Modeling and stability of balloon-borne gondolas with coupled pendulum-torsion dynamics

The objective of this paper is to fill the gap in literature on an exhaustive coupled pendulum-torsion model for balloon-borne systems. The development of such a model is required to explain the unexpected oscillatory behavior recorded on the flight data of scientific balloon-borne missions and more particularly the performance degradation due to the coupling of pendulum and azimuth dynamics through the azimuth control loop, which is classically designed using a decoupled torsion model. First, a complete dynamic model of balloon-borne systems is derived. The proposed model is applied to the Faint Intergalactic-medium Redshifted Emission Balloon (FIREBall) experiment and validated by flight data. Then, the stability issue raising from the commonly neglected coupling assumption is investigated. Sufficient stability conditions are presented by using positivity properties. Based on the FIREBall model, it is finally shown how the azimuth control can destabilize the pendulum dynamics, and how the proposed model can be used during preliminary design phases to size a flight chain and the associated control system to prevent this instability.