System Identification Using Impulse Response Including Initial States

Abstract

The paper presents a new algorithm for system identification in the time domain using impulse response. The algorithm is aimed at the identification of single-input multipleoutput (SIMO) systems with non-zero initial states; that is, where the initial state vector contains one or more non-zero elements. The Eigensystem Realization Algorithm (ERA) realizes an SIMO system with a zero initial state vector. We modify this method and first estimate the system matrix and initial states using the system's free decay response. The system matrix is then obtained by singular value decomposition in the same manner as ERA, and the initial state values are refined by recursive least squares iteration. Next, deducing the effect of the initial states from measured impulse response data, we reconstruct the ideal impulse response, then identify the input and output matrices using another recursive least squares iteration in the time domain. Numerical simulations are performed to verify the new algorithm, and the results of example cases show the validity of the new identification scheme. Finally, we apply the new algorithm to the actual on-orbit data of the Engineering Test Satellite (ETS-VIII) in orbital control mode (OCM) for its system identification.