Time‐varying robustness analysis of launch vehicles under thrust perturbations. Issue 4 (17th November 2021) - Biertümpfel, Felix
Abstract: This article presents a robustness analysis for launch vehicles during atmospheric ascent. It is based on recent advances in the worst‐case analysis of uncertain, finite horizon linear time‐varying (LTV) systems. Integral quadratic constraints are used to represent the uncertainties leading to a worst‐case gain condition based on a parameterized Riccati differential equation (RDE). This framework readily covers certain parametric uncertainties, for example, aerodynamic uncertainties. However, the effects of thrust perturbations are inherently harder to address. They directly result in mass and balance uncertainties, and a deviation from the planned trajectory. The latter amounts to a shift from the nominal/reference trajectory that has to be accounted for. Since thrust is proportional to the mass change of the launch vehicle, the thrust uncertainty is modeled as an external disturbance acting on the system. In order to cover the deviation from the reference trajectory, a dynamic uncertainty model is added in the analysis. A worst‐case aerodynamic loads and lateral drift analysis under wind disturbances is performed. The LTV results are validated against Monte Carlo simulations of the space launcher's nonlinear model. Abstract : A new approach to cover thrust perturbations in the linear‐time varying worst‐case analysis of launch vehicles is proposed. It covers the thrust disturbance as an external input and the mass as a state in the linearization process, maintaining their coupling. Furthermore, it allows covering their respective influence on the launcher's ascent trajectory in the linear analysis.