Algebraic Methods for Nonlinear Systems: Parameter Identification and State Estimation

Algebraic methods are presented for solving nonlinear least-squares type problems that arise in the parameter identification of nonlinear systems. The tracking of the induction motor rotor time constant is solved in detail. Also, an approach to estimating state variables using algebraic relationships (in contrast to dynamic observers) is discussed in the context of speed estimation for induction motors.

[1]  Layne T. Watson,et al.  Finding all isolated solutions to polynomial systems using HOMPACK , 1989, TOMS.

[2]  James P. Keener,et al.  Mathematical physiology , 1998 .

[3]  J. Grizzle,et al.  On numerical differentiation algorithms for nonlinear estimation , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  Jessy W. Grizzle,et al.  Interpolation and numerical differentiation for observer design , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[5]  Kaushik Rajashekara,et al.  Sensorless control of AC motor drives : speed and position sensorless operation , 1996 .

[6]  Michael Sebek,et al.  Numerical and symbolic computation of polynomial matrix determinant , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  Peter Vas,et al.  Sensorless vector and direct torque control , 1998 .

[8]  Martin Hromcik,et al.  New algorithm for polynomial matrix determinant based on FFT , 1999, 1999 European Control Conference (ECC).

[9]  Ricardo Femat,et al.  Blood glucose control for type I diabetes mellitus: A robust tracking H∞ problem , 2004 .

[10]  David A. Cox,et al.  Using Algebraic Geometry , 1998 .

[11]  M. Velez-Reyes,et al.  Developing robust algorithms for speed and parameter estimation in induction machines , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[12]  T. Glad,et al.  An Algebraic Approach to Linear and Nonlinear Control , 1993 .

[13]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[14]  Hassan K. Khalil,et al.  A robust torque controller for induction motors without rotor position sensors: analysis and experimental results , 1997 .

[15]  Leon M. Tolbert,et al.  A nonlinear least-squares approach for identification of the induction motor parameters , 2005, IEEE Transactions on Automatic Control.

[16]  Eva Riccomagno,et al.  Differential algebra methods for the study of the structural identifiability of biological rational polynomial models , 2000 .

[17]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

[18]  Jennifer Stephan,et al.  Real-time estimation of the parameters and fluxes of induction motors , 1992, Conference Record of the 1992 IEEE Industry Applications Society Annual Meeting.

[19]  K R Godfrey,et al.  Effect of dose, molecular size, affinity, and protein binding on tumor uptake of antibody or ligand: a biomathematical model. , 1989, Cancer research.

[20]  B. Sturmfels SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS , 2002 .

[21]  A. Holmberg On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities , 1982 .

[22]  Miguel Velez-Reyes,et al.  Decomposed algorithms for parameter estimation , 1992 .

[23]  Werner Leonhard,et al.  Control of Electrical Drives , 1990 .

[24]  George C. Verghese,et al.  Decomposed Algorithms for Speed and Parameter Estimation in Induction Machines , 1992 .

[25]  Sunil K. Agrawal,et al.  Differentially Flat Systems , 2004 .

[26]  G.C. Verghese,et al.  Recursive speed and parameter estimation for induction machines , 1989, Conference Record of the IEEE Industry Applications Society Annual Meeting,.

[27]  John Chiasson,et al.  A comparison of sensorless speed estimation methods for induction motor control , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[28]  Maria Pia Saccomani,et al.  Some Results on Parameter Identification of Nonlinear Systems , 2004 .

[29]  Thomas Kailath,et al.  Linear Systems , 1980 .

[30]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[31]  W. Cheney,et al.  Numerical analysis: mathematics of scientific computing (2nd ed) , 1991 .