Environmental Engineering Reference
In-Depth Information
phase. The first mode resulted to be dominated by a rigid rotation of the tower
around the base with a reasonably high damping ratio, whereas the second mode is
dominated by the elastic strain of the tower. For the latter, however, in the con-
trolled system a rigid rotation is also involved, so that a damping ratio of about
5%( 0.8 %) can be obtained due to the SA MR dampers.
If active devices had been involved, the force u(t) should be imposed instant by
instant to them in order to achieve the target performances of the structure. In the
present case of SA control, instead, this force has to be intended as a desired
control action, that is the one the MR dampers have to mimic in real time to lead to
an effective control of the tower response. Therefore, the CLES algorithm has been
set so as to modulate the current fed to the SA MR dampers with the aim to make
the reacting force f d (t) of each damper as close as possible to the theoretical value
u(t). This kind of logic can thus be expressed as follows:
if
f d ðÞ u ðÞ \0
! i ðÞ¼ 0
if
f d ðÞ u ðÞ 0
and
j
f d ðÞ
j \ u ðÞ
j
j ! i ðÞ¼ it dt
ð
Þþ i max it dt
½
ð
Þ= n
if
f d ðÞ u ðÞ 0
and
j
f d ðÞ
j u ðÞ
j
j ! i ðÞ¼ it dt
ð
Þþ 0 it dt
½
ð
ð 13 : 40 Þ
Þ= n
where i(t-dt) is the current commanded to the dampers in the instant before the
actual one (t), dt is the sampling time for control (1 ms), n is a dimensionless
parameter (C1) introduced to smoothen the variation of the command current
between 0 and i max .
13.5.2 Two Variables (2VAR) Algorithm
An alternative control algorithm has been formulated and adopted for the shaking
table tests of the wind turbine model. It is based on a more physical and easier
approach in respect to the above-mentioned CLES controller.
The basic idea consists in controlling the base stress and top displacement so as
to ''force'' them to be within a given range. Reducing top displacement and base
stress are two performance objectives in conflict to each other. Actually, the
demand of base bending stress can be reduced by ''relaxing'' the base restraint
(i.e., reducing the damping of the SA devices). However, as a direct consequence,
the top displacement demand (related to both the rigid body motion—due to the
base rotation—and the elastic deflection of the tower) will increase.
This controller has been developed aiming to achieve a trade-off between these
two contradictory objectives. To do that, first of all, a limit value for both base
stress and top displacement have been assumed (r lim and x lim in the following,
respectively). Then, by denoting with r(t), x(t) and x(t), respectively, the maxi-
mum stress at the base, the top displacement, and the top velocity at the instant of
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