A Projection Algorithm for Model Reduction

A least squares based algorithm is presented for the efficient computation of reduced order models of high order transfer functions using a projection matrix approach. The reduced order models produced by the proposed projection algorithm are selected from a set of admissible models consisting of all linear combinations of the subsets of a set of mode functions determined from the original system´s partial fraction expansion. The functions to be included in the reduced model are selected through a multistage optimization process, where at each stage the mode function that causes the greatest reduction in the sum of the squared error of approximation over a desired range of frequencies is added to the model of the previous stage. Through the use of an easily calculated selection factor and a set of projection matrices, it is possible to select these functions without ever completely solving for the reduced model. Then, the optimal parameters for a linear combination of the selected mode functions is found through the solution of a triangularized system of linear equations which completely determine the reduced order model. The proposed algorithm is demonstrated on an eighth order system and is found to be an effective method with several attractive properties.