Coupled nonlinear flight dynamics, aeroelasticity, and control of very flexible aircraft.

Abstract

Flight dynamics and control of rigid aircraft motion coupled with linearized structural dynamics has been studied for several decades. However, new requirements for very flexible aircraft are challenging the validity of most rigid body coupled linearized structural motion formulations, due to the presence of large elastic motions. This dissertation presents, the flight dynamics, integration, and control of the six degree-of-freedom equations of motion of a reference point on a very flexible aircraft coupled with the aeroelastic equations which govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady finite-state potential flow aerodynamics form the basis for the aeroelastic formulation. The nonlinear beam structural model is based upon the finite strain approach. Kinematic differential equations are used to provide orientation and position of the fixed reference point. The resulting governing differential equations are non-linear, first- and second-order differential algebraic equations and provide a low-order complete nonlinear aircraft formulation. The resulting equations are integrated using an implicit Modified Newmark Method. The method incorporates both first- and second-order nonlinear equations without the necessity of transforming second-order equations to first-order form. The method also incorporates a Newton-Raphson sub-iteration scheme to reduce residual error. Due to the inherent flexibility of these aircraft, the low order structural modes couple directly with the rigid body modes. This creates a system which cannot be separated as in traditional control schemes. Trajectory control techniques are developed based upon a combination of linear and nonlinear inner-loop tracking and an outer-loop nonlinear transformation from desired trajectories to reference frame velocities. Numerical simulations are presented validating the proposed integration scheme and the open and closed loop response of a representative aircraft. Open loop simulations highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analysis and show significant differences in the three reference point axes (pitch, roll, and yaw) not previously captured by rigid or linearized techniques. Closed loop simulations show the ability to track commanded trajectories in the presence of aeroelastic effects. Finally this dissertation provides several key contributions in the low-order modeling, analysis, and control of very flexible aircraft, specifically the development of (i) the six degree-of-freedom equations of motions of a reference point on a very flexible aircraft coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle, (ii) a nonlinear numerical integration scheme specifically targeted for very flexible aircraft, and (iii) a control architecture which provides closed loop trajectory tracking of a representative very flexible aircraft.