Optimal Output Feedback Control of Asymmetric Systems Using Complex Modes

[+] Author and Article Information
G. W. Fan

3-I Scientific Development Inc., Tempe, AZ 85282

H. D. Nelson

Department of Engineering, Texas Christian University, Fort Worth, TX 76129

M. P. Mignolet

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287

J. Eng. Gas Turbines Power 115(2), 307-313 (Apr 01, 1993) (7 pages) doi:10.1115/1.2906710 History: Received February 15, 1992; Online April 24, 2008


A Linear Quadratic Regulator (LQR)-based least-squares output feedback control procedure using a complex mode procedure is developed for the optimal vibration control of high-order asymmetric discrete system. An LQ Regulator is designed for a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex mode coordinates are derived. The complex mode approach appears to provide more accurate reduced-order models than the normal mode approach for asymmetric discrete systems. The proposed least-squares output feedback control procedure takes advantage of the fact that a full-state feedback control is possible without using an observer. In addition, the lateral vibration of a high-order rotor system can be effectively controlled by monitoring one single location along the rotor shaft, i.e., the number of measured states can be much less than the number of eigenvectors retained in producing the reduced-order model while acceptable performance of the controller is maintained. The procedure is illustrated by means of a 52 degree-of-freedom finite element based rotordynamic system. Simulation results show that LQ regulators based on a reduced-order model with 12 retained eigenvalues can be accurately approximated by using feedback of four measured states from one location along the rotor shaft. The controlled and uncontrolled transient responses, using various numbers of measured states, of the original high-order system are shown. Comparisons of reduced-order model results using normal modes and complex modes are presented. The spillover problem is discussed for both collocated and noncollocated cases based on this same example.

Copyright © 1993 by The American Society of Mechanical Engineers
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