TY - THES
T1 - Finite-dimensional approximation and control of shear flows
AU - Tol, Henry
PY - 2018
Y1 - 2018
N2 - Dynamical systems theory can significantly contribute to the understanding and control of fluid flows. Fluid dynamical systems are governed by the Navier-Stokes equations, which are continuous in both time and space, resulting in a state space of infinite dimension. To incorporate tools from systems theory it has become common practise to approximate the infinite-dimensional system by a finite-dimensional lumped system. Current techniques for this reduction step are data driven and produce models which are sensitive to the simulation or experimental conditions. This dissertation proposes a rigorous and practical methodology for the derivation of accurate finite-dimensional approximations and output feedback controllers directly from the governing equations. The approach combines state-space discretisation of the linearised Navier-Stokes equations with balanced truncation to design experimentally feasible low-order controllers. The approximation techniques can be used to design any suitable linear controller. In this study the reduced-order controllers are designed within an H2 optimal control framework to account for external disturbances and measurement noise. Application is focused on control of laminar wall-bounded shear flows to delay the classical transition process initially governed by two-dimensional convective perturbations, to extend laminar flow and reduce skin friction drag. The controllers are successfully tested in the vertical wind tunnel at the TU Delft.
AB - Dynamical systems theory can significantly contribute to the understanding and control of fluid flows. Fluid dynamical systems are governed by the Navier-Stokes equations, which are continuous in both time and space, resulting in a state space of infinite dimension. To incorporate tools from systems theory it has become common practise to approximate the infinite-dimensional system by a finite-dimensional lumped system. Current techniques for this reduction step are data driven and produce models which are sensitive to the simulation or experimental conditions. This dissertation proposes a rigorous and practical methodology for the derivation of accurate finite-dimensional approximations and output feedback controllers directly from the governing equations. The approach combines state-space discretisation of the linearised Navier-Stokes equations with balanced truncation to design experimentally feasible low-order controllers. The approximation techniques can be used to design any suitable linear controller. In this study the reduced-order controllers are designed within an H2 optimal control framework to account for external disturbances and measurement noise. Application is focused on control of laminar wall-bounded shear flows to delay the classical transition process initially governed by two-dimensional convective perturbations, to extend laminar flow and reduce skin friction drag. The controllers are successfully tested in the vertical wind tunnel at the TU Delft.
KW - Flow instability and control
UR - http://resolver.tudelft.nl/uuid:68de92fd-0185-4e08-b911-253358708a9c
U2 - 10.4233/uuid:68de92fd-0185-4e08-b911-253358708a9c
DO - 10.4233/uuid:68de92fd-0185-4e08-b911-253358708a9c
M3 - Dissertation (TU Delft)
SN - 978-94-6186-926-5
ER -