Balanced Model Reduction and Control of Rotor-Bearing Systems

An effective technique is applied to the suppression of vibrations in flexible rotor-bearing systems with small gyroscopic effects. A balanced linear-quadratic-Gaussian (LQG) controller design procedure is implemented. The size of the controller is reduced in two stages by using (i) a balanced model reduction, and (ii) an LQG balanced reduction. The condition for a gyroscopic matrix is developed that allows one to ignore the rotor gyroscopic effects in the process of the controller design, although they are included in the rotor dynamics. The approach is illustrated on a typical rotor-bearing system represented by a 48 degree-of-freedom finite element model.

[1]  W. Gawronski.  Balanced LQG Compensator for Flexible Structures , 1993, 1993 American Control Conference.

[2]  E. J. Gunter,et al.  A Study of the Modal Truncation Error in the Component Mode Analysis of a Dual-Rotor System , 1982 .

[3]  E. Jonckheere.  Principal component analysis of flexible systems--Open-loop case , 1984 .

[4]  Edmond A. Jonckheere,et al.  LQG balancing and reduced LQG compensation of symmetric passive systems , 1985 .

[5]  K. Kane,et al.  The Extended Modal Reduction Method Applied to Rotor Dynamic Problems , 1991 .

[6]  E. J. Gunter,et al.  Component mode synthesis of large rotor systems , 1982 .

[7]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[8]  Julius S. Bendat,et al.  Engineering Applications of Correlation and Spectral Analysis , 1980 .

[9]  Marc P. Mignolet,et al.  LQR-Based Least-Squares Output Feedback Control of Rotor Vibrations Using the Complex Mode and Balanced Realization Methods , 1993 .

[10]  Trevor Williams,et al.  Closed-form Grammians and model reduction for flexible space structures , 1988 .

[11]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[12]  C. Gregory.  Reduction of large flexible spacecraft models using internal balancing theory , 1984 .

[13]  K. E. Rouch,et al.  Dynamic Reduction in Rotor Dynamics by the Finite Element Method , 1980 .

[14]  Alan Palazzolo,et al.  Active control of transient rotordynamic vibration by optimal control methods , 1989 .

[15]  Edmond A. Jonckheere,et al.  A new set of invariants for linear systems--Application to reduced order compensator design , 1983 .

[16]  Giancarlo Genta,et al.  Consistent matrices in rotor dynamic , 1985 .

[17]  Jer-Nan Juang,et al.  Model reduction in limited time and frequency intervals , 1990 .

[18]  P. A. Blelloch,et al.  Perturbation analysis of internal balancing for lightly damped mechanical systems with gyroscopic and circulatory forces , 1987 .

[19]  Wodek Gawronski,et al.  Balanced Control of Flexible Structures , 1995 .

[20]  J. Padovan,et al.  Insights into linearized rotor dynamics , 1981 .

[21]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[22]  Dara W. Childs.  Two Jeffcott-Based Modal Simulation Models for Flexible Rotating Equipment , 1975 .

[23]  H. D. Nelson,et al.  Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis , 1980 .

[24]  W. Gawronski,et al.  RESPONSE ERRORS OF NON-PROPORTIONALLY LIGHTLY DAMPED STRUCTURES , 1997 .

[25]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[26]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[27]  Leonard Meirovitch,et al.  A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems , 1974 .