Closed-loop atmospheric ascent guidance based on finite element method

Abstract

Purpose – The purpose of this paper is to study the closed-loop guidance algorithm for launch vehicles in an atmospheric ascent phase and present a numerical trajectory reconstruction algorithm to satisfy the real-time requirement of generating the guidance commands. Design/methodology/approach – An optimal control model for an atmospheric ascent guidance system is established directly; following that, the detailed process for necessary conditions of the optimal control problem is re-derived based on the calculus of variations. As a result, the trajectory optimization problem can be reduced to a root-finding problem of algebraic equations based on the finite element method (FEM). To obtain an accurate solution, the Newton method is introduced to solve the roots in a guidance update cycle. Findings – The presented approach can accurately and efficiently solve the trajectory optimization problems. A moderate number of unknowns can yield a good optimal solution, which is well suited for the open-loop guidanc...