Environmental Engineering Reference
In-Depth Information
Table 5.2
Objectives of the designed robust controllers
Order
Controller name
Control objectives
I
Generator torque H
?
control
To reduce the wind effect in the drive train and tower side-
to-side first modes
II
Collective pitch H
?
control
To improve the regulation of the generator speed and to
reduce the wind effect in the tower fore-aft first mode
III
Collective pitch gain
scheduled control
To improve the regulation of the generator speed
IV
Individual pitch H
?
control
To reduce the wind effect in the tower side-to-side first
mode and to align the rotor plane
level when facing the disturbance signals, noise interferences, no-modelled plant
dynamics and plant parameter variations. These design objectives can be achieved
using a feedback control mechanism, but it introduces the need of sensors, bigger
system complexity and a guarantee of system stability. Since the 80s, many
authors researched the controller design using the H
?
norm [
29
,
30
] and the
applications of these controllers in different non-linear real systems. Currently, the
MATLAB Robust Toolbox [
31
] is a useful tool to solve mathematically the H
?
controller synthesis problem.
The designed H
?
controllers are LTI systems and the controller performance is
defined using weight functions, scale constants [
32
] and defining a nominal plant
among the family of linear plants where the controller synthesis is made. The most
usual feedback control problem is expressed as a mixed sensitivity problem. The
mixed sensitivity problem is based on a nominal plant and three weight functions
and it can be considered in SISO or MIMO systems. These matrices of weight
functions W
1
(s)
,
W
2
(s) and W
3
(s) define the performance of the sensitivity func-
tions S(s), T(s) and U(s) respectively in a classical mixed sensitivity problem
scenario (Fig.
5.6
), where S(s) is the output sensitivity, T(s) is the input sensitivity
and U(s) is the control sensitivity. The scale constants are used to make the scaling
of the different channels of the system. The difference between the family of plants
can be modeled as uncertainties and they can be structured or unstructured. The
unstructured uncertainties considered in the H
?
robust control design are com-
monly modeled in different representations: additive uncertainly, input multipli-
cative uncertainly, output multiplicative uncertainty, inverse additive uncertainty,
input inverse multiplicative uncertainty and output inverse multiplicative uncer-
tainty. The selected one in this chapter is the additive representation. Finally, the
calculation of the K(s) controller based on the H
?
norm reduction in this mixed
sensitivity problem consists of the resolution of two Ricatti equations, which can
be solved with the MATLAB Robust control toolbox.
In the case of the wind turbine control design, two MISO (2 9 1) mixed sen-
sitivity problems are necessary to design the MISO proposed generator torque and
collective pitch controllers based on the H
?
norm reduction. This control scenario
is based on the augmented plant (Eq.
5.7
) which is divided into the nominal plant
G(s), scale constants D
u
, D
d1
, D
d2
, D
e1
, D
e2
and weight functions W
11
(s), W
12
(s),
W
2
(s), W
31
(s) and W
32
(s). The nominal plant is the plant used to design the
