On the role of adaptivity for robust laminar flow control

Abstract

In boundary-layer flows, one may reduce skin-friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien-Schlichting (TS) waves. In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for. However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based LQG controller in wind-tunnel experiments. In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

Localised estimation and control of linear instabilities in two-dimensional wall-bounded shear flows

“…This paper focussed on optimal control and no other model uncertainties, such as input/actuator uncertainties and uncertainties in the Reynolds number were addressed. Recently in Fabbiane et al (2015) it is shown through experiments that deviations from the design conditions can destabilise optimal controllers. Future work will also focus on addressing model uncertainties by integrating this method in a H ∞ robust control framework.…”

“…This led to the use of reduced order modelling techniques for control design that make no assumptions on the flow geometry and the shape and distribution of the actuators/sensors. This approach, also known as the reduced order modelling approach, accounts for physically realisable localised actuators/sensors and has been validated in experiments (Samimy et al 2007;Pastoor et al 2008;Fabbiane et al 2015). Galerkin projection is commonly applied, in which a reduced order model (ROM) is obtained by projecting the Navier-Stokes equations onto a reduced set of modes.…”

“…The construction of an accurate linear state-space model describing the perturbation dynamics from all inputs to all outputs is the corner stone of linear model based control and is considered as a significant challenge . Limits related to unmodelled dynamics and nonlinearities are commonly assessed from case to case Fabbiane et al 2015) and/or addressed using robust design techniques such as H ∞ loop shaping (Jones et al 2015;Flinois & Morgans 2016). For example, in Jones et al (2015) the effect of nonlinearity is attenuated by a linear feedback controller that employs high loop gain over a selected frequency range.…”

Linear control of oscillator and amplifier flows1

“…An alternative approach to the robustness problem is given by adaptive control strategies 42,43 , such as the FXLMS algorithm. Rather than determining a fixed control law, a proper actuator response is identified from sensor input, based on an approximate model for the flow behavior.…”

On the wave-cancelling nature of boundary layer flow control

“…For applications in boundary layer transition control, the reader is referred to the works of Fabbiane et al [16,18], and the work of Bagheri et al [2] which presents a nice introduction to optimal control for applications in fluid mechanics. The success of LQG controllers is related to their optimality, the design being made in two steps, from the solution of two Riccati equations for the estimation and control problems, which guarantee stability, as long as the system is observable and controllable.…”