| Hypersonic air-breathing vehicles are a promising and cost-efficient technology for launching low-earth-orbit satellites and providing rapid global-response capabilities. Modeling and control of such vehicles has been an active subject of research in recent years. A first-principle, physics-based model (FPM) of the vehicle's longitudinal dynamics has been developed at the Air Force Research Laboratory, and made available to the academic community for control systems design. This model, while suitable for simulation, is intractable for model-based control, thus requiring further control-oriented modeling. A typical control objective is to track a velocity and altitude reference while maintaining physical feasibility of the control input and the state. Two control strategies are presented in this work. The first is a linear time invariant (LTI) design based on a novel formulation of a robust servo-mechanism using singular perturbation arguments. This approach does not rely on state reconstruction but does require an analysis of a family of linearized models from the FPM. The second design relies on reduced-complexity modeling of the FPM. Intractable expressions of the forces and moment in the FPM are replaced with a curve-fit model (CFM). The CFM is expressed as a linear parameter varying (LPV) system, where the scheduling variables depend on the system output. A novel LPV regulator design methodology is developed, which explicitly addresses the case of over-actuated models (i.e., models with more inputs than performance outputs). This is a non-trivial extension of the analysis and design of output regulators for LTI systems. The LPV regulator separates the control problem into a steady-state controller and a stabilizing controller. The steady-state controller produces a non-unique approximate steady-state using receding horizon constrained optimization, while the stabilizer renders the steadystate attractive. The steady-state controller represents an approach to addressing over-actuated LPV systems, alternative to static or dynamic control allocation, or standard optimal control. The stabilizer design utilizes the LPV separation principle to decompose the problem into state feedback and LPV reduced order observer design. Both approaches are applied to the FPM in simulation and their merits and drawbacks discussed. |
