93-121
Identification Of A Second-Order Mechanical System Model From A State Space Realization*
Dong-Huei Tseng**, Richard W. Longman***and Jer-Nan Juang****
Abstract
Many system identification algorithm produce models in modern state variable form. When a mechanical system is identified one knows that there must be a model in second order form. ln structural dynamics one is interested in either a modal model of the system, or in a model including a mass matrix, stiffness matrix and a damping matrix. In this paper, algorithms are developed that convert a modern state space realization into the above two representations of interest in mechanical systems. The algorithms can be used with any identification methods that produce a modern state variable representation such as the Eigensystem Realization Algorithm (ERA), its modified version by data correlation (ERA/DC), and combinations of these with Observer/Kalman Filter Ientification (OKID). An algorithm is developed that allows one to identify the damping matrix in a modal representation, so that one determines how near to modal the damping is in the system, and can therefore understand the degree to which the modes are coupled by the damping in the system. A second algorithim produced the mass, damping, and stiffness matrices, given the input and output matrices. It is assumed that the number of sensors (or the number of actuators) is greater than or equal to the number of modes in the system, and it is proved that this is a necessary condition to be able to uniquely identify these matrices. Experience with examples suggests that a singular value truncation involved in these algorithim can help one determine the true system order. This truncation has thc benefit or knowledge or the correct form for a mechanical system model, which i~ not present in the modern control identification algorithm.
*Research supported by NASA Grant NAG 1-649.
**Graduate Research Assistant, Columbia University, Seeley W. Mudd Building, New York, New York 10027-6699.
***Professor of Mechanical Engineering, Columbia University, Seeley W. Mudd Building, New York, New York10027-6699.
****Principal Scientist. Spacecraft Dynamics Branch, NASA Langley Research Center, Hampton, Virginia 23665.