Environmental Engineering Reference
In-Depth Information
Gain Scheduled Collective Pitch H
?
Control
The interpolation of LTI controllers is an important task in control systems design
for non-linear applications. In literature, the interpolation is commonly applied to
low ordered LTI controllers and it can be divided into two approaches [
33
]: Gain
Scheduling approach and LPV approach. The first one uses the family of linear
models extracted from the non-linear model to design LTI controllers in different
operating points to finally interpolate the designed controllers [
34
]. On the other
hand, the LPV approach needs LPV models [
35
] of the plant to design LPV
controls for the specified model [
36
]. The work presented in this section is focused
on the first approach and it is based on gain scheduling of LTI controllers solving a
LMI system. This technique guarantees the stability from the control design point
of view because it is considered in the formulation of the LMI system. The
adaptability of the presented gain scheduled control, which varies its behaviour
according to the different operating points in wind turbines non-linear systems,
improves the closed loop performance compared to LTI control techniques.
The non-linearities of wind turbines are more presented in the above rated zone,
mainly in the pitch angle based generator speed regulation loop. To improve the
control performance of the LTI H
?
Pitch Controller, three collective pitch H
?
controllers are designed to regulate the generator speed in three operating points in
the above rated zone for wind speeds of 13, 19 and 25 m/s respectively. So, the
above rated zone is divided into three sub-zones in this control design and each
controller is optimized in performance for each zone guaranteeing the closed loop
stability. Although the order of these controllers is high, they are perfectly inter-
polated without losing the stability and performance in all trajectories of the above
rated zone solving an LMI system carefully proposed in [
37
]. The varying
parameter p to develop the gain scheduling in the above rated zone is based on an
adaptation of the measured pitch angle to work in the range [-6, 6], which
extreme points are calculated from the stationary pitch values of the operating
points with wind speeds of [13 m/s, 25 m/s]. Figure
5.11
shows the bode diagram
of discrete gain scheduling controller in three operating points where it is
designed. The representation of the gain scheduled controller via LMI solution
is based on a gain vector which interpolates the three state space LTI controllers
previously adapted to make this interpolation.
5.3.1.3 Multivariable Individual Pitch H
?
Control
One of the most well-known control loops developed to mitigate loads in wind
turbines is the IPC. It consists of a controller which generates individual pitch
set-points for each blade. The main objective of the IPC is to reduce the asym-
metrical loads which appear in the rotor due to its misalignment caused by phe-
nomena like wind shear, tower shadow, yaw misalignment or rotational sampling
of turbulence. In [
10
,
38
], decentralized d-q axes controllers based on propor-
tional-integral (PI) controllers are proposed to solve this main objective using the
