1. © Substructural Multiobjective H-Infinity Controller Design For Large Flexible Structures: A Divide-And-Conquer Approach Based On Linear Matrix Inequalities Toker, O; Sunar, M PROFESSIONAL ENGINEERING PUBLISHING LTD, PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING; pp: 319-334; Vol: 219 King Fahd University of Petroleum & Minerals http://www.kfupm.edu.sa Summary In this paper, a novel substructural approach is proposed and successfully implemented for H. robust controller design for large flexible structures. It is assumed that sensors and actuators are discrete and located at some nodal points of the structure. In general, a finite element method (FEM)-based modelling approach results in a matrix differential equation of large dimensions. As the dimension becomes larger and larger controller design algorithms require more and more computation time, and start to have numerical problems. To cope with these difficulties, there are many known techniques in the literature, including the decentralized- and substructural-type methods. In this paper, a substructural-type approach based on the static condensation principle is adopted and the H-infinity optimal controller design problem for large flexible structures is studied. The key point in the present approach is that the static condensation is performed in the abstract state space. Geometric information about the flexible structure is utilized in deciding how to do the state decomposition, then H-infinity optimal controllers are designed at the substructure level, and finally a global controller is assembled for the whole structure. To improve the convergence of the algorithm, a multi-objective H- infinity optimization approach is adopted. More precisely, while forcing the closed- Copyright: King Fahd University of Petroleum & Minerals; http://www.kfupm.edu.sa

2. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. © loop poles to be in a given convex region to ensure fast dynamics, and hence improve the convergence of the substructural iterations, the H-infinity objective function is minimized to achieve maximum robustness. The main advantage of this approach is that both the H-infinity objective and the constraints on closed-loop poles can be expressed as a convex problem and formulated as linear matrix inequalities (LMIs), which can be solved easily, e.g. by LMI Toolbox of MATLAB. Overall, the proposed approach results in a reduction in computation time and improvements in numerical reliability as the problem of large size is decomposed into several smaller-size problems. The accuracy and effectiveness of the substructural H-infinity control technique are tested on benchmark problems, and effects of structural non-linearities are studied. References: ATLURI SN, 1988, LARGE SPACE STRUCTUR BRENNER CE, 1996, P ASCE SPEC C PROB M CHILALI M, 1995, IEEE T AUTOM CONTROL CRAIG RR, 1985, COMBINED EXPT ANAL M, V67, P1 DAY AS, 1994, STRUCT ENG REV, V6, P237 DOYLE JC, 1989, IEEE T AUTOMAT CONTR, V34, P831 DOYLE JC, 1992, FEEDBACK CONTROL THE GAHINET P, 1995, LMI CONTROL TOOLBOX GHABOUSSI J, 1995, J ENG MECH-ASCE, V121, P555 GU CX, 1996, LINEAR ALGEBRA APPL, V234, P227 GUYAN RJ, 1965, AIAA J, V3, P380 HOROWITZ I, 1991, INT J CONTROL, V53, P255 HYDE RA, 1993, IEEE T AUTOMAT CONTR, V38, P1021 HYDE TT, 1996, AIAA J, V34, P129 KONDOU T, 1997, JSME INT J C-DYN CON, V40, P187 KURAN B, 1996, J SOUND VIB, V189, P315 LEE JM, 1995, P INT IEEE IAS C IND, P624 MACIEJOWSKI JM, 1989, MULTIVARIATE FEEDBAC NIEZRECKI C, 1997, J VIB ACOUST, V119, P104 OREILLY J, 1915, CTAT 5, V10, P4 RAO SS, 1990, AIAA J, V28, P353 SKELTON RE, 1995, P 1995 AM CONTR C, V3, P2239 SKOGESTAD S, 1997, MULTIVARIABLE FEEDBA SU TJ, 1995, J GUID CONTROL DYNAM, V18, P1053 SUNAR M, 1991, INT J NUMER METH ENG, V32, P275 SUNAR M, 1992, AIAA J, V30, P2573 SUNAR M, 1993, AIAA J, V31, P714 SUNAR M, 1993, COMPUT STRUCT, V48, P913 Copyright: King Fahd University of Petroleum & Minerals; http://www.kfupm.edu.sa

3. 29. 30. 31. 32. 33. 34. 35. © SUNAR M, 1997, COMPUT STRUCT, V65, P695 TOKER O, 1995, IEEE T AUTOMAT CONTR, V40, P751 WANG JT, 1998, P 39 AIAA ASME ASCE, V1, P663 WANG R, 1995, ARCH APPL MECH-ING, V65, P457 WEAVER W, 1987, STRUCTURAL DYNAMICS, CH10 YOUNG KD, 1990, J GUID CONTROL DYNAM, V13, P703 ZAMES G, 1981, IEEE T AUTOMAT CONTR, V26, P301 For pre-prints please write to: onur@kfupm.edu.sa Copyright: King Fahd University of Petroleum & Minerals; http://www.kfupm.edu.sa