Vibration Control of Periodically Excited Nonlinear Dynamic Multi-dof Systems

Abstract

For nonlinear mechanical systems, which have stable subharmonic resonance peaks and one or more coexisting unstable harmonic solutions, a large reduction of maximum subharmonic, quasi-periodic, or chaotic displacement can be established if the coexisting unstable harmonic solution could be made stable. The control effort to obtain this goal can be very small in that case. In this article, a method for controlling nonlinear multi-degree-of-freedom (multi-dof) systems to unstable periodic solutions is developed. This is established by putting a single control force somewhere on the system. Because the selected control method uses the full state of the system and because only measured displacements and accelerations of a very limited number of dofs are assumed to be available, a reconstruction method has to be used for estimating the full state on-line. Simulations are done using a beam system supported by a one-sided spring that is control led to the unstable harmonic solution. The robustness of the method with respect to model errors, system disturbance, and measurement errors is examined. Further, the performance of the method in case of a varying excitation frequency during the control is investigated.