Feedback control of transient energy growth in subcritical plane Poiseuille flow

Subcritical flows may experience large transient perturbation energy amplifications, that could trigger nonlinear mechanisms and eventually lead to transition to turbulence. In plane Poiseuille flow, controlled via wall blowing/suction with zero net mass flux, optimal and robust control theory has been recently applied to a state-space representation of the Orr-Sommerfeld-Squire equations, leading to reduced transient growth as well as increased transition thresholds. However, to date no feedback control law has been found that is capable of ensuring the closed-loop Poiseuille flow to be monotonically stable. The present paper addresses first the possibility of complete feedback suppression of the transient growth mechanism in subcritical plane Poiseuille flow when wall actuation is available, and demonstrates that closed-loop monotonic stability cannot be achieved in such a case. Secondly, a Linear Matrix Inequality (LMI) technique is employed to design controllers that directly target the energy growth mechanism. The performance of such control laws is quantified by using Direct Numerical Simulations of transitional plane Poiseuille flow, and the increase in transition thresholds due to the control action is assessed.