Frequency domain identification of a flexible structure with piezoelectric actuators using irrational transfer function models

A more general transfer function model based on fractional derivatives has been presented for the frequency domain identification of a flexible structure with piezoelectric actuators. Of particular interest are the results obtained using an irrational transfer function that is a quotient of polynomials in s^½. These results show that this transfer function is an optimal candidate for obtaining useful finite dimensional models of the infinite dimensional system because it can take into account the presence into the system of a variety of physical phenomena, not only material damping, but viscoelasticity and anomalous relaxation also. This fact leads us to consider fractional calculus as an appropriate tool to model more accurately the dynamic features of flexible beams. It can be a particularly useful tool for the analysis and control of the so-called smart material structures. On the other hand, obtaining lower order models for the system, we can design lower order controllers. This implies that the controlled system is more robust if noise is present