Byrnes-Isidori-based dynamic sliding-mode control for nonminimum phase hypersonic vehicles

Abstract

This paper deals with the dynamic sliding-mode (DSM) control problem for nonminimum phase hypersonic vehicles (HSVs). When the elevator is the only control surface available for the altitude dynamics, the HSV model exhibits unstable zero dynamics, preventing the application of standard inversion-based control techniques. To solve this problem, a DSM control method based on Byrnes-Isidori (B-I) normalized form is proposed, achieving asymptotic tracking of velocity and Flight-Path-Angel (FPA) while stabilizing internal dynamics. First, for the pitch dynamics with nonminimum phase behavior, external dynamics and internal dynamics are determined by coordinate transformation to convert the longitudinal model to B-I normalized form, based on which a criterion of nonminimum phase property is given by the stability analysis of internal dynamics. Then, a DSM control method is proposed for the FPA subsystem of nonminimum phase, which transforms the output tracking problem into stabilization problem of an augmented system consisting of internal dynamics and dynamic compensator, making closed-loop pole adjustable, and thus improves the tracking performance. The principle of parameters determination is proposed, which is proved to achieve the stability of the system on the sliding surface. Besides, nonlinear disturbance observer is utilized to compensate the error caused by dynamic inversion control. The proposed method is compared with approximate backstepping control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems of nonminimum phase.