Saunder January 22, 2014 10:43 K15053˙Book
284 Disturbance Observer-Based Control: Methods and Applications
A nonlinear disturbance observer (NDO) [8, 132] with finite-time convergence
property for estimating the disturbances for the AHV system (16.9) is constructed
as
˙
z
0
= v
0
+
¯
f (x) +
¯
g (x)u,
˙
z
1
= v
1
,
˙
z
2
= v
2
,
ˆ
¯
x = z
0
,
ˆ
w = z
1
,
ˆ
˙
w = z
2
,
(16.12)
where z
0
=
[
z
01
, ... , z
06
]
T
, z
1
=
[
z
11
, ... , z
16
]
T
, z
2
=
[
z
21
, ... , z
26
]
T
, v
0
=
[
v
01
, ... , v
06
]
T
, v
1
=
[
v
11
, ... , v
16
]
T
, v
2
=
[
v
21
, ... , v
26
]
T
,
ˆ
¯
x the estimate of
¯
x,
ˆ
w the estimate of w,
ˆ
˙
w the estimate of
˙
w, and
v
0i
=−λ
0
L
1/3
i
|z
0i
−
¯
x
i
|
2/3
sign(z
0i
−
¯
x
i
) + z
1i
,
v
1i
=−λ
1
L
1/2
i
|z
1i
− v
0i
|
1/2
sign(z
1i
− v
0i
) + z
2i
,
v
2i
=−λ
2
L
i
sign(z
2i
− v
1i
),
for i = 1, ... ,6,λ
0
, λ
1
, λ
2
> 0 are observer coefficients.
Combining (16.11) and (16.12), ...