Chapter 12
LQG/H-Infinity Synthesis
©
National Instruments Corporation
12-13
Xmath Interactive Control Design Module
The transfer functions
W
u, i
and
W
y, j
are the input and output weighting
transfer functions, respectively. When
W
u, i
= 1 and
W
u, j
= 1, this reduces to
the previously described standard LQG controller.
Notice that integral action also can be accomplished by defining filters that
have poles on
s
= 0. This is useful if integral action is required for a subset
of the outputs. The standard toggle button for integral action applies to all
outputs.
How to Select
w
,
u
,
y
, and
z
The user has complete freedom in designating components of the input and
output vector as external disturbances (
w
), actuators (
u
act
), sensors (
y
), and
weighted outputs (
z
).
•
Sensors and actuators are disabled/enabled using the leftmost column
of toggle buttons in the Weights window. This is useful for situations
where you want to know what the value of individual sensors and
actuators is for the achievable control performance. By default,
all outputs are sensors and all inputs are actuators.
•
Input-referred disturbances and measurement noise can be selected
using the toggle buttons in the second column of the noise level display
of the Weights window. Setting a toggle button to the “off” position
corresponds to setting the noise variance of the corresponding signal to
zero.
•
Weighted outputs and inputs can be selected using the toggle buttons
in the second column of the Weights window. Setting a toggle button
to the “off” position corresponds to setting the weight of the
corresponding signal to zero.
