Sage Journals: Discover world-class research

Abstract

A design technique to simultaneously optimize the structure and controller to suppress vibration of nonlinear structures is presented. Newmark-beta explicit time integration is used to solve the nonlinear ordinary differential equations describing the closed-loop system. Computations in the integration only in volve addition and multiplication of sparse matrices, and thus it is feasible to carry out the solution for a large number of time steps. The structure and controller parameters are optimized to drive the forced nonlinear system to its zero equilibrium solution using the minimum control force. Computations in the optimization are streamlined by computing the gradients of the design variables in closed form, or semianalytically, de pending on the type of finite elements used in the model. No additional function evaluations or recursion are required to compute the gradient. A nonlinear truss is modeled using a geometrically exact structural the ory to test the nonlinear design technique. The nonlinear behavior of the truss and the optimization of the nonlinear structure and design of linear and nonlinear controllers are discussed.

Keywords

Automated design nonlinear structures nonlinear control optimization

Get full access to this article

View all access options for this article.

References

Adiguzel, E. and Oz, H. , 1991, "Direct optimal control of nonlinear systems via Hamilton's law of varying action," in Proceedings of the AIAA Guidance, Navigation and Control Conference, New Orleans, LA.

Agarwal, T. K., Storaasli, O.O. , and Nguyen, D.T. , 1990, "A parallel-vector algorithm for rapid structural analysis on high-performance computers," in Proceedings of the Structural Dynamics and Materials Conference, Long Beach, CA.

Baddourah, M.A. , Storaasli, O.O. , Carmona, E.A. , and Nguyen, D.T. , 1991, "A parallel algorithm for generation and assembly of finite element stiffness and mass matrices," in Proceedings of the Structural Dynamics and Materials Conference, Baltimore, MD.

Bathe, K.J. , 1982, Finite Element Procedures in Engineering Analysis , Prentice Hall, Englewood Cliffs, NJ.

Belvin, W. K., Maghami, P.G. , and Nguyen, D.T. , 1992, "Efficient use of high-performance computers for integrated controls and structures design," Computing Systems in Engineering Journal 3(1-4), 181-188.

Benson, D.J. , 1989, "An efficient, accurate, simple ALE method for nonlinear finite element programs," Computer Methods in Applied Mechanics and Engineering 72, 305-350.

Goh, C.J. , 1994, "Model referenced control of non-linear systems via implicit function emulation," International Journal of Control 114, 91-115.

Grace, A. , 1995, Optimization Toolboxfor Use With MATLAB: Users' Guide , Math Works, Natick, MA.

James, M.R. and Baras, J.S. , 1995, "Robust H∞ output-feedback control for nonlinear systems," IEEE Transactions on Automatic Control 40(6), 1007-1017.

10.

Junkins, J.L. and Kim, Y. , 1993, Introduction to Dynamics and Control of Flexible Structures , AIAA, Washington, DC.

11.

Lsidori, A. and Kang, W. , 1995, "H∞ control via measurement feedback for general nonlinear systems," IEEE Transactions on Automatic Control 40(3), 466-472.

12.

Math Works , 1995, MATLAB Users' Guide, Math Works , Natick, MA.

13.

Nguyen, D.T. and Niu, K.T. , 1987, "A parallel algorithm for structural sensitivity analysis on the FLEX/32 multicomputer," in Proceedings of the 6th ASCE Structures Congress, Florida, pp. 98-112.

14.

Nguyen, D.T. , Storaasli, O.O. , Qin, J. , and Qamar, R. , 1993, "Automatic differentiation for design sensitivity analysis of structural systems using multiple processors," Multidisciplinary Parallel-Ntctor Computation Center, Old Dominion University , Norfolk, VA.

15.

Pai, P.E. and Palazotto, A.N. , 1995, "Polar decomposition theory in nonlinear analysis of solids and structures," Journal of Engineering Mechanics 12(4), 568-581.

16.

Sardar, H.M. and Ahmadian, M. , 1992, "A modified model referenced adaptive control technique for nonlinear dynamic systems," Journal of Vibration and Acoustics 114, 154-160.

17.

Slater, J.C. , 1993, "Nonlinear modal control," Ph.D. thesis, State University of New York at Buffalo, NY

18.

Slotine, J. and Li, W. , 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.

19.

Song, X. , 1996, "Design and control of nonlinear structures," Master's thesis, Department of Mechanical Engineering, North Carolina A&T State University, Greensboro, NC.

20.

Taylor, J.H. and Jin Lu , 1993, "Robust nonlinear control system synthesis method for electro-mechanical pointing systems with flexible modes," in Proceedings of the American Control Conference, San Francisco, CA.

An Automated Design Technique for Nonlinear Structures and Controllers

Abstract

Keywords

Get full access to this article

References