Active control of a structure with continuously closely spaced natural frequencies

In this paper, active control of a structure with continuously closely spaced natural frequencies is discussed. To simplify the analysis, a fundamental case is examined for a structure with three degrees of freedom and a single control input, and the control algorithm is velocity feedback. Perturbation method is used to analyze the relationship between modal damping ratios and control gain. Through the analysis of the effect of different spacing of natural frequencies, it is found that a single input can only control one of the three modes of the closely spaced natural frequencies and the modal damping ratios of the rest close modes will approach zero. The influence of uncertainty parameters on control effect is also analyzed and it shows that the sum of modal damping is independent of uncertainty parameters of the system, but depends only on the control gain.