Optimal and Robust Control of Magnetohydrodynamic Channel Flow Instabilities

Active closed-loop control of subcritical and supercritical instabilities amplified in a channel flow submitted to a constant normal magnetic field is investigated. The control is carried out at both the upper and the lower wall by blowing and suction or by a perturbation of the normal magnetic field. A robust formulation (H_∞) of the control has been performed to take into account uncertainties coming from the state disturbances and the measurement noise. Optimal and robust dynamic controls have been tested, with full state information or only wall informations. As expected, we found that the closed-loop control modifies the optimal perturbation. However the lift-up mechanisms are still in action. In the supercritical case we found that the control acts almost exclusively on the unstable mode, whose real part becomes negative.