Longitudinal wind shear flight control laws are developed for the dynamics of a twin-jet transport aircraft using nonlinear dynamic inversion. Time-scale decomposition simplifies controller design by partitioning it into slow and fast time scales. The effects of time-varying winds are explicitly considered in the derivation of the controllers. Three inverting controllers are developed and evaluated: airspeed/climb rate, groundspeed /climb rate, and throttle/climb rate. The implementation of a climb rate scheduling strategy makes it possible for the resultant flight paths to mimic the essential features of optimal escape trajectories developed in an earlier study, where altitude is exchanged for airspeed as a function of microburst strength.
NomenclatureD = drag, Ibf E s = specific Energy, ft F = nondimensional wind shear hazard index g = acceleration due to gravity, ft/s 2 h = altitude, ft I yy = moment of inertia about body y axis, slug-ft 2 L = lift, Ibf M = pitching moment m = mass, slugs q = pitch rate, rad/s R = radius of downdraft column, ft r = rate of climb, ft/s s = Laplace variable T = engine thrust, Ibf t = time, s f^max = maximum horizontal wind speed, ft/s u = aircraft control vector V a = airspeed, ft/s Vi = groundspeed, ft/s W = weight, Ibf w x = wind component along the x axis, ft/s w h = wind component along the h axis, ft/s jc = distance along the x axis, ft x = aircraft state vector y = control system command vector Zmax = altitude of maximum outflow, ft a = angle of attack, rad y = flight-path angle, rad A* = range from core, ft 8 E = elevator deflection, deg 8 T = throttle setting, % 0 = pitch attitude, rad Subscripts a, A = air-mass referenced quantity c = commanded value i, I = inertially referenced quantity
