Time Domain State Space Identification of Structural Systems

Abstract

An integrated time domain state space identification technique for structural systems is presented. This technique integrates the Observability Range Space Extraction identification algorithm, Balanced Realization model reduction algorithm, and Least Square model updating algorithm to generate low order and highly accurate state space models for structural systems based upon time domain data. The algorithms are integrated in such a manner that the Observability Range Space Extraction identification algorithm is used to generate an initial overparameterized state space model and then the Balanced Realization model reduction and Least Square model updating algorithms are used to iteratively reduce and update the model to achieve minimum prediction errors in time domain. We shall present the Observability Range Space Extraction identification algorithm and the Least Square model updating algorithm and discuss the integrated identification technique. The MIT Middeck Active Control Experiment (MACE) is used as an application example. MACE is an active structure control experiment to be conducted in the Space Shuttle middeck. Results of ground experiments using this technique will be discussed.

System Identification and Model Reduction for a Single-Link Flexible Manipulator

“…This section presents a brief introduction to the ORSE algorithm [6]. In experiment, the output y(k) is contaminated by unknown measurement noise w(k) giving the measured output yJ (k),…”

“…The third objective of the study is to develop a new model updating scheme that is more e$cient than the iterative LS model updating algorithm used in reference [6]. The low e$ciency of this algorithm is due to simultaneously modifying all the elements of the system matrices using the gradient information.…”

“…The reduced order model must be updated to correct errors caused by truncation of some modes. A procedure for model reduction and updating is proposed in reference [6]. The procedure employs the balanced realization (BR) technique to transfer the model into a balanced form such that the importance of each mode is indicated by its corresponding diagonal element of the joint Gramian matrix or Hankel singular value [12].…”

“…For model updating, an iterative least-squares (LS) model updating algorithm is used in reference [6]. The model to be updated is assumed to be su$ciently accurate so that the prediction error of the model can be approximated by the product of the gradient matrix and the parameter updating vector.…”

“…For general response data, the Observer/Kalman "lter identi"cation algorithm (OKID) can be used and it consists of three steps, i.e., computation of the observer Markov parameters, recovery of the system and observer gain Markov parameters, and realization of a state-space model [1,5]. The Observability Range Space Extraction (ORSE) algorithm [6] is developed by generalizing the Q-Markov Covariance Equivalent Realization (Q-Markov Cover) [7] and the ERA. The ORSE algorithm can obtain a state-space model directly from general input/output data.…”