Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia1 Wing Rock Dynamics and Differential Flatness W. LU F. Mora-Camino A. Acha ï bou

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 2 Outline Introduction  Wing Rock Dynamics  Differential Flatness Flatness Based Controller Design  Flatness of Wing Rock Dynamics  Control Law Design  Simulation Results Conclusion

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 3 Wing Rock Dynamics A rolling oscillation motion due to loss of damping at high angle-of-attack. High swept delta wing/arrow wing with slender body configurations Breakdown of asymmetrical flow/vortex (unpredictable theoretically) High nonlinearity CFD/Experiments efforts (mathematical model)

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 4 Supersonic Transport Aircrafts

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 5 Differential Flatness (1) Origin  Differential flatness has been first introduced by M. Fliess, J. Lévine, P. Martin, P. Rouchon. Definition  A system is said to be differentially flat if and only if the state and input can be determined by a set of variables, called flat output, which may possess physical meanings. Application  The control input of a flat system can be determined from a given trajectory of the flat output.

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 6 Differential Flatness (2) A nonlinear system given as: is differentially flat if there exists a vector such that Numerous nonlinear systems have been proved to be differentially flat.

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 7 Flatness of Wing Rock Dynamics (1) Mathematical Model  Proposed by Hsu and Lan

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 8 Flatness of Wing Rock Dynamics (2) Differential Equations

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 9 Flat output of Wing Rock Dynamics Roll angle is a flat output:

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 10 Control Law Design (1) Trajectory based control Law  Open-loop control Performing output tracking of inherently stable systems  Close-loop control Enhance output tracking capability for stable systems Perform output tracking of inherently unstable systems

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 11 Control Law Design (2) Linearized System

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 12 Control Law Design (3) Close-loop control law Error dynamics Characteristic polynomial

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 13 Control Law Design (4) Control command Example of given output trajectory

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 14 Simulation Results (1)

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 15 Simulation Results (2)

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 16 Conclusions The wing rock dynamics, according to the retained model, is shown to be differentially flat. The flatness approach demonstrates a comparatively simple way to design an effective non control law for the wing rock motion. The proposed close-loop controller can stabilize the wing rock dynamics Large overshoot can emerge for small control gains. High-gain control can enhance the capability to track the desired trajectory at the expense of the saturation of actuators.

Nov. 22~24, st International Conference on Research in Air Transportation, Zilina, Slovakia 17 Question...