Atmospheric Re-Entry Trajectory Tracking and Control for an Unmanned Space Vehicle with a Lyapunov Approach

The paper presents the tracking and control of a selected set of state variables for a winged unmanned re-entry vehicle, during the last of its descent towards the Earth. The aerodynamic has been treated as bi-dimensional (within the vertical plane) and the system is modeled as a rigid body. A complete analysis of the possible control solutions has been done, in terms of both control variables and actuators. A controller has been synthesized by applying the Lyapunov asymptotic stability theory: different Lyapunov functions have been implemented and the best one is here proposed. From the actuators point of view, different sets have been analyzed; the best one in terms of state variables tracking turned out to be made of elevons, vectorable thrust and a moveable mass. According to the settled Lyapunov function, taking into account each actuator saturation, the selected state variables - the angle of attack, the Mach number and the pitch angular velocity - are correctly tracked, while the remaining are tracked with a dynamic gap. A comparison with a Proportional Integrative controller showed the benefits of the Lyapunov approach. All aerodynamic data come from simulations done according to a possible configuration of the first Italian prototype under development to test a new re-entry vehicle completely unmanned.