Passivity-based feedback control of a channel flow for drag reduction

A new active-closed-loop linear time-invariant robust control strategy for reducing drag in a channel flow is presented. Using the theory of passive systems, controllers were designed so as to make the closed-loop system as close to passive as is possible. Physically, this means minimising the maximum bound on perturbation energy production within the system. Although the resulting controllers are linear, the nonlinearity, inherent in all fluidic systems, is accounted for and included as an exogenous feedback forcing. Passivity-based controllers were generated for a Re = 2230 channel flow for a range of spatial wavenumber pairs and then analysed. They were shown to be capable of greatly restricting transient energy growth.