Model reduction for flexible structures

Several conditions for a near-optimal reduction of general dynamic systems are presented focusing on the reduction in balanced and modal coordinates. It is shown that model and balanced reductions give very different results for the flexible structure with closely-spaced natural frequencies. In general, balanced reduction is found to give better results. A robust model reduction technique was developed to study the sensitivity of modeling error to variations in the damping of a structure. New concepts of grammians defined over a finite time and/or a frequency interval are proposed including computational procedures for evaluating them. Application of the model reduction technique to these grammians is considered to lead to a near-optimal reduced model which closely reproduces the full system output in the time and/or frequency interval.

[1]  Frederick W. Fairman,et al.  Balanced realization of orthogonally symmetric transfer function matrices , 1987 .

[2]  Frederick W. Fairman,et al.  A note on cross Grammians for orthogonally symmetric realizations , 1986 .

[3]  P. Kabamba.  Balanced gains and their significance for L^{2} model reduction , 1985 .

[4]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[5]  R. Skelton,et al.  Component cost analysis of large scale systems , 1983 .

[6]  C. P. Kwong,et al.  Optimal chained aggregation for reduced-order modeling† , 1982 .

[7]  T. Williams,et al.  Closed-form Grammians and model reduction for flexible space structures , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

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

[9]  Robert E. Skelton,et al.  Comments on "Balanced gains and their significance for L 2 model reduction" , 1986 .

[10]  D. Wilson.  Optimum solution of model-reduction problem , 1970 .

[11]  Robert E. Skelton,et al.  COMPONENT MODEL REDUCTION BY COMPONENT COST ANALYSIS , 1988 .

[12]  Richard Dean Colgren,et al.  METHODS FOR MODEL REDUCTION , 1988 .

[13]  P. Hughes,et al.  Modal cost analysis for linear matrix-second-order systems , 1980 .

[14]  H. G. Natke,et al.  Balancing linear systems , 1987 .

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

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

[17]  Wodek Gawronski.  Model reduction for flexible structures - Test data approach , 1991 .

[18]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[19]  Jer-Nan Juang,et al.  Grammians and model reduction in limited time and frequency intervals , 1988 .

[20]  D. Bernstein,et al.  The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore , 1985 .

[21]  D. Wilson,et al.  Model reduction for multivariable systems , 1974 .

[22]  Leonard M. Silverman,et al.  Singular value analysis of deformable systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[23]  R. Skelton.  Cost decomposition of linear systems with application to model reduction , 1980 .

[24]  Wodek Gawronski,et al.  Model reduction for flexible space structures , 1991 .

[25]  H. Saunders,et al.  Book Reviews : DYNAMICS OF STRUCTURES R.W. Clough & J. Penzien McGraw-Hill Book Co., New York, New York (1975) , 1976 .

[26]  Robert E. Skelton,et al.  Order reduction for models of space structures using modal cost analysis , 1982 .

[27]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[28]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[29]  H. Nicholson,et al.  On the cross-Gramian for symmetric MIMO systems , 1985 .