Comparative study of the active vibration control using LQR and H-infinity norm in a beam of composite material

The use of active vibration control techniques applyind piezoelectric actuators can show satisfactory results in terms of vibration attenuation, but its power consumption is also something that must be considered for seeking a better combination between vibration reduction and energy consumption. This paper proposes a comparison between controllers designed under different theories: Optimal Control and H-infinity. It has the goal of analyzing the best efficiency in terms of attenuation of vibration and energy consumption. The control effort determined by the controllers is applied to a piezoelectric actuator connected to a composite material structure; thus, it forms a smart composite structure. The Optimal Control and the H-infinity norm are solved by linear matrix inequalities allowing the insertion of uncertainties that results in the project of robust controllers. On both of the controllers, the composite structural model is stablished for rectangular shape beam by eight nodes, five mechanical degrees of freedom per node, and eight electrical degrees of freedom per piezoelectric layer. The model of the composite material structure, which in this work consists of a beam, is implemented using Serendipity finite elements along with the first order shear deformation theory. In the beam model, the Mixed Theory was used, which is based on the use of a single equivalent layer to the discretization of the mechanical displacement field and the representation of the adopted electric field layer. The temperature effects are disregarded for both. The results showed the effectiveness of both the controllers used in the active control of vibration in a beam made of composite material.