MATLAB CONTROL SYSTEM TOOLBOX 9 Guia do Utilizador descarregar pdf (Página 345)

100

101

LQG Regulation

9-37

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)

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, design theKalman estimator with the function

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.

30 s 30

+()⁄

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