
Saunder January 22, 2014 10:43 K15053˙Book
Disturbance Rejection for Magnetic Leviation Suspension System 205
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Operating
Point
Settings
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–
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(z
t
– z)
Nonlinear
MAGLEV
Systems
Dierential
equation
(12.19)
Disturbance observer
LQR
z
t
Figure 12.2 Block diagram of the proposed DOBC method for the nonlinear MA-
GLEV system.
where t
0
is the initial time and k
i
is the integral coefficient to be designed. To find
an appropriate integral coefficient, a variable x
4
=
t
t
0
[
z
t
(τ ) −z(τ )
]
dτ is taken as
an augmented state. For the augmented system, the LQR method is used to get the
control gain. The penalty matrixes are selected as
Q
I
=
Q 0
0 q
i
,