Specifications

10 Design Case Studies
10-36
ans =
'x-gap'
'x-force'
The second output 'x-force' is the rolling force measurement. The LQG
regulator willusethismeasurement to drive thehydraulic actuatorandreduce
disturbance-induced thickness variations .
The LQG design involves two steps:
1 Design a full-state-feedback gain that minimizes an LQ performance
measure of the form
2 Design a Kalman filter that estimates the state vector given the force
measurements
'x-force'.
The performance criterion penalizes low and high frequencies equally.
Because low-frequency variations are of primary concern, eliminate the
high-frequency content of with the low-pass filter and use the
filtered value in the LQ performance criterion.
lpf = tf(30,[1 30])
% Connect low-pass filter to first output of Px
Pxdes = append(lpf,1) * Px
set(Pxdes,'outputn',{'x-gap*' 'x-force'})
% Design the state-feedback gain using LQRY and q=1, r=1e-4
kx = lqry(Pxdes(1,1),1,1e-4)
δ
x
Ju
x
()
q
δ
x
2
ru
x
2
+
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td
0
∞
ò
=
Ju
x
()
δ
x
30 s 30+
()⁄