Robustness Analysis for Terminal Phases of Reentry Flight

A NOVEL approach to analyze the robustness of a flight control system (FCS) with respect to parametric uncertainties is presented, which specifically applies to gliding vehicles in the terminal phases of reentry flight. Robustness analyses are particularly challenging for these systems. Their reference trajectories are appreciably time-varying and encompass a broad variety of flight regimes. Furthermore, significant uncertainties on some critical design parameters affect the vehicle model, most notably those related to the aerodynamic behavior [1]. Current practice in FCS robustness analysis for this kind of application mainly relies on the theory of linear time-invariant (LTI) systems. In this approach, the original nonlinear system is linearized around a limited number of representative time-varying trajectories, including the nominal one. Then thewell-known frozentime approach [2] is applied, yielding multiple LTI models. In this way, classical stability margins [3] or more sophisticated LTI-based robustness criteria, such as analysis [4] and D-stability analyses [5], can be evaluated. Recently, a Lyapunov-based criterion coupled to interval analysis techniques [6] has been proposed for establishing robustness of a FCS. This approach does not resort to linearization of the system dynamics, but still requires the introduction of fictitious equilibrium points obtained by a frozen-time approach. Even if the flight experience demonstrated that frozen-time approaches are indeed operative, they are widely recognized as inefficient [7]. In fact, because the nominal trajectory may not be an equilibrium trajectory for the system in offnominal conditions, frozen-time analyses can provide only indicative, and often heavily conservative, results. To overcome such problems, further investigations are usually performed to identify a limited set of worst-case combinations of uncertain parameters to be used for FCS design refinement. In this case, nonlinear simulations in specific offnominal conditions, selected using sensitivity analysis and designer’s experience, represent the current practice. Optimization-based worst-case search has also been proposed [8], which may disclose the mutual effects of multiple uncertainties, but to a limited extent. In fact, the complexity of reentry dynamics under multiple uncertainties implies that actual worst cases relevant for FCS design refinement are difficult to identify. In any case, worst-case analysis can select only a limited number of test cases, hiding possible further causes of requirement violations, thus driving wrong refinement strategies that would not solve (or even worsen) FCS robustness problems. Monte Carlo (MC) analysis is, in practice, the only tool that is capable of investigating the combined effect of all uncertainties with a reasonable effort. However, being only a verification tool, when unsatisfactory robustness is discovered at this stage, the identification of its causes can require considerable postprocessing effort [9]. This yields one of the major limitations of this approach: that is, the limited support to the FCS design refinement when a requirement violation occurs due to poor robustness. As a result, in these cases, one is forced to iterate the design with scarce additional information. The present paper contributes toward advancing the current practice used in robustness analysis for FCS design refinement by introducing a method that takes into account nonlinear effects of multiple uncertainties over the whole trajectory, to be used before robustness is finally assessed withMC analysis. Themethod delivers feedback on the causes of requirement violation and adopts robustness criteria directly linked to the original mission or system requirements, such as those employed in MC analyses. The first objective is achieved estimating the region of requirement compliance in the space of the uncertain parameters. In this way, the approach provides an exhaustive coverage of the uncertainty’s effects on the FCS robustness. To translate mission requirements into robustness criteria over the whole trajectory, rather than at isolated points as in frozen-time approaches, we make use of the practical stability concept [10], which, to the authors’ knowledge, has never been applied to robustness analyses of atmospheric reentry vehicles.