Assessment and Future Directions of Nonlinear Model Predictive ...

558 S. Gros et al.translation from the position (x =0[m],y =0[m],z =0[m],φ=0[rad]) to theposition (x =1[m],y =1[m],z =1[m],φ =2π [rad]) will be considered. Thespeeds and accelerations are zero initially. The control problem is unconstrained.The controllers are computed using the simplified model, while the simulationsare done with the original model. Perturbations are introduced in the aerodynamicalparameters C s and C d to represent the uncertainty resulting fromself-induced turbulences and surface effects: Cs 1 , Cd 1, C2 s , Cd 2 are perturbed +50percent and Cs 3, C3 d , C4 s , C4 d −50 percent, Ck d and Ck s being the aerodynamicalcoefficients of propeller k.4.3 MPCThe choice of cost function for the MPC scheme is:J = 1 2∫t k +T[(¯x − ¯x sp ) T Q(¯x − ¯x sp )+ū T Rū]dtt kx [m]y [m]z [m]2.521.510.500 2 4 6 81.510.500 2 4 6 810.80.60.40.200 2 4 6 8eta1 [rad]0.40.30.20.10−0.1−0.2−0.30 2 4 6 8eta2 [rad]0.60.40.20−0.2−0.4−0.60 2 4 6 8654321phi [rad]00 2 4 6 8Fig. 3. Simulation results for the MPC scheme