Near-Optimal Control of Altitude and Path Angle During Aerospace Plane Ascent

Altitude and e ight-path-angle control during the posttransonic airbreathing segment of aerospace plane ascent is addressed, with objectives to minimize fuel usage and respect the vehicle e ight envelope. Based on a time-scale separation between energy/mass and altitude/path-angle dynamics, the altitude/path-angle control problem is viewedina singularperturbation framework asan initialboundary-layerproblem. Afeedbacklawapproximating theminimum-fuelinitialboundary-layercontrolisobtainedbysolvinganeighboring-optimalproblem.Tofacilitate this derivation, the state constraint that is active on the slow solution is modeled in the boundary layer using an appropriatepenaltyfunction.Theneighboring-optimalfeedbacklawperformswellaslongastemporaryconstraint violations are acceptable in the boundary layer. An alternate linear feedback law is derived with gains calculated to reduce constraint violations, but this law leads to increased fuel usage. Numerical results are presented for a lifting-body cone guration of an aerospace plane and a Mach 8 e ight condition. The results show that fuel usage and control activity are reduced when the peak dynamic pressure is allowed to increase. Differences in fuel usage are small for the vehicle model employed.

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