Active vibration control of smart beam by μ-synthesis technology: modeling via finite element method based on FSDT

This article proposes an efficient strategy for the active vibration control of smart beam that combines the Finite Element Method (FEM) and advanced robust control to suppress vibration. The piezoelectric actuator and sensor are coupled as part of the smart structure by using the 2D First-order Shear Deformation (FSDT) plate theory. The accurate modeling of the mechanical displacement field and electric potential field is achieved by approximating the sub-layered coupling of the piezoelectric potential field in the z-axis direction. In practice, most active controls of smart structures do not take into account the influence of the piezoelectric itself and the piezoelectric effect on the natural frequency of the smart structures, and they do not emphasize the internal stability and stability margin of the control system. Regarding the above questions, a modeling method of a generalized uncertain plant for the piezoelectric smart beam is proposed in this article. Fully considering the uncertainty of the system model caused by parameter perturbation and modeling error, a dynamic controller is designed with the μ-Synthesis technology. The proposed approach is numerically verified to have good robust performance on piezoelectric smart beam, which can effectively enhance the performance of smart structure control in other scenarios.