Finite-Time Backstepping Attitude Controller for First-Stage Booster Recovery by Parafoil System

Abstract

Controllable parafoil is one of the most important means to fulfill the recovery of first-stage booster of a rocket due to its high reliability and low cost. However, as a lightweight flexible aircraft, the parafoil and first-stage booster combination (PFC) suffers numerous challenges in attitude control such as external wind disturbances, internal relative motion, and uncertainties. Accordingly, a finite-time backstepping attitude controller for PFC is proposed in this paper. First, the 9-degree-of-freedom model of PFC, of which the relative motion between parafoil and first-stage booster is considered, is established based on dynamic and kinematic analyses. Second, a backstepping controller with finite-time Lyapunov stability theory is presented to guarantee the global stability and robustness of PFC attitude control. Then an extended state observer (ESO) is exerted to accurately estimate the total disturbance of PFC including internal uncertainties such as aerodynamic uncertainty, apparent mass moment coupling, and unknown recovery moment as well as external wind disturbances. Furthermore, a tracking differentiator (TD) is used to solve the derivative of the virtual control variable to avoid differential expansion. Simulation experiments results show that the finite-time backstepping attitude controller with TD and ESO has the advantages of high robustness, fast convergence, and small steady-state error.