This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H ∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl's theory of sheared turbulence. To illustrate the application of these techniques, a H ∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall-shear stress in plane channel flow. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller.

This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skinfriction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in the nonlinear turbulent regime. The novel strategy is effective in reducing the supply of available energy to feed the turbulent fluctuations, expressed as reducing a bound on the supply rate to a quadratic storage function. The nonlinearity present in the equations that govern the dynamics of the flow is known to be passive and can be considered as a feedback forcing to the linearised dynamics (a Lur'e decomposition). Therefore, one is only required to control the linear dynamics in order to make the system close to passive. The ten most energy-producing spatial modes of a turbulent channel flow were identified. Passivity-based controllers were then generated to control these modes. The controllers require measurements of streamwise and spanwise wall-shear stress, and they actuate via wall transpiration. Nonlinear direct numerical simulations demonstrated that these controllers were capable of significantly reducing the turbulent energy and skin-friction drag of the flow.

In this paper we present a multiphysics simulation model of Halcyon, an autonomous unmanned surface vehicle (USV). The simulation model presented in this paper has been developed to rapidly progress the design, development and validation of Halcyon's autonomy management system, particularly in challenging sea conditions. Using simulation for this purpose enables extensive testing across the full environmental operating envelope of the vessel, hence greatly reducing the need for real-world sea-trials. The simulator is comprised of a novel and comprehensive sea-surface wave environment model, a six degree of freedom nonlinear unified seakeeping and manoeuvring boat dynamics model, an actuation dynamics model, an autopilot and an interface with an autonomy management system. Results are presented that show good agreement between real-world and simulated sea-trials data.

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