Optimal feedback gains determination method for nominal reentry guidance

Abstract

This paper presents a new method for solving feedback gains in guidance based on optimal control theory. The determination of feedback gains is a critical problem for nominal guidance, because landing precision benefits from appropriate feedback gains. The magnitude of the bank angle is determined by minimizing the total error of final altitude as well as downrange requirement to the landing site. The problem is formulated as an optimal control problem by means of the Pontryagin's maximum principle, and backward integration is used to solve the problem based on homogeneous property. The proposed approach not only can avoid linearizing the nonlinear dynamic equations, but also are applicable to different guidance equations. Validation shows that the proposed approach can provide consistent results with that of Apollo. Despite employment of nominal guidance in the entire reentry of lunar mission, the proposed approach demonstrates good performance in all simulation cases while subject to significant disturbances. Figure 3. The 5000 dispersed cases of simulation results. (a) Latitude versus longitude, (b) histogram of load factor, (c) histogram of maximal heat rate, and (d) histogram of heat load. 221 OPTIMAL FEEDBACK GAINS FOR REENTRY GUIDANCE