Active Control of Structures in Nonlinear Response

The need to account for geometric and material nonlinearities in the active control of highly flexible, large, space structures is emphasized herein. The performance index of the control problem is minimized subject to equations of state and costate using a variable metric algorithm. Unlike the conventional techniques for active control, the present algorithm is able to exploit the sparsity and symmetry of the mass and stiffness matrices of the finite element models of structures. The algorithm thus has the potential of being able to control moderately large‐scale, finite element models of highly flexible, large, space structures in a cost‐effective manner. The proposed algorithm is validated in suppressing the nonlinear vibrations of an impulsively loaded, highly flexible beam, and the need for inclusion of nonlinearities is demonstrated.