Extending Closed-Loop Control of Two-Dimensional Supersonic Boundary-Layer Instabilities Beyond a Single Operating Point

Abstract

This paper investigates two control strategies to maintain low perturbation amplitudes of second Mack mode instabilities in a two-dimensional boundary layer with freestream velocity variations of ±5% around M∞=4.5: the multimodel synthesis and the gain scheduling method, both based on the structured mixed H2/H∞ synthesis to handle simultaneously, in an optimal way, the problems of nominal performance, stability, and performance robustness. The multimodel synthesis is based on a single linear-time invariant (LTI) controller optimized over multiple operating points, whereas the gain scheduling method results in a control law based on the interpolation of multiple LTI controllers designed at the various operating points. Both methods are compared with simple LTI controllers based solely on the nominal operating point in two sensor–actuator architectures: in feedforward (respectively, feedback) the estimation sensor is located upstream (respectively, downstream) of the actuator. In the feedforward case, significant performance loss is observed in off-design conditions, regardless of the method used. In the feedback case, multimodel synthesis enhances slightly performance robustness (but improvement is weak because of the wide range of freestream velocity variation), while the gain scheduling approach succeeds in strongly reducing the perturbation amplitude over the entire range of variation.