Q-Markov Cover identification and integrated MCA-OVC controller design for flexible structures

Ketao Liu, Purdue University

Abstract

The main objective of this research is to develop methods for identification and control of flexible structures. The specific problems this research focused upon are the following, (1) applying the Q-Markov Cover theory to the identification of flexible structures, (2) developing an integrated model reduction and controller design method, (3) developing a controller design method to accommodate finite wordlength errors for flexible structure controls at fast sampling rates. This research takes a linear algebra approach to simplify the existing solutions of the Q-Markov Cover problem. The new solutions are used to develop Q-Markov Cover identification algorithm and to analyse its identification errors due to measurement noises. Under the assumption that the measurement noises have rational spectrums, analytic formulas of the errors are obtained. These formulas reveal that, under certain conditions, some system parameters (eigenvalues for example) can be correctly identified. Based upon this analytical result, a new algorithm which is capable of identifying some system parameters correctly is developed. The MCA model reduction and OVC controller design algorithms are integrated into an iterative method for low order high performance controller designs based upon high order models. The resulting integrated MCA-OVC controller design method is a heuristic method which probes the stability boundaries of the closed loop systems formed by the high order model and low order controllers and searches for the maximum accuracy of the low order controllers. This research studies the effects of the finite wordlength errors on the LQG controllers. Under the assumptions that the controls are computed by fix point computations and that the external excitations are white, the lower and upper bounds of the influences of the finite wordlength errors on control systems are analysed. An optimal control design method which is capable of accommodating the finite wordlength errors is developed. NASA's ACES structure is a ground test facility for flexible space structure controls. The effectiveness of the Q-Markov Cover identification and the integrated MCA-OVC controller design algorithms are successfully demonstrated by the identification and control experiments on the ACES structure.

Degree

Ph.D.

Advisors

Skelton, Purdue University.

Subject Area

Aerospace materials

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