This paper focuses on the characterization of the response of a very flexible aircraft in flight. 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 finite-state potential flow aerodynamics form the basis for the aeroelastic model. The nonlinear beam structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the finite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. The equations of motion are integrated using an implicit modified generalized-alpha method. The method incorporates both first and second order nonlinear equations without the necessity of transforming the equations to first order and incorporates a Newton-Raphson sub-iteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted which encompass nonlinear rigid body, nonlinear rigid body coupled with linearized structural solutions, and full nonlinear rigid body and structural solutions. Simulations are presented which highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analyses in a representative High Altitude Long Endurance (HALE) vehicle. Results show significant differences in the three reference point axes (pitch, roll, and yaw) not previously captured by linearized or rigid body approaches. The simulations using both full and empty fuel states include level gliding descent, low-pass filtered square aileron input rolling/gliding descent, and low-pass square elevator input gliding descent. Results are compared for rigid body, linearized structural, and nonlinear structural response.

This paper focuses on the characterization of the response of a very flexible aircraft in flight. 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 finite-state potential flow aerodynamics form the basis for the aeroelastic model. The nonlinear beam structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the finite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. The equations of motion are integrated using an implicit modified generalized-alpha method. The method incorporates both first and second order nonlinear equations without the necessity of transforming the equations to first order and incorporates a Newton-Raphson sub-iteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted which encompass nonlinear rigid body, nonlinear rigid body coupled with linearized structural solutions, and full nonlinear rigid body and structural solutions. Simulations are presented which highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analyses in a representative High Altitude Long Endurance (HALE) vehicle. Results show significant differences in the three reference point axes (pitch, roll, and yaw) not previously captured by linearized or rigid body approaches. The simulations using both full and empty fuel states include level gliding descent, low-pass filtered square aileron input rolling/gliding descent, and low-pass square elevator input gliding descent. Results are compared for rigid body, linearized structural, and nonlinear structural response.

This paper focuses on trajectory control of the six-degree-of-freedom body fixed reference frame located on a very flexible aircraft. The six-degree-of-freedom equations of motion of a reference point on the aircraft are coupled with a low-order strain-based nonlinear structural analysis and an unsteady finite state potential flow aerodynamics model. Because of the inherent flexibility of the aircraft, the low-order structural frequencies are of the same order as the rigid-body mode frequencies. This coupling is accounted for in the controller development. A heuristic approach based upon pilot behavior is developed. The 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, whereas 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 used. Differences between the desired and actual trajectories are handled using a nonlinear proportional, integral, derivative approach. The closed-loop time integration is accomplished using an implicit modified Newmark method. A capstone numerical simulation is presented, highlighting the strengths and weaknesses of the method.

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