Normal Forms, Averaging and Resonance Control of Flexible Structures

In this paper, we address a novel averaging method for analysis and control of high dimensional, stiff nonlinear differential equations governing the dynamics of a variety of flexible structures. The method yields significant reduction of the initial equations by the averaging of high oscillatory elastic distortions over slow rigid-body motions which can be given in either analytical or numerical form. The averaging allows the stiff property to be overcome. In the averaging equations only exceptional resonance nonlinear terms persist which actually control the plant’s stability. A stabilization problem is addressed for an averaging nonlinear plant and the error involved in such an approximation is estimated. A nonlinear stabilizing control is then evaluated in terms of the averaging normal form and the resonance feedback is shown to be an efficient design procedure.