Modeling, control and evaluation of fluid flow systems using adaptation based linear parameter varying models

In this paper a systematic method is proposed for the modeling and control of flow problems, as well as the evaluation of closed loop performance and robustness. A nonlinear Galerkin model representing the flow dynamics is approximated with an adaptation based linear parameter varying (LPV) system, and it is shown that the LPV model can represent the Galerkin model with acceptable error. This allows for one to use the simple LPV model in place of the more complex nonlinear Galerkin model for modeling the flow process. The error vector is interpreted as an external disturbance for the model and the parameter range suggested by the adaptation process is interpreted as the uncertainty range in which the the control design must perform satisfactorily. The approach developed is illustrated on a sample problem of controlling a flow governed by the Navier-Stokes equations.