The objective of the present paper is to evaluate the application of a promising new mathematical technique called interval analysis for reentry flight clearance. Whereas a Monte Carlo approach clears the vehicle only for a finite number of sets of uncertainty parameters, the new approach clears the vehicle within prespecified uncertainty parameter intervals. The new approach is applied to the reentry trajectory of the Delft Aerospace Reentry Test Demonstrator, a hypothetical ballistic reentry vehicle equipped with an attitude-stabilizing flight control system. As the clearance requirement, the stability of the system is chosen, which is evaluated using two different mathematical criteria: worst-case linear eigenvalue analysis and nonlinear Lyapunov analysis. The new approach, based on interval analysis, is applied in an evaluation of both criteria. Subsequently, Monte Carlo analysis was performed to verify the validity of these results. I. Introduction R EENTRY flight is inseparable from the present and future spaceflight missions. During the reentry flight, a vehicle has to follow a predefined trajectory toward a designated landing area. Trajectory tracking, flight stability, and landing precision are important aspects in the reentry flight. The predefined trajectory has to be tracked with a sufficient margin of error. The stability margin has to be fulfilled against the variation and uncertainty in flight parameters such as aerothermodynamic parameters, mass, and inertia.Theaccuracyoflandingisimportantaswelltoensurethatthe vehicle and its contents reach the target ground intact. All of these aspects need to be analyzed and evaluated in a systematic way to ensure the stability and performance of the reentry vehicle. To certify a reentry vehicle as safe to fly, the reentry flight model has to be evaluated before actual flight. This is known as the reentry flight model clearance, or reentry flight clearance for short. One exampleofthe flightmodelclearanceistheevaluationofthestability and performance of the reentry vehicle model in its flight envelope. AsillustratedinFig.1,thereentry flightenvelopeisdefinedalongthe nominal flight trajectory. The flight safety is checked by evaluating the regions in the flight envelope using predefined stability or performance criteria. The region in which the criteria are fulfilled is then “cleared,” which means that, under the defined flight condition, the vehicle can fly safely in this region. The right-hand side of Fig. 1 shows a blown-up view of the envelope with flyable and nonflyable regionsasaresultoftheclearance.The flyableareasareshownbythe shaded rectangles in the flight envelope. Thechallengeforthereentry flightclearanceliesinthefactthatthe mathematical models of reentry vehicles and the environments are generally nonlinear. Moreover, the models may contain uncertainty due to the unknowns and variations in the dynamics or parameters. Therefore, to produce a reliable clearance result, mathematical analysis methods that account for the nonlinearity and uncertainty in the models are needed. To answer this question, this paper contributesasystematic approachtoperform reentry flightclearance using interval analysis. This method can meet the aforementioned challenge,for itcanbeapplied tolinearaswellasnonlinearsystems, and can account for the uncertainty in the system model. To give the reader an overview of the method, the algorithm is described in Sec. V. The strong point of the method is illustrated using an example of clearance for a nonlinear system. In the sequence, we perform clearance on a reentry vehicle model with a flight control system, with stability robustness in the presence of uncertainty as the clearance criteria (see Sec. VI). The mathematical modelofthesystemisnonlinearwithuncertainparameters.Toshow that the method canbe applied tolinear as well as nonlinear systems, both linearized and nonlinear models of the system are evaluated. The clearance is performed inside the vehicle’s reentry flight envelope. For the linearized system, the eigenvalue criteria is applied, whereas for the nonlinear system, the Lyapunov function isevaluated.TheresultsarevalidatedusingMonteCarloanalysis.As literature survey,Secs.IIandIIIprovidethereader withanoverview of the current clearance practice and of the available methods, which leads to the choice of the clearance method in this paper.
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