
Saunder January 22, 2014 10:43 K15053˙Book
Nonlinear Disturbance Observer-Based Control for Systems 105
where
¯
α(x) = [
¯
α
1
(x),
¯
α
2
(x),
¯
α
3
(x)], and
¯
α
1
(x) =−
t
1
b
1
+ k
q
b
2
k
1
+
(
k
2
+ m
1
)
f
1
(α) +(1 +k
2
k
q
) f
2
(α)
,
(7.46)
¯
α
2
(x) =−
t
1
b
1
+ k
q
b
2
(k
1
k
q
+ k
2
+ m
1
), (7.47)
¯
α
3
(x) = 1 −
t
1
b
1
+ k
q
b
2
(k
2
b
1
+ k
2
k
q
b
2
+ m
1
b
1
+ b
2
), (7.48)
γ (ω,
˙
ω,
¨
ω) =
t
1
b
1
+ k
q
b
2
(k
1
ω + k
2
˙
ω +
¨
ω). (7.49)
Since all nonlinear functions including
¯
f (x),
¯
h(x), g
1
(x), g
2
(x), and
¯
α(x) are avail-
able, nonlinear disturbance compensation gain β(x)isobtained by using (7.19).
The composite nonlinear disturbance observer-based robust control (NDOBRC)
law is then given by
u = u
ndic
+ β(x)
ˆ
d, (7.50)
where u
ndic
is NDIC ...