Model reduction of flat-plate solar collector using time-space discretization

Three model reduction schemes, namely, balanced truncation, singular perturbation balanced truncation, and Han-kel norm approximation are used to develop a reduced-order model to the partial differential system representing the dynamic behavior of the flat-plate solar collector system. To get a tractable finite-dimensional model instead of the infinite-dimensional model, the finite difference method is applied to the PDEs where a discretization of both time and space will result in a high-order linear time-invariant discrete state-space model. Then, a reduced-order model is computed via the three aforementioned schemes from the resultant high-order model. A substantial order reduction is shown to be possible and the obtained discrete reduced-order models are tractable for the purposes of simulation and control via digital controllers.