Modeling and control of flow problems by adaptation-based linear parameter varying models

Abstract

In this paper a systematic modeling and control-approach for,flow problems is considered. A nonlinear Galerkin model is obtained from the partial differential equations (PDEs) describing the flow; and a Linear Parameter Varying (LPV) model is constructed to approximate the Galerkin Model, where the parameter variation of the LPV model is controller by an adaptation mechanism. The LP V model is then treated as a surrogate on which the control design is carried out, where the parameter variations provide a range of uncertainty in which the control design must perform satisfactorily. It is shown that if certain conditions are met, then such a controller design will succeed when applied to the nonlinear Galerkin model. The ideas developed in the present paper are illustrated through a flow control example governed by the Navier-Stokes (NS) PDEs, where it is observed that a controller design based on the proposed approach is successful in achieving a desired regulation within the flow domain. In addition, it is seen that the LPV model can be used to predict certain robustness properties of the closed-loop system.