Environmental Engineering Reference
In-Depth Information
e
i
þ
1
e
i
q
The q \ 1 condition is sufficient for the algorithm convergence. Indeed, the real
trajectory consists of an infinite number of segments. The total variance is given by
ðÞ¼
X
e
jj
e
jj
1
þ
q
þ
q
2
þ
¼
e
jj
1
q
Var
ð
2
:
46
Þ
Therefore, the algorithm obviously converges.
The convergence time is to be estimated now. Consider an auxiliary variable
g
¼
y
z
ð
2
:
47
Þ
g
¼
e when e
¼
0. Thus, g tends to zero. Its derivative
e
¼
B
2
sgn
ð
e
Þ
G
ð
2
:
48
Þ
satisfies the inequalities
0\B
2
/
gsgn
ð
e
I
rd
Þ
B
2
þ
/
ð
2
:
49
Þ
The real trajectory consists of an infinite number of segments between g
i
¼
e
i
and g
i
þ
1
¼
e
i
þ
1
associated to the time t
i
and t
i+1
, respectively. Consider t
c
, the total
convergence time.
8
<
t
c
¼
P
t
i
þ
1
t
i
Þ
P
g
jj
B
2
/
ð
B
2
/
P
e
jj
1
t
c
ð
2
:
50
Þ
:
e
jj
B
2
/
t
c
ð
Þ
1
q
ð
Þ
This means that the observer objective is achieved. It exist t
c
such as x
r
¼
W.
The above-presented sensorless HOSM control strategy using a HOSM speed
observer is illustrated by the block diagram in Fig.
2.8
.
2.4 Simulation Using the FAST Code
The proposed HOSM control strategy, the high-gain, and the HOSM speed
observers have been tested for validation using the NREL FAST code [
20
]. The
FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code is a compre-
hensive aeroelastic simulator capable of predicting both the extreme and fatigue
loads of two- and three-bladed horizontal-axis wind turbines. This simulator has
been chosen for validation because it is proven that the structural model of FAST
