Robust active vibration control of flexible smart beam by μ-synthesis
Shubo Zhang, Zhong Chen, Xianmin Zhang
Abstract
This paper presents a comprehensive method for designing a robust active vibration control system to suppress low-frequency vibrations in smart structures. A novel finite element method based on the first-order shear deformation theory is used to calculate the dynamic response of a smart beam. Through a comprehensive system identification process, the uncertain model of the smart beam is extracted considering both the magnitude and phase. The model fits the experimental data successfully. In addition, a generalized low-frequency vibration control performance function is designed for the piezoelectric smart beam. Using a linear fractional transformation, the system is converted into a standard μ -synthesis control framework, and the controller K is synthesized using structural singular values μ . The effectiveness of the proposed method is experimentally validated using a setup with a piezoelectric smart beam. The experimental results suggest that the proposed control method exhibits robust stability and robust performance, effectively enhancing the performance of smart structure control in various scenarios. The proposed control framework utilizes structured singular value analysis to provide optimal robust stability margins and superior robust control performance, effectively addressing system uncertainties and non-linearities.