Saunder January 22, 2014 10:43 K15053˙Book
58 Disturbance Observer-Based Control: Methods and Applications
4.2.3 High-Order Disturbance Case
Disturbances d(t)in(4.1) are assumed to be high-order ones, which are depicted by
d(t) = d
0
+ d
1
t + ···+d
q
t
q
, (4.14)
where d
0
, d
1
, ... , d
q
are constant but unknown. A high-order disturbance observer
for estimating the disturbances in (4.14) is proposed in [11], given by
˙
z = F
+
f (x, u; t) +
0
g
0
(t) +···+
q
g
q
(t),
ˆ
d =
0
g
0
(t) +···+
q
g
q
(t),
(4.15)
with
g
k
(t) =
F
+
x − z,(k = 0),
t
0
g
k−1
(τ )dτ,(k ≥ 1),
(4.16)
for k ∈ [0, q], where
k
= diag
{
γ
k1
, ... , γ
kr
}
,(k = 0, ... , q), and γ
ij
’s are
chosen such that the polynomials
p
j
(s ) = s
q+1
+ γ
0 j
s
q
+ ···+γ
(q−1) j
s +γ
qj
(4.17)
for j = 1, ... , r are Hurwitz stable.
Combining (4.2)