Dynamic Modeling and Control of Blimps with Flexible Hull and Fins

The growing interest in blimp technology underscores the need for dynamic models that capture their flight behavior and improve control strategies. This paper presents, for the first time, a unified analysis of the aeroelastic stability and control of fully flexible blimps. The hull and fins are modeled as Euler–Bernoulli beams with free–free and fixed–free boundary conditions, respectively. Equations of motion are derived in the body frame using the Euler–Lagrange approach, incorporating hull added-mass effects and aerodynamic forces on the hull and fins. A perturbation approach divides the problem into a zeroth-order rigid-body dynamics for steady-level flight and a linearized first-order aeroelastic model. The zeroth-order solution supplies constant inputs to the first-order problem, which is then applied to the Skyship-500 with standard and thin-skin designs. Stability analysis confirms the model against prior work and identifies hump-mode flutter as the dominant instability. For thin-skinned blimps, this occurs at low forward speeds, while soft flutter emerges at higher speeds. To address maneuverability during hump-mode flutter, a linear quadratic regulator is applied. Results show that control inputs for a fully flexible blimp differ substantially from those of rigid or partially elastic models, emphasizing the importance of accounting for fin elasticity.