| Renewed interest in scramjet propulsion has motivated efforts to construct models of the scramjet engine flow path that capture transient flow dynamics to an extent that allows model-based control design. In particular, a model of the propagation of the shock wave due to a change in backpressure is needed for use in designing a controller for unstart prevention. A simplified modeling process considers the engine as the cascade of an inlet/isolator subsystem and a combustor subsystem, with emphasis placed on constructing a model of the (axisymmetric) isolator. Two types of models were considered in this effort: physics-based models constructed through spatial discretization of the compressible Euler equations and data-based models constructed through system identification using computational fluid dynamics (CFD) data. While physics-based models constructed from the two-dimensional Euler equations were found to be too expensive, a reduced-order model based on the one-dimensional Euler equations was found appropriate for the task at hand. Concurrently, a set of linear isolator models were constructed through application of subspace state-space identification technique to CFD data. An unstructured representation of uncertainty in this model was constructed from covariance data. Combining these results with error and residual analysis, a single linear model was chosen for consideration in control design. Based on a mixed-sensitivity approach, an unstable and a stable controller were designed for this model with the goal of anchoring the shock wave at a specified location in the presence of an input disturbance. While both controllers were successful in maintaining the shock location within 3 cm of the expected location for the nominal model, it was found that the controller with stable dynamics resulted in enhanced robustness for the closed-loop system. The model was then validated in closed-loop with the physics-based model, where the controller successfully meets the design goal despite limitations in the nonlinear model. This shows the promise of applying reduced-order model-based control design to the problem of active unstart prevention in a scramjet engine. |
