Explicit nonlinear predictive control for a magnetic levitation system

Asian Journal of Control

Volumn 12, Issue 3, 2010, Pages 434-442

  Ulbig, A ^a   Olaru, S ^a   Dumur, D ^a   Boucher, P ^a  

^a SUPELEC   (France)

Author keywords

Magnetic levitation; Piecewise affine control law; Predictive control

Indexed keywords

CLOSED LOOP SYSTEMS; CONTROL THEORY; MODEL PREDICTIVE CONTROL;

CONSTRAINED FINITE TIME OPTIMAL CONTROLS; CONTROL LAWS; GENERAL NONLINEAR SYSTEMS; MAGNETIC LEVITATION SYSTEMS; NONLINEAR CONTROL LAWS; NONLINEAR PREDICTIVE CONTROL; PIECEWISE AFFINE SYSTEMS; PREDICTIVE CONTROL;

MAGNETIC LEVITATION;

EID: 77955340399     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1002/asjc.191     Document Type: Article

References (25)

1. Allgower, F, R. Findeisen, and Z. K. Nagy, "Nonlinear model predictive control: from theory to application," J. Chin. Inst. Chem. Eng., Vol. 35, No. 3, pp. 299-315 (2004).
2. Morari, M. and J. H. Lee, "Model predictive control: past, present and future," Comput. Chem. Eng., Vol. 25, pp. 667-682 (1999).
3. Mayne, D. Q., J. B. Rawlings, C. V Rao, and R O. M. Scokaert, "Constrained model predictive control: stability and optimality," Autornatica, Vol. 36, No. 6, pp. 789-814 (2000).
4. Garcia, C. E., D. M. Prett, and M. Morari, "Model predictive control: theory and practice-a survey," Autornatica, Vol. 25, pp. 335-348 (1989).
5. Bemporad, A., F. Borrelli, and M. Morari, "Explicit solution of LP-based model predictive control", Proc. 39th IEEE Conf. Decis. Control, Sydney, Australia (2000).
6. Bemporad, A., M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Autornatica, Vol. 38, No. 1, pp. 3-20 (2002).
7. Seron, M., G. Goodwin, and J. D. Dona, "Characterisation of receding horizon control for constrained linear systems," Asian J. Control, Vol. 5, No. 2, pp. 271-286 (2003).
8. Olaru, S. and D. Dumur, "Avoiding constraints redundancy in predictive control optimization routines," IEEE Trans. Autom. Control, Vol. 50, No. 9, pp. 1459-1466 (2005).
9. Borrelli, R, "Constrained Optimal Control of Linear and Hybrid Systems," Lecture Notes in Control and Information Sciences, Vol. 290, Springer, Berlin, Heidelberg (2003).
10. Johansen, T. A. and A. Grancharova, "Computational aspects of approximate explicit nonlinear model predictive control," IEEE Trans. Autom. Control, Vol. 48, pp. 810-815 (2003).
11. Bemporad, A. and C. Filippi, "An algorithm for approximate multiparametric convex programming," Comput. Optim. Appl, Vol. 35, No. l,pp. 87-108(2006).
12. Jones, C. N., M. Bari'c, and M. Morari, "Multiparametric linear programming with applications to control," Eur. J. Control, Vol. 13, No. 2-3, pp. 152-170(2007).
13. Olaru, S., D. Dumur, and S. Dobre, "On the geometry of predictive control with nonlinear constraints," In Informatics in Control, Automation and Robotics IV, Filipe, J., J.-L. Ferrier, J. A. Cetto, and M. Carvalho (eds). Springer, Berlin, Heidelberg (2008).
14. Fotiou, I. A., Ph. Rostalski, B. Sturmfels, and M. Morari, "An algebraic geometry approach to nonlinear parametric optimisation in control", Proc. Am. Control Conf, Minneapolis, USA (2006).
15. Sontag, E. D., "Nonlinear regulation: the piecewise linear approach," IEEE Trans. Autom. Control, Vol. 26, No. 2, pp. 346-358(1981).
16. Heemels W. P. M., B. De Schutter, and A. Bemporad, "Equivalence of hybrid dynamical models," Autornatica, Vol. 37, No. 7, pp. 1085-1091 (2001).
17. Fiacchini, M., T. Alamo, and E. F. Camacho, "Suboptimal model predictive control of hybrid systems through spherical discretization mesh," IFAC Workshop NMPC East Syst., Grenoble, France (2006).
18. Tyner, D. R. and A. D. Lewis, "Jacobian linearisation in a geometric setting," 42nd IEEE Conf. Decis. Control, Maui, Hawaii (2003).
19. Bianchini, R. M. and G. Stefani, "Controllability along a trajectory: a variational approach," SIAM J. Control Optim., Vol. 31, No. 4, pp. 900-927 (1993).
20. Kvasnica, M., P. Grieder, and Baotic M., "Multi-Parametric Toolbox (MPT)", control.ee. ethz.ch/mpt (2004).
21. Gasca, M. and Th. Sauer, "Polynomial interpolation in several variables," Adv. Comput. Math., Vol. 12, pp. 377-410 (2000).
22. Canale, M., L. Fagiano, and M. Fagiano, "Set Membership approximation theory for fast implementation of Model Predictive Control laws," Autornatica, Vol. 45, No. 1, pp. 45-54 (2009).
23. Canale, M., L. Fagiano, and M. Fagiano, "On the use of approximated predictive control laws for nonlinear systems," 47th IEEE Conf Decis. Control, pp. 4712-4717, Cancun, Mexico (2008).
24. Henni, A. and H. Siguerdidjane, "Robust nonlinear control of a magnetic suspension system," IEEE Conf. ControlAppl, Vol.2,pp. 1307-1312, Istanbul (2003).
25. D'Errico J., "PolyfitN Function," Mathworks Central Repository, www.mathworks.com (2006).