National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 72)

Chapter 8 H-Infinity Synthesis
© National Instruments Corporation 8-3 Xmath Interactive Control Design Module
Opening the Synthesis Window
The H
∞ window can only accept H∞ controllers. If the current controller is
of type H
∞ (perhaps from the History window) and the H∞ window is
opened, the current controller is read into the H
∞ window; that is, the
parameters are set to the appropriate values.
If the current controller is not of type H
∞, and the user attempts to open
the H
∞ Synthesis
window, a dialog box appears and warns the user that
proceeding with opening the synthesis window will overwrite the current
controller with the controller.
The H
∞ window remembers its parameter settings. When it is opened, the
parameters will be exactly as they were when the window was last closed,
or they will be set to default values if the H
∞ window has not been opened
in this ICDM session.
Setup and Synthesis Method
This section describes the closed-loop transfer matrix (refer to Figure 8-2).
The H
∞ synthesis procedure can be described using the following standard
setup:
where y is the plant output signal
w
1
is a normalized (input-referred process) noise
w
2
is a normalized (sensor) noise
z
1
is the normalized actuator signal
z
2
is the weighted plant output signal
P is the plant transfer function
C is the controller transfer function
W is the output weight transfer function
y P u w
1
+
( )
= u C –
( ) y νw
2
+
( )
=
z
1
ρu
= z
2
W
y
=