National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 84)

Chapter 10 Alternate Plant Window
Xmath Interactive Control Design Module 10-4 ni.com
Normalization
The form of the transfer function of the alternate plant depends on the
normalization selected. With high-frequency normalization, the alternate
plant transfer function is:
where K is the gain (shown in the slider and Variable Edit box),
are the zeros, and are the poles shown in the plot. The alternate
plant is required to be proper, that is, have at least as many poles as zeros
(
).
For high-frequency normalization there is no restriction on the poles or
zeros.
With DC normalization, the alternate plant transfer function is:
where K is the gain (shown in the slider and Variable Edit box),
are the zeros, and are the poles. For DC normalization the poles
and zeros are restricted to be nonzero. If you want the alternate plant to have
either poles or zeros at s = 0, you must use high frequency normalization.
Notice that with DC normalization the gain is exactly the DC gain of the
alternate plant, that is, K = P
alt
(0).
Manipulating the Parameters
The gain K can be changed using the slider or the Variable Edit box. The
poles and zeros of P
alt
can be manipulated graphically, using the buttons to
the right of the plot. Refer to the Graphically Manipulating Poles and
Zeros section of Chapter 2, Introduction to SISO Design , for a general
discussion of how to graphically edit poles and zeros.
You cannot add a zero if the addition would result in an improper alternate
plant transfer function. Similarly, you cannot delete a pole if the deletion
would result in an improper alternate plant transfer function. With DC
normalization, you cannot create any poles or zeros at s = 0, and you cannot
move existing poles or zeros to s = 0.
P
alt
s ( ) K
s z
1
–
( )… s z
m
–
( )
s p
1
–
( )… s p
n
–
( )
------------------------------------------- =
z
1
… z
m
, ,
p
1
… p
n
, ,
n m ≥
P
alt
s ( ) K
1 s z
1
⁄
–
( )… 1 s z
m
⁄
–
( )
1 s p
1
⁄
–
( )… 1 s p
n
⁄
–
( )
--------------------------------------------------------- =
z
1
… z
m
, ,
p
1
… p
n
, ,