Optimum design of control system for large degrees-of-freedom structure to assure stability against high mode vibrational disturbance

Abstract

A new method on optimum design of control system of small degrees of freedom (DOF) is proposed for a structure of large DOF in order to assure stability against disturbance which includes high mode vibration. The original structure is modeled by the finite element method (FEM). A modal model of p DOF is made with this FEM model, in which p is the number of the modes whose stability have to be assured. A small model of n DOF (n < p) is made by system identification with the frequency response function. A feedback control system is composed with the n DOF model. The optimum values of the weighting coefficients of the performance index in the optimum regulator theory are determined by sensitivity analysis under the condition that the n DOF control system is stable against the vibration of p natural modes in order to prevent spillover phenomenon without adopting any additional means. Vibration of a steel plate till llOOHz in which nine natural modes are included can be suppressed with a control system of only two DOF in an experiment with using the proposed method.