Environmental Engineering Reference
In-Depth Information
It is worth to notice that the procedure described before works also if only a portion
of a CL eigenvector is desired to have a given shape. In other words, the selection
can be also referred to portions of some or all CL eigenvectors. Due to the approx-
imate calculations introduced before, the less demanding is the eigenvector selection,
the most accurate is the result, i.e., the closer are CL and desired eigenvectors.
Provided that more than one independent controller be available and that the
positioning of such controllers yields a controllable system, for a feed-back con-
trolled wind turbine it is thus possible to directly design the modal behavior, in
terms of both modal frequencies and damping ratio, and modal shapes. When there
is only one controller available, as in the case of the experimental activity
described herein, it is possible to directly design modal frequencies and damping
ratio only, and to indirectly control modal shapes.
13.5.1 Closed-Loop Eigenstructure Selection (CLES)
Algorithm
A simplified structural model of the wind turbine mock up described in the pre-
vious sections is shown in Fig.
13.14
. It is a 2 DOFs system whose equations of
motion in the absence of any external disturbance are:
d
el
d
rig
þ
þ
d
el
d
rig
d
el
d
rig
m
T
m
T
c
T
0
00
k
T
0
02
k
s
l
s
=
h
0
m
a
=
h
f
d
0
2
l
d
¼
ð
13
:
28
Þ
or
Md
þ
C d
þ
K d
¼
p f
d
ð
13
:
29
Þ
where:
m
T
= m
top
+ m
tow
is the translational mass of the model;
m
top
= 280 kg
is the translational mass at the top of the tower;
m
tow
= 15.4 kg
is the 1st mode translational mass of the vertical structure;
m
a
= 8,329 kg m
2
is the rotational mass of the model;
c
T
= 32.4 Ns/m
is the equivalent linear viscous damping of the tower;
k
T
= 13,855 N/m
is the lateral stiffness of the tower;
k
s
= 89,000 N/m
is the stiffness of each base spring;
l
s
= 0.65 m
is distance between each spring and the hinge;
l
d
= 0.45 m
is distance between each SA MR damper and the hinge;
h = 5.26 m
is the height of the tower;
f
d
is the force exerted by each SA MR damper;
a
is the rotation of the base;
d
rig
= a 9 h
is the rigid portion of the top displacement;
