Robust Nonlinear Control of a Hypersonic Aircraft in the Presence of Aerothermoelastic Effects

Hypersonic flight conditions produce temperature variations that can alter the flight dynamics. A nonlinear temperature dependent, parameter varying state-space repre- sentation is proposed to capture the aerothermoelastic effects in a hypersonic vehicle. This model includes an uncertain pa- rameter varying state matrix, an uncertain parameter varying non-square (column deficient) input matrix, and a nonlinear additive bounded disturbance. A Lyapunov-based continuous robustoutputfeedbackcontrollerisdevelopedthatyieldsglobal exponential tracking of a reference model, despite the presence of disturbances that do not satisfy the linear-in-the parameters (LP) assumption. I. INTRODUCTION 1 Design of guidance and control systems for airbreathing hypersonicvehicles (HSV) isa challengingtask becausethe dynamics of the HSV are complex and highly coupled (1). Moreover, temperature-induced stiffness variations impact the structural dynamics (2). The structural dynamics, in turn, affect the aerodynamic properties. Vibration in the forwardfuselagechangestheapparentturnangleoftheflow, which results in changes in the pressure distribution over the forebody of the aircraft. The resulting changes in the pressure distribution over the aircraft manifest themselves as thrust, lift, drag, and pitching moment perturbations (1). To develop control laws for the longitudinal dynamics of a HSV capable of compensating for these structural and aerothermoelasticeffects, surfacetemperature variationsand structural dynamics must be considered. Several results have examined the challenges associated withthedynamicsandcontrolofHSVs.Adetailedanalytical model of the longitudinal dynamics was undertaken by Chavez and Schmidt (3). A slightly different approach to develop the model was undertaken by Bolender and Doman in (1) and (4), which was further developed by the same authors in (5) and (6). Another model of the hypersonic vehiclewasdevelopedusingpistontheory(7).Severalresults discuss various control strategies and sensor placement for the vehicle using the above models (8), (9). In (10)-(12), HSVflightcontrollersaredesignedusinggenetic algorithms to search a design parameter space where the nonlinear lon- gitudinal equations of motion contain uncertain parameters. The control designs in (10) and (11) utilize Monte Carlo simulations to estimate system robustness at each search