User`s guide

LQG Regulation
9-45
Accordingly, the thickness gaps and rolling forces are related to the outputs
of the - and -axis models by
Let’s see how the previous “decoupled” LQG design fares when cross-coupling
is takeninto account.Tobuild the two-axesmodel shown inFigure 9-2, append
the models
Px and Py for the - and -axes.
P = append(Px,Py)
For convenience, reorder the inputs and outputs so that the commands and
thickness gaps appear first.
P = P([1 3 2 4],[1 4 2 3 5 6])
P.outputname
ans =
'x-gap'
'y-gap'
'x-force'
'y-force'
Finally, place the cross-coupling matrix in series with the outputs.
gxy = 0.1; gyx = 0.4;
CCmat = [eye(2) [0 gyx*gx;gxy*gy 0] ; zeros(2) [1 –gyx;–gxy 1]]
Pc = CCmat * P
Pc.outputname = P.outputname
To simulate the closed-loop response, also form the closed-loop model by
feedin = 1:2 % first two inputs of Pc are the commands
feedout = 3:4 % last two outputs of Pc are the measurements
cl = feedback(Pc,append(Regx,Regy),feedin,feedout,+1)
δ
x
f
x
...,,
x
y
δ
x
δ
y
f
x
f
y
100g
yx
g
x
01g
xy
g
y
0
001g
yx
–
00g
xy
– 1
δ
x
δ
y
f
x
f
y
=
cross-coupling matrix
            
x
y