Specifications

LQG Regulation: Rolling Mill Example
10-37
Note: lqry expects all inputs to be commands and all outputs to be
measurements. Here the command
'u-x' and the measurement 'x-gap*'
(filtered gap) are the first input and first output of Pxdes.Hence,usethe
syntax
Pxdes(1,1) to specify just the I/O relation between 'u-x' and
'x-gap*'.
Next,designtheKalmanestimatorwiththefunction
kalman.Theprocessnoise
has unit covariance by construction. Set the measurement noise covariance to
1000 to limit the high frequency gain, and keep only the measured output
'x-force' for estimator design.
estx = kalman(Pxdes(2,:),eye(2),1000)
Finally, connect the state-feedback gain kx and state estimator estx to form
the LQG regulator.
Regx = lqgreg(estx,kx)
This completes the LQG design for the -axis.
Let’s look at the regulator Bode response between 0.1 and 1000 rad/sec.
w
x
w
ex
w
ix
=
x