HIGH-FIDELITY LINEAR FRACTIONAL REPRESENTATION OF THE BENDING MODES OF A LAUNCH VEHICLE
Authors:   Avio S.p.a., Colleferro, Italy, Aveta Mirko , Patrizia Cotugno Miss , Leto Giuseppe , Lopez Alessandro , Curti Gianluca 
Published: January 2024

In the design phase of a new launcher, particular attention must be paid to the modelling of the global bending modes, which denote the flexible behaviour of the launch vehicle. This system, in fact, represents a very complex structural environment from a design and control point of view. Indeed, during its flight phase, it is strongly impacted by several structural loads which can cause large oscillations and instability.
For this reason, when designing a launch vehicle, one must bear in mind that a low structural mass is desired, but it can be the source of significant flexible body dynamics. This makes it clear that exists a strong correlation between the structural characteristics and the bending modes parameters. In this context, this article focuses on the definition of a high fidelity Linear Fractional Representation (LFR) of the global bending modes’ parameters which reconstructs all the dependencies of these parameters with the structural ones coming from the Finite Element Model (FEM). As a result, with this approach it is possible to model the FEM outcomes within the LFR of the launch vehicle itself and improve in this way the representativeness of the launcher model for GNC studies.
This is a challenging task but with a high potential in terms of system understanding of the fundamental trade-offs.
The activity illustrated in this paper has been carried out during the preliminary design of the VEGA E (Evolution) launcher, which has been therefore taken as object of study for the presented work.
A Monte Carlo (MC) campaign of the launcher FEM model has been performed by scattering the mass and stiffness budgets, and the payload configurations. Then, the data obtained from the MC have been used to construct a high-fidelity LFR of the bending modes to be applied for both control design and verification purposes. The strength point of the LFR obtained with this approach is that its internal structure allows to model more closely the dispersions on the bending modes parameters, by explicitly displaying not only the correlations with trajectory effects but also the essential dependency on the structural and mass budget dispersions.
Moreover, for this task special attention has been put on correctly modelling the slosh modes, in order to also provide a fully dispersed slosh-bending dynamic behaviour.
To assess the outcome of this analysis in terms of stability in an agile and robust way, a structured H∞/H∞ problem has been defined for the tuning of the bending filter. At this purpose, the high-level stability requirements have been converted into low level H∞ requirements on the input sensitivity and input complementary sensitivity functions.
The final goal of this activity is to obtain a larger robustness of such uncertainty models to payload variations and last-minute mission changes in order to improve the availability and flexibility in the missionization process. Finally, the developed methodologies also improve the consistency between the FEM models, the control design models and the high-fidelity time-domain simulators.