Chapter 4 ControllerSynthesis
© National Instruments Corporation 4-5 MATRIXx Xmath Robust Control Module
herethe w eighting matrices are transfer matrices, whereas in the LQG
setup they are constants.
A description of the plant in Figure 4-3 is as follows:
• Dynamical system Gdyn:
• Measured variables y=ysens+n:
• Input weight Win:
• Output weight Wout:
Weight Selection
In the standard LQG formulation, the weighting functions (Wdist, Wnoise,
Wreg, and Wact) are all constant matrices. In fact, if Qreg and Qact are positive
definite matrices in the LQ cost, for example,
then the following apply:
Similarly, if Rproc and Rsens are positive definite matrices corresponding to
the process and measurement noise intensities, then the following apply:
x
·Ax BdistdB
actu++=
yreg Cregx=
ysens Csensx=
d
n
Wdist 0
0Wnoise
wdist
wnoise
Win
wdist
wnoise
==
ereg
eact
Wreg 0
0Wact
yreg
u
Win
yreg
u
==
J1
2
---x'Qregxu'Qactu+
0
∞
∫
⎝⎠
⎜⎟
⎛⎞
dt=
Wreg Qreg
12/
=Wact Qact
12/
=
Wdist Qproc
12/
=Wnoise Qsens
12/
=