Environmental Engineering Reference
In-Depth Information
Recently, these smart devices has been successfully used also in a wide
experimental campaign to SA control earthquake-induced vibrations of a 3D large
scale steel structure installed on a shaking table facility at the University of
Basilicata (Italy), allowing a comparison of four different control algorithms and
resulting very effective in reducing structural response [
18
]. Herein, the high
versatility of SA control strategies based on MR dampers is demonstrated.
13.5 Control Algorithms
The first controller adopted for the shaking table tests is based on the eigen-
structure selection theory [
10
,
11
]. It is a full-state feedback algorithm relying on
real-time definition of a desired control force and on the ability of the SA reacting
forces to mimic it during the motion. The second algorithm instead is designed to
bound the stress at the base within acceptable, given limits, also controlling the top
displacement to avoid the occurrence of significant second order effects.
A simplified, lumped-mass model of a wind turbine tower mounted on a
rotating base is shown in Fig.
13.13
. The base is linked to the ground through two
elastic elements (springs), two SA MR dampers and a hinge, as described in
Sect.
13.2
. In the figure:
h
is the height of the tower;
m
1
-m
r
are the lumped masses of the model;
k
1
-k
r
are the stiffnesses associated to the various DOFs;
c
1
-c
r
are the viscous damping coefficients associated to the various
DOFs;
a
is the rotation of the base;
d
0
= a 9 h
is the corresponding rigid displacement of the top of the tower;
d
1
-d
r
are the elastic displacements of the lumped masses;
k
s
is the stiffness of each base spring;
f
d1
-f
dm
are m independent control forces available;
l
s
is the distance between each spring and the hinge;
l
d
is the distance between each SA MR damper and the hinge.
The equations of motion of the n = r + 1 DOFs system in the absence of any
external disturbance are
Md
þ
C d
þ
K d
¼
Pf
d
ð
13
:
4
Þ
where M, C and K are, respectively, the mass, damping, and stiffness matrices,
P is the n 9 m allocation matrix of the control forces f
di
collected in the control
vector f
d
and d = [d
0
d
1
… d
r
]
T
is the vector collecting the DOFs, whose com-
ponents are scalar functions of time. However, the dependency from time will be
explicitly written only when needed.
