Robust trajectory tracking of flat nonlinear systems

In this paper 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.