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 guidance. To meet the requirements of the rapidity and accuracy for the close-loop guidance, the fewer number of unknowns is artificially chosen to reduce the calculation time, and the on-board trajectory planning strategy can increase the precision of the optimal solution along with the decrease of time-to-go. Practical implications -The closed-loop guidance algorithm based on an FEM can be found in this paper, which can solve the optimal ascent guidance problems for launch vehicles in the atmospheric flight phase rapidly, accurately and efficiently. Originality/value -This paper re-derives the necessary conditions of the optimal solution in a different way compared to the previous work, and the closed-loop guidance algorithm combined with the FEM is also a new thought for the optimal atmospheric ascent guidance problems.

Endoatmospheric Ascent Optimal Guidance with Analytical Nonlinear Trajectory Prediction

“…Trajectory with Zero AOA. In (10), the right side of the differential equation of V b can be divided into the following two parts:…”

“…In the boost phase, the flight-path angle varies slightly; therefore, the linear term sin γ 0 + c 1 Δθ b is much larger than the rest terms. Therefore, according to the regular perturbation method presented in Appendix A, (10) can be modified as…”

“…Further research and development on improving this method are referred to [7][8][9]. In [10], Lu et al presented a numerical trajectory reconstruction algorithm based on a finite element method, which satisfies the real-time requirement of generating the guidance commands. In [11,12], Dukeman et al proposed an endoatmospheric ascent guidance for rocket-powered launch vehicles, in which multiple shooting method is employed to solving TPBVP with a high computational efficiency.…”