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)
wproc is an (input referred) process noise
y is the (plant) output signal
is the weighted output signal
wsens 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 wproc and wsens are white; that is, they have constant power
spectral densities (PSDs). The parameter υ is the ratio of the PSD of wsens
to the PSD of wproc.
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 wsens to the
intensity of the process wproc 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
wproc
wsens
JE
t∞→
lim ρut()
2yt()
2
+()=