Comparison of Stabilization of Piezoelectric Euler-Bernoulli Beam Models

Piezoelectric materials are used in many control and
sensing applications via a strip of piezoelectric material
also known as a piezoelectric beam. Applications
can be vibration control in (complex) mechanical
structures and on-line measurement or compensation
in high-precision technology for shape control of beams
and surfaces. To manipulate or observe the electric-
field of the beam, a plate capacitor can be used, see
Fig. 1. The behavior of piezoelectric beams depends
on the interaction between the electrical, magnetic and
mechanical effects and is non trivial. Many different
assumptions for the mechanical part of the beam and
the electric-field can be used. For stabilization, and
more generally, controller design, a finite-dimensional
approximation must be used.