Setup And Terminology; Standard Lqg (All Toggle Buttons Off) - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Chapter 7 LQG Synthesis

Setup and Terminology

r=0

Standard LQG (All Toggle Buttons Off)

Xmath Interactive Control Design Module
The different modes are described using the following basic terminology:
y P u w
= +
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 is an (input referred) process noise
proc
y is the (plant) output signal
y ˜
is the weighted output signal
w is a sensor noise
sens
P is the plant transfer function
C is the controller transfer function
W is the output weight transfer function
The noises w and w
proc
spectral densities (PSDs). The parameter
to the PSD of w .
proc
u
C(s)
w
proc
Figure 7-2. Block Diagram Showing the Basic Setup for LQG Synthesis
In LQG synthesis mode, the controller minimizes a weighted sum of the
steady-state actuator and output variance:
where E denotes expectation, is the Control cost parameter, and the
parameter gives the ratio of the intensity of the sensor noise w
intensity of the process w
u C
= –
proc
are white; that is, they have constant power
sens
y
P(s)
2
J lim E u t
=
t
noise (which are assumed to be white).
proc
7-4
y w y ˜ Wy
+ =
sens
is the ratio of the PSD of w
y
W(s)
w
sens
2
y t
+
sens
sens
to the
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