Neighboring Optimal Maximum Range Glide Phugoid-Damping Guidance Law

This paper explicitly solves for the neighboring optimal control to the singularly perturbed maximum range glide slope. The result is a flight path angle feedback gain which augments the maximum lift-to-drag ratio angle of attack in order to optimally damp the phugoid mode of the aircraft. The feedback gain is given explicitly in terms of the aerodynamic coefficients for a linear lift and parabolic drag model.The explicit feedback gains are comparable to previous work which had the same structure for the controller but numerically optimized the feedback gain. Additionally, the guidance law is evaluated using a high lift-to-drag supersonic vehicle. Although derived assuming constant aerodynamic coefficients, the gliding performance in the presence of Mach-dependent aerodynamics for the supersonic vehicle was over 99% optimal for each case tested.