A neighboring optimum feedback control scheme based on estimated time-to-go with application to re-entry flight paths

A modification of the perturbation feedback control scheme of Refs. 1-3 is presented which greatly increases its capability to handle disturbances in cases where the final time is not specified. The modified control scheme uses a set of precalculated gains which allows inflight estimation of the change in the final time due to perturbations from a nominal path. The time-to-go, determined from the predicted change in final time, is used to enter tables of precalculated feedback control gains. This modified guidance scheme is applied to a reentry glider entering the atmosphere of the earth at supercircular velocities. Beginning at the bottom of the pull-up maneuver (nominal altitude 188,000 ft, nominal velocity 33,000 fps) the glider is guided to a terminal altitude of 220,000 ft and zero (0) flight-path angle with maximum terminal velocity. For initial altitudes between 167,000 and 216,000 ft the terminal error in altitude is less than two ft; for initial velocities between 23,000 and 43,000 fps the terminal altitude error is less than 13 ft. In addition, the terminal velocity is very close to optimal for these initial conditions. The suggestion for using such a scheme was first given by Kelley4 who used performance index-to-go as the index variable. He called this a "transversal comparison" scheme. Time-to-go has the advantage that it always decreases monotonically whereas this is not always true of performance index-to-go. A monotonically changing index variable must be used if the transversal comparisons are to be made over the entire flight. The transversal comparison is used here in an iterative scheme to predict the time-to-go. Kelley's suggestion is also extended to include nonstationary systems and in-flight changes in the terminal constraints.