Assessment and Future Directions of Nonlinear Model Predictive ...

562 S. Gros et al.5 ConclusionThis paper has proposed a two-time-scale control scheme that uses repeated trajectorygeneration in a slow loop and time-varying linear feedback based on theneighboring-extremal approach in a faster loop. The slow loop provides reasonablereference trajectories, while the fast loop ensures robustness. Feedforwardtrajectory generation is obtained using flatness-based system inversion.The two-time-scale approach as well as MPC have been used in simulationto control a VTOL flying structure. Though the simplified model of the structureis flat, control based on feedback linearization is not appropriate because itlacks robustness with respect to the model uncertainties typically encountered inVTOL structures. MPC requires a high re-optimization frequency and, in addition,cannot accommodate large model uncertainties. In contrast, the proposedtwo-time-scale control scheme is sufficiently robust that it does not require recalculationof the reference trajectories. The flatness-based approach is very fast,and will be used for experimental implementation on a laboratory-scale VTOLstructure, for which re-generation of the reference trajectories may be necessary.References[1] Bemporad, A. (1998). Reducing conservatism in predictive control of constrainedsystems with disturbances. In: 37th IEEE Control and Decision Conference.Tampa, FL. pp. 1384–89.[2] Bemporad, A. and M. Morari (1999). Robust Model Predictive Control: A Survey.Springer Verlag.[3] Bryson, A. E. (1999). Dynamic Optimization. Addison-Wesley, Menlo Park, California[4] Camacho, E. and Bordons C. (2005). Nonlinear Model Predictive Control: anIntroductory Survey NMPC05, Freudenstadt, Germany[5] Christofides, P.D. and Daoutidis P. (1996). Feedback Control of Two-Time-ScaleNonlinear Systems International Journal of Control. 63, 965–994[6] DeHaan D. and Guay M. (2005). A New Real-Time Method for Nonlinear ModelPredictive Control NMPC05, Freudenstadt, Germany[7] Fliess, M., J. Lévine, Ph. Martin and P. Rouchon (1995) Flatness and defect ofnonlinear systems: Introductory theory and examples International Journal ofControl 61(6), 1327–1361.[8] Fliess, M., J. Lévine, Ph. Martin and P. Rouchon (1999). A Lie-Bäcklund approachto equivalence and flatness of nonlinear systems IEEE Trans. Automat. Contr.38, 700–716.[9] Gros, S. (2005). Modeling and control of a vtol structure. Internal Report.Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne[10] Hagenmeyer V. and Delaleau E. (2003). Exact feedforward linearization based ondifferential flatness International Journal of Control 76, 573–556.[11] Kouvaritakis, B., J. A. Rossiter and J. Schuurmans (2000). Efficient robust predictivecontrol. IEEE Trans. Automat. Contr. 45(8), 1545–49.[12] Lee, J. H. and Z. Yu (1997). Worst-case formulations of model-predictive controlfor systems with bounded parameters. Automatica 33(5), 763–781.