
Saunder January 22, 2014 10:43 K15053˙Book
218 Disturbance Observer-Based Control: Methods and Applications
where c(t) =
˙
a(t). A linear ESO can be constructed as follows [4]:
˙
z
1
= z
2
− 2p(z
1
− x) +bu
˙
z
2
=−p
2
(z
1
− x)
(13.5)
where −p (p > 0) is the desired double pole of ESO, z
1
is the estimate of x
1
, and z
2
is the estimate of a(t). Here, according to the analysis in [186], z
1
(t)isanestimate
of the output x(t), while z
2
(t)isanestimate of the lumped disturbance a(t), i.e.,
z
1
(t) → y (t) and z
2
(t) → a(t).
A composite control law is designed as follows
u = u
0
−
z
2
b
, u
0
= k(x
∗
− z
1
) (13.6)
where x
∗
is the reference input of x.
13.3.2 Speed Controller Design
The main ...