ABSTRACT
In this chapter we focus on the real-time implementation of feedback controls for the attenuation of transverse beam vibrations due to transient pulsation. In particular, we will consider an aluminum cantilever beam to which two piezoceramics patches are mounted in a symmetric opposing fashion. The sensing device to be used for observation is a proximity probe, and thus the sensor loading effects on the beam (an extremely thin metallic surface mounted on the beam) are assumed to be negligible and are not taken into account in the modeling of the beam. Also, it is assumed that the beam vibration occurs transversely (with no out of plane torsion or twisting about the axis of the beam), a reasonable assumption for beams that have relatively small thickness when compared to width. Hence we can make use of the Euler-Bernoulli beam model that we developed earlier in Chapter 6. Most of the facts presented in this section are standard knowledge and can be found in the textbook literature (see, e.g., [1, 2, 4, 5, 6, 17]).
