Control-oriented Modeling of an Air-breathing Hypersonic Vehicle
Sudalagunta, Praneeth Reddy
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Design and development of future high speed aircraft require the use of advanced modeling tools early on in the design phase to study and analyze complex aeroelastic, thermoelastic, and aerothermal interactions. This phase, commonly referred to as the conceptual design phase, involves using first principle based analytical models to obtain a practical starting point for the preliminary and detailed design phases. These analytical models are expected to, firstly, capture the effect of complex interactions between various subsystems using basic physics, and secondly, minimize computational costs. The size of a typical air-breathing hypersonic vehicle can vary anywhere between 12 ft, like the NASA X-43A, to 100 ft, like the NASP demonstrator vehicle. On the other hand, the performance expectations can vary anywhere between cruising at Mach 5 @ 85; 000 ft to Mach 10 @ 110; 000 ft. Reduction of computational costs is essential to efficiently sort through such a vast design space, while capturing the various complex interactions between subsystems has shown to improve accuracy of the design estimates. This motivates the need to develop modelling tools using first principle based analytical models with "needed" fidelity, where fidelity refers to the extent of interactions captured. With the advent of multidisciplinary design optimization tools, the need for an integrated modelling and analysis environment for high speed aircraft has increased substantially over the past two decades. The ever growing increase in performance expectations has made the traditional design approach of optimize first, integrate later obsolete. Designing a closed-loop control system for an aircraft might prove to be a difficult task with a geometry that yields an optimal (L/D) ratio, a structure with optimal material properties, and a propulsion system with maximum thrust-weight ratio. With all the subsystems already optimized, there is very little freedom for control designers to achieve their high performance goals. Integrated design methodologies focus on optimizing the overall design, as opposed to individual subsystems. Control-oriented modelling is an approach that involves making appropriate assumptions while modelling various subsystems in order to facilitate the inclusion of control design during the conceptual design phase. Due to their high lift-to-drag ratio and low operational costs, air-breathing hypersonic vehicles have spurred some interest in the field of high speed aircraft design over the last few decades. Modeling aeroelastic effects for such an aircraft is challenging due to its tightly integrated airframe and propulsion system that leads to significant deflections in the thrust vector caused by flexing of the airframe under extreme aerodynamic and thermal loads. These changes in the orientation of the thrust vector in turn introduce low frequency oscillations in the flight path angle, which make control system design a challenging task. Inclusion of such effects in the vehicle dynamics model to develop accurate control laws is an important part of control-oriented modeling. The air-breathing hypersonic vehicle considered here is assumed to be a thin-walled structure, where deformations due to axial, bending, shear, and torsion are modeled using the six independent displacements of a rigid cross section. Free vibration mode shapes are computed accurately using a novel scheme that uses estimates of natural frequency from the Ritz method as initial guesses to solve the governing equations using SUPORE, a two-point boundary value problem solver. A variational approach involving Hamilton's principle of least action is employed to derive the second order nonlinear equations of motion for the flexible aircraft. These nonlinear equations of motion are then linearized about a given cruise condition, modal analysis carried out on the linearized system, and the coupling between various significant modes studied. Further, open-loop stability analysis in time domain is conducted.
- Doctoral Dissertations