Searching the optimal order for high order models - SISO case

The goal of System Identification is to obtain a reduced order model capable of reproducing the key features of the true system behavior. Some system identification methods require, as a starting point, a high order linear model of the system. Such model is then adopted as the system most reliable description and, based on it, the desired reduced order model is derived. In this scenario, one could ask “what is the best order of the high order model?”. The reply to this question is not addressed in the specialized literature. This paper presents an optimization strategy that maximizes the fit index to deal with this subject.