Abstract
Output-based controllers are known to be fragile with respect to model uncertainties. The standard mathcal {H}_{infty }-control theory provides a general approach to robust controller design based on the solution of the mathcal {H}_{infty }-Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.
Highlights
We will approach this question through a semi-discrete and linearized approximation to (1), model order reduction to cope with the high dimensionality of the controller design problem, and the design of controllers that can compensate for a large class of system uncertainties
Our argument is that discretization and model reduction errors are of the same nature such that a proven robustness margin can possibly overcome unmodeled uncertainties, too
In order to potentially work in physical setups, any model-based controller needs a certain robustness against inevitable model errors
Summary
The variables v and p describe the evolution of the velocity and pressure fields in a given flow setup that is parametrized through the Reynolds number , the operator B models the actuation through the controls, and C is the output operator We will approach this question through a semi-discrete and linearized approximation to (1), model order reduction to cope with the high dimensionality of the controller design problem, and the design of controllers that can compensate for a large class of system uncertainties. We provide a complete numerical approach that makes H∞-controller design feasible for large-scale Navier–Stokes systems and provides computable bounds on the robustness of the performance with respect to both linearization errors [14] and model reduction errors [37]. 3, we discuss numerical methods for the solution of large-scale Riccati equations that implicitly respect the incompressibility constraint and provide a summary of steps for the design of robust low-dimensional controllers with the accompanying formulas.
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