Impact of Added Mass on the Control Laws Design

The exploitation of aircraft flying in the stratosphere to perform a variety of applications has gained increasing interest in recent years. The design of these aircraft and related missions requires suitable dynamics modelling and effective control strategies, in order to accommodate for the peculiar behaviour of the vehicles. The authors have already dealt with modelling of light stratospheric vehicles, specifically focusing on the role that added mass plays in the open-loop system dynamics. In the present work, the need of taking the added mass phenomenon into account from the perspective of control system design is assessed and its effect is evaluated. To this end, two different model-based designs of basic attitude control laws are considered, one including the added mass modelling and the other completely ignoring it; both designs use the same parameters and are scheduled across the flight envelope to achieve uniform performance. Several numerical analyses, both deterministic and probabilistic, are applied to these designs. Obtained results, presented in the paper, highlight that the differences in the performance of the two final closed-loop systems are quite negligible, whereas the robustness of the design which takes into account the added mass is dramatically higher. In fact, it is expected because neglecting dynamics of a system naturally takes to a stability margins reduction; however, the entity of reduction was not obvious and the analyses carried out allow to quantify it. These results confirm that the added mass modelling for very light flying vehicles is not an option, but a crucial element of the model while designing control laws.