National Instruments Xmath Interactive Control Design Module ICDM Bedienungsanleitung Seite 65

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Chapter 7 LQG Synthesis
Xmath Interactive Control Design Module 7-4 ni.com
Setup and Terminology
The different modes are described using the following basic terminology:
Figure 7-1 shows a block diagram with the basic setup for LQG synthesis,
where u is the actuator signal (output of the controller)
w
proc
is an (input referred) process noise
y is the (plant) output signal
is the weighted output signal
w
sens
is a sensor noise
P is the plant transfer function
C is the controller transfer function
W is the output weight transfer function
The noises w
proc
and w
sens
are white; that is, they have constant power
spectral densities (PSDs). The parameter υ is the ratio of the PSD of w
sens
to the PSD of w
proc
.
Figure 7-2. Block Diagram Showing the Basic Setup for LQG Synthesis
Standard LQG (All Toggle Buttons Off)
In LQG synthesis mode, the controller minimizes a weighted sum of the
steady-state actuator and output variance:
where E denotes expectation, ρ is the Control cost parameter, and the
parameter ν gives the ratio of the intensity of the sensor noise w
sens
to the
intensity of the process w
proc
noise (which are assumed to be white).
yPuw
proc
+()= uC()yw
sens
+()= y
˜
Wy=
y
˜
y
P(s)
r=0
W(s)
y
C(s)
u
w
proc
w
sens
JE
t
lim ρut()
2
yt()
2
+()=
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