Dynamic Modeling and Observer-Based Fixed-Time Backstepping Control for a Hypersonic Morphing Waverider

This paper proposes a fixed-time backstepping control method based on a disturbance observer for a hypersonic morphing waverider (HMW). Firstly, considering the disturbance of attitude channels, a dynamic model of a variable-span-wing HMW considering additional forces and moments is established, and an aerodynamic model of the aircraft is constructed using the polynomial fitting method. Secondly, the fixed-time stability theory and backstepping control method are combined to design an HMW fixed-time attitude controller. Based on the fixed-time convergence theory, a fixed-time disturbance observer is designed to achieve an accurate online estimation of disturbance and to compensate for the control law. In order to solve the problem of the "explosion of terms", a nonlinear first-order filter is used instead of a traditional linear first-order filter to obtain the differential signal, ensuring the overall fixed-time stability of the system. The fixed-time stability of the closed-loop system is strictly proven via Lyapunov analysis. The simulation results show that the proposed method has good adaptability under different initial conditions, morphing speeds, and asymmetric morphing rates of the HMW.