Guidance law for hypersonic gliders based on piecewise constant control

Abstract

A midcourse guidance law is developed for the descent of a hypersonic glider, initially in level flight, to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat Earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N + \ nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14% of the true values are obtained for the downrange and crossranges considered. Nomenclatureof gravity at sea level, ft/s 2 h = altitude, ft K = coefficient of parabolic drag polar M -Mach number m = mass, slugs N = number of intervals R = planet radius, ft S r = aerodynamic reference area, ft 2 T g = guidance period, s V = velocity, ft/s v = dimensionless velocity, -ln(V/V 0 ) X = downrange, ft Y = crossrange, ft a = angle of attack, rad ft = sideslip angle, rad fi e = density scale height, ft y = flight path angle, rad i/r = heading angle, rad p -atmospheric density, slugs/ft 3 p e = density at sea level, slugs/ft 3