NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER L. Mederreg, F. Diaz and N. K. M’sirdi LRV Laboratoire de Robotique de Versailles, Université de Versailles Saint Quentin en Yvelines, 10, avenue de l’Europe 78140, Vélizy, France.

1 Introduction. 2 4 rotors Helicopter model Presentation 3 Back stepping controller synthesis 4 Back stepping controller synthesis with observer 5 Simulation and results 6 Conclusion. OUTLINE

Introduction Thanks to its special configuration, the 4 rotor helicopter allows to achieve many tasks in different fields.  Symmetry of the platform geometry  Low weight  Low cost Autonomous flight  Non linear control law Synthesis.  Complexity of the dynamical system  Presence of Perturbations due to the wind  Unavailability of some state variables

4 rotors Helicopter model Presentation

Absolute velocities / Earth frame Orientation angels: Yaw, Roll, Pitch. State vector: Gravity center c oordinates Angular velocities / Helicopter frame Aero dynamical forces Aero dynamical Momentums

The state representation is given by:

System of 4 equations 4 unknowns System outputs: Desired outputs: Control laws: Back stepping controller synthesis We consider that all the state vector is measurable

SIMULINK bloc diagram of the controller

We include in the expression of V the observing errors to be cancelled Back stepping controller synthesis with observer We shall observe the absolute velocity vector : Difficult to measure We consider that all the other parameters are measurable Where V is a LYAPUNOV candidate function System 4 equations 4 unknowns Convergence of the tracking errors Convergence of observing errors

Simulation and results  Simulation of a vertical helix trajectory flight in presence of perturbations (7 newton front wind blowing)  The controller gains are adjusted by doing intensive simulations Tracking Trajectory : Initiales positions:

3D Tracking trajectory

Tracking errors for the BACKSTEPPING controller

Observation Errors for the BACKSTEPPING Observer

Tracking Errors for the BACKSTEPPING controller with Observer

Conclusion : This approach has shown :  Good robustness of the Controller  Good convergence of the couple controller observer  allows to decrease the number of the required sensors