Reduced-Order Controller of Transverse-Torsional Coupled Vibration Based on Linear Matrix Inequalities

Abstract

This paper is concerned with the application of reduced-order controller to a flexible structure hav ing the transverse-torsional coupled vibration modes. The dynamical model of the structure is first presented and then the robust controller for the structure is designed by using the H _∞-control theory. Furthermore, the order of the controller is reduced by using the combination of the alternating-projection method and the weighted-balanced realization. The performance of the reduced-order controller is examined through simu lation and experiment. To verify its robustness and validation in the transverse-torsional coupled vibration condition, the lumped mass is added on the right side at the 3rd story. From these results, it is made clear that the reduced-order controller obtained by the proposed method is effective in reducing the vibration of the structure, where the order of the controller can be reduced to 8th order from 30th order.

Keywords

Key Words: Reduced-order controller transverse-torsional coupled control alternating-projection method weighted- balanced realization

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References

Anderson, B.D.O. , 1993, "Controller design: Moving from theory to practice" , 1992 Bode Prize Lecture IEEE Control Systems 13, 16-25.

Anderson, B.D.O. and Liu, Y. , 1989, "Controller reduction: Concept and approach," IEEE Transaction on Automatic Control 34 (8), 802-819.

Chang, J.C.H. and Soong, T.T. , 1980, "Structural control using active tuned mass dampers " , Journal of the Engineering Mechanics Division, Proceeding of american Society of Civil Engineering 106(6), 1091-1098.

Doyle, J.C. , Glover, K. , Khargonekar, P.P. , and Francis, B.A. , 1989, "State space solutions to standard H2 and H∞ control problems," IEEE Transaction on Automatic Control 34(8 ), 831-847.

Enns, D.F. , 1984, "Model reduction with balanced realization: An error bound and a frequency weighted generalization," in Proceedings of IEEE Conference on Decision and Control, Las Vegas, NV , December, pp. 127-132.

Grigoriadis, K.M. , 1995, "Optimal H∞-model reduction via linear matrix inequalities: Continuous and discrete time cases," Letters 26(5), 321-333.

Grigoriadis, K.M. and Skelton, R.E. , 1994, "Fixed-order control design for LMI control problems using alternating projection methods," in Conference on Decision and Control , Lake Buena Vista, FL, December, pp. 2003-2008.

Grigoriadis, K.M. and Skelton, R.E. , 1996, "Low-order control design for LMI control problems using alternating projection methods," Automatica 32(8), 1117-1125.

Liu, Y. and Anderson, B.D.O. , 1986, "Controller reduction via stable factorization and balancing, " International Journal of Control 44(2),507-531.

10.

Sakawa, Y. and Luo, Z.H. , 1989, "Modeling and control of coupled bending and torsional vibrations of flexible beams", IEEE Transaction on Automatic Control 34(9), 970-977.

11.

Watanabe, T. and Yoshida, K. , 1996, "H∞ -control of transverse-torsional coupled vibrations using multiple active dynamic vibration absorbers," JSME International Journal Series C, 39-4, 728-737.

12.

Wu, F. , 1996, "Induced norm model reduction of polytopic uncertain linear systems," Automatica 32(10), 1417-1426.