User`s guide

LQG Regulation
9-47
MIMO LQG Design
Start with the complete two-axis state-space model Pc derived above. The
model inputs and outputs are
Pc.inputname
ans =
'u-x'
'u-y'
'w-ex'
'w-ix'
'w_ey'
'w_iy'
P.outputname
ans =
'x-gap'
'y-gap'
'x-force'
'y-force'
As earlier, add low-pass filters in series with the 'x-gap' and 'y-gap' outputs
to penalize only low-frequency thickness variations.
Pdes = append(lpf,lpf,eye(2)) * Pc
Pdes.outputn = Pc.outputn
Next, design the LQ gain and state estimator as before (there are now two
commands a nd two measurements).
k = lqry(Pdes(1:2,1:2),eye(2),1e–4*eye(2)) % LQ gain
est = kalman(Pdes(3:4,:),eye(4),1e3*eye(2)) % Kalman estimator
RegMIMO = lqgreg(est,k) % form MIMO LQG regulator