Simplified Dynamic Models for Modern Flying Vehicles

This dissertation contributes to the definition of minimum–complexity approaches that allows for representing realistic effects typical of modern fixed- and rotary-wing configurations, limiting as much as possible increase in order and overall complexity of the dynamic model of the class of aerial vehicles considered. In particular, the thesis deals with (1) the development of a novel low–order mathematical model for including structural deformation effects in the analysis of response to control inputs of flexible aircraft; (2) the derivation of a simplified models for unsteady aerodynamic effects, with an application to helicopter main rotor; (3) modeling and assessment of the maneuvering potential for a novel quadrotor configuration with tilting rotors. A mixed Newtonian–Lagrangian approach is proposed for the derivation of flexible aircraft equations of motion, where Lagrange equations are used for flexible degrees of freedom, discretized by means of Gal¨erkin method, whereas the evolution of transport degrees of freedom (position and attitude variables) is obtained by means of Newton second law and generalized Euler equation. A strong link with conventional rigid aircraft equations of motion is maintained, that allows highlighting those terms less relevant for aircraft response. When negligible, these terms are removed and a minimum complexity flexible aircraft model is derived, suitable for real–time simulation and control law synthesis. Similarly, unsteady aerodynamic effects over a rotating blade are modeled by means of an available approach, namely the ONERA dynamic stall model. Some reasonable simplifying assumptions based on the comparison of simulation results with a quasi–static aerodynamic model are then derived and a minimum complexity, 6 degree–of–freedom helicopter model is proposed which takes into account the issues related to retreating blade stall. Finally, an existing inverse simulation algorithm is applied for the first time to the determination of the control laws for tracking desired maneuvers by means of an unconventional quad-rotor configuration featuring four tilting rotors. This novel configuration allow access to an extended maneuver envelope and ad hoc instruments are needed for assessing its maneuvering potential. For all the considered problems, the approaches developed are demonstrated by means of numerical results, applied to a particular class of modern fixed- or rotary-wing aircraft, but the possibility of extending the results to different classes of vehicles is also highlighted.