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Chapter 4 Controller Synthesis
© National Instruments Corporation 4-15 MATRIXx Xmath Robust Control Module
This expression can be converted into the following form [Gu80]:
If R(jω) is not a function of frequency, then C
12
= 0 and D = I.
Note The system has a new input v and the old input u is now the output of the system.
This structure is only used for computational convenience.
Define:
Thus,
After the system is put in this form, you are ready to use the
fsregu( )
function. For more information on the
fsregu( ) syntax, refer to the
Xmath Help.
x
·
x
·
′
A
11
A
12
A
21
A
22
x
x′
B
1
B
2
v+=
⎧
⎪
⎨
⎪
⎩
⎧
⎨
⎩
u
0 C
12
x
x′
Dv+=
⎧
⎪
⎨
⎪
⎩
{
A
c
B
c
C
c
D
c
x
A
x
x'
=
x
·
A
A
c
x
A
B
c
v+=
uC
c
x
A
D
c
v+=
J
1
2
---
x
A
*
R
xx
A
x
A
v
*
R
uu
A
v 2x
A
*
+ R
xu
A
v+()dω
∞
∫
=