Influence of orthogonal methods on design process of vibration control system for cantilever beam with non-collocated piezo-elements

In this paper, we consider the influence of the model reduction on the dynamics of the real closed-loop system. A simple cantilever beam is the object of consideration since we are able to formulate the exact analytical model of such structure. As a result of reduction, the model with low frequency resonances is usually separated from the high frequency dynamics because high frequency part of the model is naturally strong damped. In order to estimate dynamical system for control purposes in the paper, we applied a few orthogonal methods such as: modal and Schur decompositions. As it is shown, all methods well calculate resonances frequencies but generate different antiresonances frequencies. In the vibration control systems, the antiresonances play essential role. They influence the stability and dynamics of the closed-loop systems. The controllers designed for different reduced models were applied to real full plant. Dynamics behavior of the closed-loop systems with such controllers were analyzed and compared. The theoretical considerations were confirmed by experimental investigations. In conclusion, we should carefully choose model reduction methods in the design process of the vibration control system.