Model reduction by minimizing the weighted equation error

A method for model reduction is proposed which minimizes the equation error and yields a stationary exact model. With this model, the desired state variables, or their physically meaningful linear combinations, are reproduced. This approach to the reduction problem leads to linear equations; thus no search routines are needed. Moreover, a time-varying weighting matrix is introduced, so that even unstable linear time-invariant models can be reduced. Especially, the characteristics of very low order reduced models depend highly on the weighting matrix. The reduction for a distillation column of the 45th-order is carried out.