Time‐varying robustness analysis of launch vehicles under thrust perturbations

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.

Linearized State-Space Model-Based Attitude Control for Rocket With Four Controllable Fins—Part 1-1: Basic Modeling and Identification

“…Biertumpfel et al [16] of the Dresden University of Technology attempted a robustness analysis for launch vehicles ascending in the atmosphere. They presented a finite-horizon linear time-varying system assuming worstcase scenarios.…”