Environmental Engineering Reference
In-Depth Information
the rotor and generator inertia, which are connected with springs, dampers, and a
gearing. FAST is not equipped with any blade pitch actuators, these are therefore
added to the model after the linearization. A blade pitch actuator is the mechanism
that physically rotates the turbine blade. The linear model obtained from FAST
without any pitch actuators is in the following standard state-space form.
x
¼
Ax
þ
Bu
;
y
¼
Cx
;
ð
6
:
5
Þ
where x is the state vector with dimensions
R
n
1
, u is the control signal with
dimensions
R
p
1
, y is the model outputs with dimensions
R
m
1
and A, B and C are
the state-space matrices with dimensions
R
n
n
,
R
n
p
and
R
m
n
, respectively.
y contains measurements for platform pitch angle, rotor speed, and generator
speed. The specific dimensions for system (
5
) are; n = 6, p = 3, and m = 3.
This chapter deals with individual pitch control, therefore three blade pitch
actuators are added to the linear model. The three second-order actuators are
considered to be equal to each other, their properties are specified in the appendix.
The DOFs for the updated model are; blade I actuator, blade II actuator, blade III
actuator, platform pitch, drive train and generator. This gives a total of six DOFs
with twelve states, i.e., one position- and velocity state for each degree of freedom.
Then, an augmented system can be derived and represented in the following state-
space formulation
X
¼
A
t
X
þ
B
1
x
þ
B
t
u
;
z
¼
C
z
X
þ
D
z
u
;
y
¼
C
t
X
;
ð
6
:
6
Þ
where X is an augmented state vector which contains all the aforementioned 12
states and w and z are disturbance and controlled output, respectively. The updated
dimensions for system (
6
) are; n = 12, p = 3, and m = 3. The state-space
matrices A
t
, B
t
and C
t
are defined as follows:
"
#
I
3
A
a
0
B
C
a
A
I
3
B
a
0
A
t
¼
;
B
t
¼
ð
6
:
7
Þ
C
t
¼
0
½
C
;
where A
a
;
B
a
and C
a
are the state-space matrices for the pitch actuator, the matrix
values can be found in the appendix. The rest of the state-space matrices B
1
;
C
z
and
D
z
are defined in Sect.
6.4
.
