Trajectory Control for Very Flexible Aircraft

Abstract

This paper focuses on trajectory control of the 6-DOF body flxed reference frame located on a very ∞exible aircraft. The 6-DOF equations of motion of a reference point on the aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady flnite-state potential ∞ow aerodynamics form the basis for the aeroelastic model. The nonlinear beam flnite element structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the flnite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. Due to the inherent ∞exibility of the aircraft modeling, the low order structural frequencies are of the same order as the rigid body modes. This creates a coupling which cannot be separated by previous control schemes. The ∞exibility must be accounted for directly in the controller development. To accomplish this a heuristic approach based upon pilot behavior is developed. This approach separates the problem into two parts: a fast inner-loop and a slower outer-loop. Dominant kinematic nonlinearities are handled in the outer-loop while the inner loop is further separated into a lateral and longitudinal motion. Control of the inner-loop lateral motion is accomplished using a standard Linear Quadratic Regulator. For the longitudinal motion Dynamic Inversion is utilized. Difierences between the desired and actual trajectories are handled in the nonlinear outer-loop using traditional proportional-integral-derivative design guidelines. The closed loop time integration is accomplished using an implicit modifled Newmark method. Numerical simulations are presented highlighting the strengths and weaknesses of the method.