Assume appropriate mode shapes for the bending and torsional modes and establish a multi-mode...

Assume appropriate mode shapes for the
bending and torsional modes and establish a multi-mode vibration model of the
box beam. Determine the first two bending and first two torsional modes and
natural frequencies in terms of appropriate non-dimensional parameters. (ii)
Choose appropriate locations for bonding the PZT patches on both sides of the
plate and assume that it can be electrically actuated anti-symmetrically. The
patches are networked such that only two independent controls are available to
excite the first two bending modes and two independent controls are available
to excite the first two torsion modes, while at least the next three bending
and the next three torsion modes are not excited. Obtain the transformation
relating the control inputs to the inputs to the patch actuators. (iii) Assume
that 16 displacement sensors have been bonded to the plate at various locations.
The sensors are interconnected such that only the modal amplitudes of the first
two bending and the first two torsion modes are measured, while at least the
modal amplitudes of the next three bending and the next three torsion modes do
not corrupt the measurements. Obtain the transformation relating the sensor
outputs to the three desired modal amplitudes. (iv) Assume appropriate
measurement and process disturbances and design an H∞ optimal controller
to minimize the H∞-norm of the transverse displacement at the 3/4; chord
point from the leading edge. (v) If the number of sensors and actuators is also
reduced to five, is it feasible to design an H∞ controller avoiding
spillover effects? Design an H∞ controller to minimize spillover effects
and investigate if any spillover is present by investigating the response of
the first 10 modes.