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Robust trajectory tracking of flat nonlinear systems

We propose to use the important work made in the area of linear robust control to ameliorate the global robustness of a flatness based control. The main idea consists in adding a linear feedback on the nominal flat control. This feedback is calculated on the linearised system of the error tracking. From the linearised system (depending on the desired trajector) is defined a polytopic representation including the trajectory. A pole localization using a polytopic representation leads to the solve of a set of LMI and gives the feedback gain. At last, parameter uncertainties and integral term are included in the constructive approach to design the robust control law. A magnetic levitation of a ball is used as example and the different simulation results confirm the robustness of the proposed approach.