Optimal Structural Design for Flexible Space Structure with Control System Based on LMI

  • Park, Jung-Hyen (Faculty, Department of Automotive Engineering, Silla University) ;
  • Cho, Kyeum-Rae (Faculty, Department of Aerospace Engineering, Pusan National University)
  • Published : 2002.01.01

Abstract

A simultaneous optimal design problem of structural and control systems is discussed by taking a 3-D truss structure as an object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider a minimum weight design problem for structural system and disturbance suppression problem for the control system. The structural objective function is the structural weight and the control objective function is $H_{\infty}$ norm from the disturbance input to the controlled output in the closed-loop system. The design variables are cross sectional areas of the truss members. The conditions for the existence of controller are expressed in terms of linear matrix inequalities (LMI) By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimal design by which the balance of the structural weight and the control performance is taken. We showed in this paper the validity of simultaneous optimal design of structural and control systems.

References

  1. Box, M. J., Davies, D. and Swann, W. H., 1972, 'Non Linear Optimization Methods,' Baihukan Press. (in Japanese)
  2. Grandhi, R. V., 1989, 'Structural and Control Optimization of Space Structures,' Journal of the Computers and Structures, Vol. 31, No. 2, pp. 139-150 https://doi.org/10.1016/0045-7949(89)90222-8
  3. Han, S. Y., 2000, 'An Improved Element Removal Method for Evolutionary Structural Optimization,' Trans. of KSME International Journal, Vol. 14, No. 9, pp. 913-919 https://doi.org/10.1007/BF03185793
  4. Iwatsubo, S., Kawamura, J. and Adachi, Y. 1993, 'Research trend and Problem in the future concerning Simultaneous Optimum Design of Structural and Control Systems for Machine Structure,' Trans. of JSME, Vol. 59, No. 559, pp. 631-637 (in Japanese) https://doi.org/10.1299/kikaic.59.631
  5. Kajiwara, H., Tsujioka, D. and Nagamatsu, J., 1993, 'Simultaneous Optimum Design of Structural and Control Systems by Complex Method,' Trans. of JSME, Vol. 59, No. 563, pp. 2124-2131 https://doi.org/10.1299/kikaic.59.2124
  6. Khot, N. S., 1988, 'Structure/Control Optimization to Improve the Dynamic Response of Space Structures,' Journal of the Computational Mechanics, Vol. 88, No. 3, pp. 179-186
  7. Kim, M. H., Suh, M.W. and Bae Dongho, 2000 'Optimum Shape Design of the Bus Window Pillar Member Based on B-Spline,' Trans. of KSME International Journal, Vol. 14, No. 11, pp. 1179-1186
  8. Mita, J., 1994, 'Control,' Shokodou Press (in Hapanese)
  9. Mori, D., 1989, 'Introduction of Finite Element Method by C language,' Morikita Press, (in Japanese)
  10. Obinata, G., et al., 1996 'Combined Optimal Design of Structural and Control Systems for Machine Structure (Formulation of Optimal Design Problem based on Descriptor Representasion),' Trans. of JSME, Vol.62, No. 597, pp. 1765-1772 (in Japanese) https://doi.org/10.1299/kikaic.62.1765
  11. Ohara, T., and Masu, K., 1997, 'Progressing of Matrix Inequality and Control System Design Method,' Trans. of ISCIE, Vol. 41, No. 1, pp. 28-34 (in Japanese)
  12. Onoda, J. and Haftka, R. T., 1987, 'An Approach to Structure/Control Simultaneous Optimization for Large Flexible Spacecraft,' AIAA Journal, Vol. 25, No. 8, pp. 1133-1138 https://doi.org/10.2514/3.9754
  13. Rao, S. S., et al., 1990, 'Robustness Improvement of Actively Controlled Structures through Structural Modifications,' AIAA Journal, Vol. 28, No. 2, pp. 353-361 https://doi.org/10.2514/3.10396
  14. Salama, M., et al., 1988, 'Simultaneous Optimization of Controlled Structures,' Journal of the Computational Mechanics, Vol. 88, No. 3, pp. 275-282 https://doi.org/10.1007/BF00368961
  15. Sung, Y. Y., Lee, J. W. and Kim, H. M., 2001 'A Robust Control Approach for Maneuvering a Flexible Spacecraft,' Trans. of KSME International Journal, Vol. 15, No. 2, pp. 143-151
  16. Tada, Y., Ikeda, M. and Terao, H., 1997 'Structural Optimal Design for Suppression of the Effect of Disturbance by Control (in case of Output Feedback),' Trans. of JSME, Vol. 63, No. 610, pp. 1956-1961 (In Japanese) https://doi.org/10.1299/kikaic.63.1956
  17. Tada, Y. and Park, J. H., 2000, 'Simultaneous Optimal Design of Structural and Control Systems for Flexible Structure,' Trans. of ISCIE, Vol. 13, No. 1, pp. 14-19 (in Japanese)
  18. Yim, J. G. and Park, J. H., 2001 'Robust Control of Robot Manipulator with Actuators,' Trans. of KSME International Journal, Vol. 15, No. 3, pp. 320-326
  19. Youn, I. J., 2000 'Optimal Design of Discrete Time Preview Controllers for Semi-Active and Active Suspension Systems,' Trans. of KSME International Journal, Vol. 14, No. 8, pp. 807-815 https://doi.org/10.1007/BF03184467
  20. Yoo, S. M., Choi, M. J. and Kim, Y. J., 2000 'Model Development of Flexible Disk Grinding Process,' Trans. of KSME International Journal, Vol. 14, No. 10, pp. 1114-1121 https://doi.org/10.1007/BF03185065