Reactive control of second Mack mode in a supersonic boundary layer with free-stream velocity/density variations

We consider closed-loop control of a two-dimensional supersonic boundary layer at $M=4.5$ that aims reducing the linear growth second Mack mode instabilities. These instabilities are first characterized with local spatial and global resolvent analyses, which allow us to refine strategy select appropriate actuators sensors. After input–output reduced-order models have been identified, multi-criteria structured mixed $H_{2}$ / $H_{\infty }$ synthesis allows fix beforehand controller structure minimize norms various transfer functions: norm guarantee performance (reduction perturbation amplification in nominal condition), maintain robustness (with respect sensor noise) stability uncertain free-stream velocity/density variations). Both feedforward feedback set-ups, i.e. estimation placed respectively upstream/downstream actuator, energy below given threshold over significant distance downstream even case noisy sensors or density variations. However, set-up becomes completely ineffective when convective time delays altered by velocity variations $\pm$ 5 %, highlights strong relevance for convectively unstable flows.