Explicit guidance of a rocket with non-uniform thrust

Abstract

Most of the available closed-loop explicit guidance algorithms either use constant thrust or constant acceleration thrust models. These assumptions which simplify the computation of thrust integrals are too restrictive for non-uniform thrusts. The inaccuracy in the thrust modelling works equivalent to corresponding perturbations in thrust values, and manifests in large changes in steering angles as well as inaccuracy in the injection condition and non-optimality. In this paper, a non-uniform thrust is modelled as linearly varying either increasing, decreasing or of constant magnitude over limited time segments. The corresponding thrust integrals are developed in a simple way. An earlier developed algorithm is extended where each of these linearly varying thrust segment is considered equivalent to a stage of a multi-stage rocket while solving the guidance problem. These thrust integrals can be used by most of the explicit guidance algorithms and help in improving performance considerably with non-uniform thrust. The numerical simulation results show that the algorithms using these thrust integrals provide significantly better results as compared to ones using constant thrust models or a model using remaining thrust constant.