User`s guide

9 Design Case Studies
9-42
LQG Design for the y-Axis
TheLQG design for the -axis (regulation of the thickness)followsthe exact
samestepsasforthe -axis.
% Specify model components
Hy = tf(7.8e8,[1 71 88^2],'inputn','u-y')
Fiy = tf(2e4,[1 0.05],'inputn','w-iy')
Fey = tf([1e5 0],[1 0.19 9.4^2],'inputn','w-ey')
gy = 0.5e–6 % force-to-gap gain
% Build open-loop model
Py = append([ss(Hy) Fey],Fiy)
Py = [–gy gy;1 1] * Py
set(Py,'outputn',{'y-gap' 'y-force'})
% State-feedback gain design
Pydes = append(lpf,1) * Py % Add low-freq. weigthing
set(Pydes,'outputn',{'y-gap*' 'y-force'})
ky = lqry(Pydes(1,1),1,1e–4)
% Kalman estimator design
esty = kalman(Pydes(2,:),eye(2),1e3)
% Form SISO LQG regulator for y-axis and close the loop
Regy = lqgreg(esty,ky)
cly = feedback(Py,Regy,1,2,+1)
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