Identification of General Linear Mechanical Systems

Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identifiability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e. identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.