A shifting method for dynamic system Model Order Reduction

Abstract

Model Order Reduction (MOR) is becoming increasingly important in computational applications. At the same time, the need for more comprehensive models of systems is generating problems with increasing numbers of outputs and inputs. Classical methods, which were developed for Single-Input Single-Output (SISO) systems, generate reduced models that are too computationally inefficient for large Multiple-Input Multiple-Output (MIMO) systems. Although many approaches exclusively designed for MIMO systems have emerged during the past decade, they cannot satisfy the overall needs for maintaining the characteristics of systems. This research investigates the reasons for the poor performances of the proposed approaches, using specific examples. Inspired by these existing methods, this research develops a novel way to extract information from MIMO systems, by means of system transfer functions. The approach, called Shifting method, iteratively extracts time-constant shifts from the system and splits the transfer function into several simple systems referred to as contour terms that outline the system structure, and a reducible system referred to as remainder system that complement the Contour Terms. This algorithm produces a remainder system that existing approaches can reduce more effectively. This approach works particularly well for systems with either tightly clustered or well separated modes, and all the operations are O(n). The choice of shifts is based on an optimization process, with Chebyshev Polynomial roots as initial guesses. This paper concludes with a demonstration of the procedure as well as related error and stability analysis.