Constructing Second-Order Models of Mechanical Systems from Identified State Space Realizations. Part I: Theoretical Discussions

This paper and its companion study constitute a two-part attempt at providing a common framework for some methodologies used in obtaining physical parameters of mechanical systems from identified state space models. In the theoretical part, the authors discuss the basic ideas and formulations involved in such algorithms. It is argued that the problem of extracting the physical matrices of the underlying second-order model is equivalent to the identification of certain linear transformation matrices, and that each of the evaluated approaches differs from the others mainly in the particular physically meaningful state space model it chooses as its objective. The choice of this state space model, and the formulations employed therein, define the applicability of the methodologies in terms of the number of sensors and/or actuators they require for a complete identification.