Control and estimation of wall bounded flow systems

Abstract: This thesis focuses on the application of linear feedback control and estimation to channel flow. Both the initial stage of the transition and the low Reynolds number turbulent cases are studied. From sensors at the wall, the state of the flow is estimated, using a stochastic description of the flow disturbances. The estimated state is in turn fed back to the flow system in order to achieve a control objective. This model based scheme uses the linearised Navier-Stokes equations as a dynamic model for the flow evolution. The emphasis is here put on the estimation procedure, that was so far the limiting factor for the overall control performance. We show that the estimation performance rely on a correct description of the flow disturbances. We apply model reduction on the controller, and show that we can maintain the control performance even with a highly truncated system. We then introduce a representation of the feedback by means of transfer functions, and discuss the implication of the transfer function for the interpretation of the feedback, and for possible implementation of the control loop.