Robust Nonlinear Control Design for a Hypersonic Aircraft Using Sum–of–squares Method

In recent years, Sum–Of–Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. This paper utilizes SOS method to design a robust nonlinear controller for longitudinal dynamics of a hypersonic aircraft model. Specifically, the searching of the nonlinear robust controller is reformulated as a robust SOS/robust LMI problem, and then solved via a stochastic iterative algorithm. As the simulation results show, the designed controller is capable of stabilizing the aircraft and following pilot commands in presence of parametric uncertainties in the aircraft model. NOMENCLATURE a speed of sound, m/s CD drag coefficient CL lift coefficient CM(q) pitching moment due to pitch rate CM(α) pitching moment due to angle of attack CM(δE) pitching moment due to elevator deflection CT thrust coefficient c̄ reference length, 24.38 m h altitude, m Iyy moment of inertia, 9490725 kg-m 2 m mass, 136818 kg M Mach number q pitch rate RE radius of the earth, 6371387 m S reference area, 335 m V airspeed, m/s ∗Address all correspondence to this author. α angle of attack, rad β equivalence ratio, ∈ [0 , 20] δE elevator deflection, rad ∈ [−2π/9 , 2π/9] γ flight-path angle, rad μ gravitational constant, 3.94×1014 m/s ρa density of air, kg/m 3