The design of a vibration control system for an aluminum plate with piezo-stripes based on residues analysis of model

Abstract.The design process of an active vibration control system for many mechanical structures using smart devices requires determining reduced and precise mathematical models. Such requirements cause orthogonal methods to be used and carefully analyzed. In the present paper, a plate with two simple supported edges and two free edges (SFSF) is an object of consideration. It is known that this structure represents a flexible structure wherein high natural frequencies are separated from low frequencies because they are naturally damped. Thus, in order to estimate the dynamical features of the control system, some orthogonal methods, such as the Schur and modal decomposition, were applied. A detailed analysis of the chosen methods showed us that each of them properly generates resonance frequencies while calculating different values of the anti-resonance frequencies. From the strategy control point of view, it is known that the anti-resonances play an essential role because they directly influence the dynamics of the whole control system. Thus, in order to check this behavior, different controllers are designed for various reduced models and, next, they are applied in a real mechanical structure. The dynamical behavior of the control systems with such controllers was analyzed and tested on a laboratory stand. In conclusion, we should carefully choose model reduction methods in the design process of the vibration control system. The sum of the residues of the reduced model appeared to be the best indicator during the choice process of the reduction method. It is particularly important when we design the vibration control system for a non-existent yet, but newly designed, structure.