Specifications

10 Design Case Studies
10-34
Model Data for the x-Axis
Model Data for the y-Axis
LQG Design for the x-Axis
As a first approximation, ignore the cross-coupling between the - and -axes
and treat each axis independently. That is, design one SISO LQG regulator for
each axis. The design objective is to reduce the thickness variations and
due to eccentricity and input thickness disturbances.
Start with the -axis. First specify the model components as transfer function
objects.
% Hydraulic actuator (with input "u-x")
Hx = tf(2.4e8,[1 72 90^2],'inputname','u-x')
H
x
s
()
2.4 10
8
×
s
2
72s 90
2
++
-------------------------------------
=
F
ix
s
()
10
4
s 0.05+
--------------------
=
F
ex
s
()
310
4
×
s
s
2
0.125s 6
2
++
------------------------------------------
=
g
x
10
6–
=
H
y
s
()
7.8 10
8
×
s
2
71s 88
2
++
-------------------------------------
=
F
iy
s
()
210
4
×
s 0.05+
--------------------
=
F
ey
s
()
10
5
s
s
2
0.19s 9.4
2
++
--------------------------------------------
=
g
y
0.5 10
6–
×
=
xy
δ
x
δ
y
x