Kenneth J. Badcock

Nikolaos D. Tantaroudas, Andrea Da Ronch, Ilias Karachalios et al.

A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around equilibrium states, retaining up to third-order terms, and projects the high-dimensional system onto a small basis of eigenvectors of the coupled-system Jacobian matrix. The biorthonormality of right and left eigenvectors ensures optimal projection, while higher-order operators are computed via matrix-free finite difference approximations. The methodology is validated on three test cases of increasing complexity: a three-degree-of-freedom aerofoil with nonlinear stiffness (14 states reduced to 4), a HALE aircraft configuration (2,016 states reduced to 9), and a very flexible flying-wing (1,616 states reduced to 9). The reduced-order models achieve computational speedups of up to 600 times while accurately capturing the nonlinear dynamics, including large wing deformations exceeding 10% of the wingspan. The second-order Taylor expansion is shown to be sufficient for describing cubic structural nonlinearities, eliminating the need for third-order terms. The framework is independent of the full-order model formulation and applicable to higher-fidelity aerodynamic model

Nikolaos D. Tantaroudas, Andrea Da Ronch, Ilias Karachalios et al.

Identification of worst-case gust loads is a critical step in the certification of very flexible aircraft, yet the computational cost of nonlinear full-order simulations renders exhaustive parametric searches impractical. This paper presents a reduced-order model (ROM) based methodology for rapid worstcase gust identification that achieves computational speedups of up to 600 times relative to full-order nonlinear simulations. The approach employs nonlinear model order reduction via Taylor series expansion and eigenvector projection of the coupled fluid-structure-flight dynamic system. Three test cases of increasing complexity are considered: a three-degree-of-freedom aerofoil (14 states, worst-case identified from 1,000 design sites), a Global Hawk-like UAV (540 states, 80 parametric calculations with 30 times speedup), and a very flexible flying-wing (1,616 states, 37 parametric calculations reduced from 222 hours to 22 minutes). The linear ROM is shown to be accurate for deformations below 10% of the wingspan, while the nonlinear ROM with second-order Taylor expansion accurately captures the large-deformation regime. The methodology provides a practical tool for integrating worst-case gust search into aircraft certification workflows.

Nikolaos D. Tantaroudas, Andrea Da Ronch, Ilias Karachalios et al.

This paper investigates the effects of geometric nonlinearity and structural flexibility on the flight dynamics of high-aspect-ratio wings representative of high-altitude long endurance aircraft configurations. A coupled aeroelastic flight dynamic framework is developed, combining a geometrically exact beam formulation for the structure, unsteady two-dimensional strip theory for the aerodynamics, and quaternion-based rigid-body equations for the flight dynamics. The three subsystems are monolithically coupled through consistent load and motion transfer at each time step. A systematic parametric study is conducted by varying the wing stiffness across several orders of magnitude, spanning from nearly rigid to very flexible configurations. The study reveals that increasing flexibility fundamentally alters trim conditions, flutter boundaries, and dynamic gust response. In particular, large static deformations create an effective dihedral that modifies the lift direction and necessitates higher trim angles of attack. The phugoid mode is shown to destabilise at high flexibility levels, consistent with findings in the literature. Flutter speed degradation is quantified as a function of the stiffness parameter, showing significant reductions for very flexible configurations when the pre-stressed equilibrium is correctly accounted for. The framework is validated against published aircraft benchmarks, demonstrating good agreement in natural frequencies, flutter speeds, and nonlinear static deflections. Results provide quantitative guidance on when linear analysis is acceptable and when fully coupled nonlinear tools become essential.

Nikolaos D. Tantaroudas, Andrea Da Ronch, Guanqun Gai et al.

Model Reference Adaptive Control based on Lyapunov stability theory is developed for gust load alleviation of nonlinear aeroelastic systems. The controller operates on a nonlinear reduced-order model derived from Taylor series expansion and eigenvector projection of the coupled fluid-structure-flight dynamic equations. The complete MRAC formulation is presented, including the reference model design that encodes desired closed-loop damping characteristics, the adaptive control law with real-time gain adjustment, and the Lyapunov derivation of the adaptation law that guarantees asymptotic tracking in the linear case and bounded tracking under a Lipschitz condition on the nonlinear residual. The adaptation rate matrix is identified as the single most important design parameter, governing the trade-off between convergence speed, peak load reduction, and actuator demand. Two test cases are considered, a 3DOF aerofoil with cubic stiffness nonlinearities, and a Global Hawk type unmanned aerial vehicle. For the UAV under a discrete gusts, MRAC achieves significant wing-tip deflection reductions, outperforming the H infinity robust control benchmark with comparable control effort. Under Von Karman stochastic turbulence, meaningful reductions are also obtained, with performance scaling with the adaptation rate. The results demonstrate that MRAC provides an effective framework for GLA of flexible aircraft operating in both deterministic and stochastic disturbance environments.

Nikolaos D. Tantaroudas, Andrea Da Ronch, Ilias Karachalios et al.

A complete, self-contained mathematical framework for modelling the coupled aeroelastic and flight dynamic behaviour of free-flying flexible aircraft subject to atmospheric gust encounters is presented. The framework integrates three physical disciplines: geometrically-exact nonlinear beam theory for structural dynamics, unsteady two-dimensional strip aerodynamics based on Theodorsen thin-aerofoil theory with indicial functions for shed-wake and gust-penetration effects, and quaternion-based rigid-body flight dynamics for singularity-free attitude propagation. The coupled system is assembled into a first-order state-space form amenable to time-domain simulation, model order reduction, and control design. Detailed derivations of all coupling terms, including coordinate transformations between aerodynamic and structural frames, the Jacobian block structure, and gust input matrices, are provided. Two gust models are treated: the certification-standard discrete gust and the Von Karman continuous turbulence spectrum. The framework is verified against published benchmarks, including high-altitude long-endurance aircraft configurations and a very flexible flying-wing, demonstrating close agreement in structural frequencies, flutter speed, and static aeroelastic deflections. This paper serves as a self-contained reference for researchers implementing coupled aeroelastic-flight dynamic analysis tools for very flexible aircraft.

Nikolaos D. Tantaroudas, Andrea Da Ronch, Ilias Karachalios et al.

H Infinity robust control synthesis for gust load alleviation of very flexible aircraft is presented. The controller is synthesised on a compact reduced-order model comprising 8 degrees of freedom for the UAV configuration and 9 for the flying-wing, obtained through nonlinear model order reduction of the coupled fluid-structure-flight dynamics system, and validated on the full nonlinear model. The control architecture employs trailing-edge flap deflection as the actuator and wing-tip displacement as the performance output, with an input-shaping weighting function Kc that governs the trade-off between structural load alleviation and rigid-body trajectory deviation. Results are presented for a Global Hawk-like UAV and a very flexible flying-wing configuration. The methodology demonstrates that H infinity controllers designed on low-order ROMs can robustly alleviate gust loads when applied to high-dimensional nonlinear aeroelastic systems.