
Saunder January 22, 2014 10:43 K15053˙Book
86 Disturbance Observer-Based Control: Methods and Applications
Disturbance
compensation
State
feedback
Plant
Extended State Observer
b
d
x(t) x(t)
y
o
(t)
S
–1
I
y
m
(t)
yˆ
m
(t)
–
ˆ
x(t)
–
ˆ
x(t)
–
ˆ
x(t)
d
ˆ
(t) = x
ˆ
n+1
(t)
c
o
C
m
A
A
–
–
b
u
K
x
u
d(t) = f(x,d(t), t)
L
b
u
–
C
m
S
–1
I
K
d
Figure 6.1 Configuration of the proposed GESOBC method.
or
u = K
x
ˆ
x + K
d
ˆ
d, (6.14)
where K
x
is the feedback control gain, and K
d
is the disturbance compensation gain,
designed as
K
d
=−[c
o
(A + b
u
K
x
)
−1
b
u
]
−1
c
o
(A + b
u
K
x
)
−1
b
d
. (6.15)
Remark 6.5 The disturbance compensation gain K
d
in (6.15) is a general case and
suitable for both matching and mismatching cases. For the matching case, ...