Adaptive guidance for an aero-assisted boost vehicle

Abstract

An adaptive guidance system incorporating a dynamic pressure constraint is developed for a single stage to low Earth orbit, with thrust gimbal angle as the control variable. The ascent profile is represented in the form of a two-segment cubic spline function whose parameters are optimized for maximum payload. The flight to low Earth orbit is divided into initial and terminal phases. In the initial phase, a fully adaptive scheme is used wherein a new ascent profile is generated for the remainder of flight whenever the simulated vehicle deviates beyond a prescribed limit. In the terminal phase, a semiadaptive scheme with a linear feedback control is used to keep the vehicle close to the nominal path. This two-phase adaptive guidance algorithm is applied to a generic aeroassisted booster.endpoint altitude for initial guidance phase hi = intermediate altitude where the two spline segments are connected des = desired altitude as given by spline ascent profile, Eq. (8) h a = current altitude of the booster vehicle hf = final altitude Ki,K 2 = feedback gains L -aerodynamic lift LQ = longitude M = Mach number m = mass of the boost vehicle ra 0 = initial mass (t = 0) m p -final mass at h = h f q -dynamic pressure = Vip Vl R = position vector T = thrust V = current inertial velocity V 0 = inertial velocity on the surface of Earth Vf, Vi = inertial velocity at h = h f and h\ 9 respectively ROI -radius vector from Earth's center to origin of Xny n z n system xyz = rectangular coordinate system Bandu N. 587 0! 0 7 6 e X = angle of attack = coefficient in the exponential atmospheric density model = flight-path angle = semivertex angle of the booster = percent error margin (A/*//*) = geographical latitude = thrust gimbal angle iin = maximum and minimum limits, respectively, of thrust gimbal angle = angular velocity of the Earth about its own axis = differentiation with respect to inertial velocity = differentiation with respect to time Subscripts b e i n max = body = Earth-related = inertial = navigational = maximum value