Nonlinear and Linearized State-Space Models for Flight Dynamics of Elastic, Free-Flying Aircraft

Abstract

The goal of this thesis is the development of a reduced order time domain model, that describes the flight mechanic, structural- and aerodynamic behavior of a free flying aircraft. The structural dynamics will be modeled using the modal approach formulated as a linear state space model. A linear "black box" model is identified to describe the rigid body aerodynamics as well as the generalized aerodynamic forces on the structural modes. The rigid body motion and the structural deformation will be inputs to the aerodynamic model, along with control surface deflections. The aerodynamic model thus couples the flight mechanic and structural degrees of freedom. Generalized aerodynamic forces (GAF) are generated using aerodynamic methods of varying complexity, here the Doublet-Lattice method (DLM) and Computational Fluid Dynamics (CFD) are employed. Matrices of non-parametric transfer functions in the frequency domain are built from those generalized aerodynamic forces and the corresponding inputs. The VECTOR FITTING routine is used to identify the time domain black box model from the GAF matrices, it serves as a rational function approximation. A good approximation of the frequency response can be found with relatively small state space models. The structural- and aerodynamic models are coupled to the aeroelastic state space and simulated in the time domain for a clamped wind tunnel model without flight mechanic degrees of freedom. The validation with data from a similar model shows good results. For a free flying transport aircraft configuration (XRF1), the flight mechanics are described using the rigid body eigenmodes from a free-free eigenmode analysis. The model is validated with a CFD time domain simulation, but the results are not satisfactory, especially for the structural deformations, and the rigid body modes show unstable behavior. To solve this problem, the non-linear equations of motion for the rigid body degrees of freedom are numerically integrated in a co-simulation with the aeroelastic state space. This approach delivers good results, and due to the small aeroelastic state space, this model can still be simulated with relatively low computational cost.