Environmental Engineering Reference
In-Depth Information
where T
a
is observed. Then we will have
T
a
e
T
¼
2k
opt
x T
a
K
t
x
T
g
ð
2
:
28
Þ
If we define the following functions
F
¼
2k
opt
x
G
¼
2k
opt
x T
a
K
t
x
ð
2
:
29
Þ
Þ
T
a
ð
then
e
T
¼
F T
g
þ
G
ð
2
:
30
Þ
Let us consider the following observer based on the supertwisting algorithm
[
16
,
19
].
T
g
¼
y
þ
B
1
e
j
2
sgn e
ðÞ
y
¼þ
B
2
sgn e
ðÞ
ð
2
:
31
Þ
The gains B
1
and B
2
are chosen as
8
<
B
1
[
U
2
C
m
B
2
4U
2
C
M
A
1
þ
U
1
ð
Þ
C
m
A
1
U
1
ð
2
:
32
Þ
ð
Þ
\U
2
0\C
m
F\C
M
:
G
Thus, we will guaranty the convergence of e
T
to 0 in a finite time t
c
. The
aerodynamic torque estimation is then deduced.
T
a
¼
T
opt
;
t [ t
c
:
ð
2
:
33
Þ
The above-proposed high-gain observer principal is illustrated by the block
diagram in Fig.
2.6
.
2.3.4 High-Order Sliding Mode Speed Observer
Figure
2.7
illustrates the main reference frames on which is based the proposed
speed observer development.
In this case, h
s
can be easily determined using stator voltage measurements and
a PLL.
If the stator flux is assumed to be aligned with the d-axis,
