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A non-linear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures the complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations-of-motion for the flexible aircraft are derived using Lagrange's Equations. The equations-of-motion capture inertial coupling effects between the pitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are shown to be unstable, and in most cases, exhibit non-minimum phase behavior. The linearized model also indicates that there is an aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode. Furthermore, the short-period mode is very strongly coupled with the bending mode of the fuselage.

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The focus of this paper is on control design and simulation for an air-breathing hypersonic vehicle. The challenges for control design in this class of vehicles lie in the inherent coupling between the propulsion system, and the airframe dynamics, and the presence of strong flexibility effects. Working from a highly nonlinear, dynamically-coupled simulation model, control designs are presented for velocity, angle-of-attack, and altitude command input tracking for a linearized version of a generic air-breathing hypersonic vehicle model linearized about a specific trim condition. Control inputs for this study include elevator deflection, total temperature change across the combustor, and the diffuser area ratio. Two control design methods are presented, both using linear quadratic techniques with integral augmentation, and are implemented in tracking control studies. The first approach focuses on setpoint tracking control, whereas in the second, a regulator design approach is taken. Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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