Lumped-parameter model development and robust control of systems governed by 2-D parabolic convection-diffusion equation

In the present paper, proper orthogonal decomposition (POD) method is employed to derive a lumped-parameter model for systems governed by two-dimensional (2- D) parabolic convection-diffusion (PCD) equation. The POD method employs singular value decomposition (SVD) to explore the content of a data set in order to identify the most and least variation to choose lower-order basis functions that provide close approximations of the original data set. In this work, POD is utilized to determine a low-order model that is suitable for control design purposes; using the low-order model, an H
_∞
controller is then designed to ensure closed-loop system stability and reference tracking. This control design framework is chosen since the low-order model presents both parametric uncertainty and unmodeled high frequency dynamics arising from the derivation of the low-order model. The loop-shaping method is adopted for the design a robust H
_∞
controller to achieve desired tracking and disturbance rejection in the closed-loop system. The simulation results show that the robust controller designed on the basis of the low-order model provides satisfactory reference tracking performance for the system described by the full-order PCD model.