètude thèorique, mèthodes effective et bornes de complexè. PhD thesis, École Polytéchnique, Paris, France (1990)
Ljung, L., Glad, S.T.: On global identifiability for arbitrary model parameterisations. Automatica 30(2), 265–276 (1994)
Margaria, G., Riccomagno, E., Chappell, M.J., Wynn, H.P.: Differential algebra methods for the study of the structural identifiability of biological rational polynomial models (2004) (preprint)
Saccomani, M.P.: Some results on parameter identification of nonlinear systems. Cardiovascular Engineering: An Internation Journal 4(1), 95–102 (2004)
Diop, S.: Elimination in control theory. MCSS 4, 17–32 (1991)
Leonhard, W.: Control of Electrical Drives, 3rd edn. Springer, Berlin (2001)
Chiasson, J.: Modeling and High-Performance Control of Electric Machines. John Wiley & Sons, Chichester (2005)
Stephan, J., Bodson, M., Chiasson, J.: Real-time estimation of induction motor parameters. IEEE Transactions on Industry Applications 30(3), 746–759 (1994)
Stephan, J.: Real-time estimation of the parameters and fluxes of induction motors. Master’s thesis, Carnegie Mellon University (1992)
Chiasson, J., Bodson, M.: Estimation of the rotor time constant of an induction machine at constant speed. In: Proceedings of the European Control Conference ECC 2007, Kos, Greece, pp. 4673–4678 (July 2007)
Oteafy, A., Chiasson, J., Bodson, M.: Online identification of the rotor time constant of an induction machine. In: Proceedings of the American Control Conference, St. Louis MO, pp. 4373–4378 (2009)
Wang, K., Chiasson, J., Bodson, M., Tolbert, L.: A nonlinear least-squares approach for estimation of the induction motor parameters. IEEE Transactions on Automatic Control 50(10), 1622–1628 (2005)
Wang, K., Chiasson, J., Bodson, M., Tolbert, L.M.: An on-line rotor time constant estimator for the induction machine. In: Proceedings of the IEEE International Electric Machines and Drives Conference, San Antonio TX, pp. 608–614 (May 2005)
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Chiasson, J., Oteafy, A. (2010). Elimination Theory for Nonlinear Parameter Estimation. In: Lévine, J., Müllhaupt, P. (eds) Advances in the Theory of Control, Signals and Systems with Physical Modeling. Lecture Notes in Control and Information Sciences, vol 407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16135-3_6
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