Vibration Control Design for Nonlinear Systems using Frequency Response Function
For control engineers dealing with nonlinear mechanical systems, this work provides a systematic approach to vibration control using frequency response, though it is incremental as it extends existing FRF concepts to nonlinear systems.
The paper proposes an adaptive vibration controller for nonlinear mechanical systems using nonlinear Frequency Response Functions, enabling desired closed-loop frequency response. The method is validated on a building structure with cubic stiffness and a satellite system.
A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are studied by using the convergence (contraction) theory. If the system under consideration is: 1) convergent, it directly enables to derive a nonlinear FRF for a band of excitation inputs, 2) non-convergent, first a controller is used to obtain the convergence and then the corresponding FRF for a band of excitation inputs is derived. Now the gains of the proposed adaptive controller are tuned such that a desired closed-loop frequency response, in the presence of excitation inputs is achieved. Finally, a building structure with nonlinear cubic stiffness and a satellite system are considered to illustrate the theoretical results.