Limitations of linear closed-loop control applied to practical fluid flows

The performance of the closed-loop control of turbulent flows has so far been modest. More precisely, the achievable closed-loop bandwidth has typically been an order of magnitude less than the characteristic frequency defined by the Strouhal number. In this talk, the reasons for the limited success of linear control laws are explored by drawing on results from several experimental and numerical studies. The Bode sensitivity integral – a classical theorem in control theory – limits the degree to which fluctuations in the flow can be rejected by the action of the controller. The finite authority of the actuator, along with the transport delay inherent between the control action and the sensor, are shown to combine with Bode's theorem to produce an active constraint on the closed-loop performance. The requirements to bring the closed-loop bandwidth into line with that of the open-loop dynamics are addressed, and the potential of approaches that harness sparse sensing and neural networks is discussed