Normalization; Manipulating The Parameters - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Chapter 10 Alternate Plant Window

Normalization

Manipulating the Parameters

Xmath Interactive Control Design Module
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),
p
are the zeros, and
1
plant is required to be proper, that is, have at least as many poles as zeros
n m
( ).
For high-frequency normalization there is no restriction on the poles or
zeros.
With DC normalization, the alternate plant transfer function is:
P
alt
where K is the gain (shown in the slider and Variable Edit box),
p
are the zeros, and
1
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
The gain K can be changed using the slider or the Variable Edit box. The
poles and zeros of P
alt
the right of the plot. Refer to the
Zeros section of Chapter 2,
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.
s z
–
1
P s K
------------------------------------------ -
=
alt
s p
–
1
p
are the poles shown in the plot. The alternate
n
1 s z
–
1
s K
-------------------------------------------------------- -
=
1 s p
–
1
p
are the poles. For DC normalization the poles
n
(0).
alt
can be manipulated graphically, using the buttons to
Graphically Manipulating Poles and
Introduction to SISO
10-4
s z
–
m
s p
–
n
z
1
1 s z
–
m
1 s p
–
n
z
1
Design, for a general
z
m
z
m
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