Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

Abstract

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is obtained by numerically integrating the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in real-time operation, the bending strain of the beam is measured by fiber-optical sensors at discrete locations along the span, whereas both the angular velocity and translational acceleration are measured at a single point by an inertial measurement unit. Another aspect in this paper is finding the analytical and numerical solutions of the beam dynamics based on limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions of the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.