Predictive Control of a Munition Using Low-Speed Linear Theory

CDD = fin cant rolling aerodynamic coefficient CLL, CMM, CNN = roll, pitch, and yaw control aerodynamic coefficients CLP, CMQ, CNR = roll, pitch, and yaw damping aerodynamic coefficients Cmax = pitch and yaw control limit CNA = normal force aerodynamic coefficient Cx0 = zero yaw drag aerodynamic coefficient Cx2 = yaw squared drag aerodynamic coefficient D = reference diameter e = impact-error vector emax = impact-error stopping criterion g = gravitational constant I = munition inertia matrix IXX , IYY , IZZ = moments of inertia IXY , IYZ, IXZ = products of inertia K = predictive control gain matrix kmax = control iteration limit ~ L, ~ M, ~ N = external moments in the nonrolling frame ~ LA, ~ MA, ~ NA = aerodynamic moments in the nonrolling frame ~ LC, ~ MC, ~ NC = control moments in the nonrolling frame ~ LUA, ~ MUA, ~ NUA = unsteady aerodynamic moments in the nonrolling frame m = mass ~ p, ~ q, ~ r = angular velocity components in the nonrolling frame R AX = distance from the mass center to the aerodynamic center along the station line. s = nondimensional arc length ~ u, ~ v, ~ w = velocity components in the nonrolling frame ~ uw, ~ vw, ~ ww = wind velocity components in the nonrolling frame V = total velocity Vx, Vz = longitudinal velocity components ~ w0, ~ q0, 0 = vertical velocity, pitch rate, and pitch in nonrolling frame at the beginning of an update interval x, y, z = inertial positions of the mass center ~ X, ~ Y, ~ Z = external forces in the nonrolling frame ~ XA, ~ YA, ~ ZA = aerodynamic forces in the nonrolling frame ~ XW , ~ YW , ~ ZW = weight in the nonrolling frame xI , yI , zI = predicted-impact position components xT , yT , zT = target position components , = aerodynamic angle of attack and side slip , 1, 1 = longitudinal equation’s pole, real, and imaginary components = atmospheric density 2, 2 = lateral equation’s real and imaginary components , , = Euler roll, pitch, and yaw angles