Robust non-fragile dynamic vibration absorbers with uncertain factors

In this paper, the design problem for non-fragile dynamic vibration absorbers (DVAs) is investigated. Due to the imprecision of the manufacturing process or the variation during the operation, uncertainty in the parameters of the DVA is unavoidable. The uncertainty may degrade the performance of the designed DVA or even deteriorate the system. Hence, it is practically demanding to propose a design method for a non-fragile DVA, i.e., when the parameters of the DVA vary in an admissible range, an expected vibration suppression level should be guaranteed. The uncertainty of the DVA is feasibly assumed to be norm-bounded. Then, the design problem for the DVA is converted into a static output feedback (SOF) control problem. Sufficient condition for the existence of the non-fragile DVA with a prescribed H∞H∞ level is derived by using a bilinear matrix inequality (BMI). An iterative linear matrix inequality (ILMI) method is employed to solve the BMI condition. Finally, a design example is given to show the effectiveness of the proposed approach.