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

Authors: COŞKU KASNAKOĞLU

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 LPV 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.

Keywords: Flow control, Navier-Stokes, linear parameter varying (LPV) proper orthogonal decomposition (POD), Galerkin projection (GP), input separation (IS), adaptive control, robust control, disturbance rejection

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