Sensing and Control the Static Deflection of a Cantilever Beam by Using Piezoelectric Patches

Different mechanical structures when comes under static and dynamic loadings then they respond. It is very important to sense it so that the dynamic behavior of the structure in terms of natural frequencies, its mode shapes, and viscous damping coefficients can be successfully predicted or measured. The accurate prediction of the dynamic response of the oscillating structure always plays an important role to design its physical parameters. However, in this paper, the simulated and experimental study is conducted to accurately sense the static deflection of the cantilever beam by using piezoelectric patches. The accurate prediction of the static deflection of the beam and its control through piezoelectric patches is the novelty of the present work. Mostly, the finite element model of the beam is developed to predict its dynamic behavior. The finite element modeling provides an approximate solution. In this regard, the finite element model updating technique such as the direct updating algorithm is used in this study to correct the simulated finite element model of the beam. The updated simulated finite element model is then used to predict the accurate value of the static deflection. It is observed that the maximum percentage error between the predicted and measured static deflection is 29.1%. The updated simulated finite element model is also used to design the controller. The direct output feedback controller is developed and it is found that the static deflection of the beam has been reduced by 46.65%.