National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 49)

Chapter 5 Root Locus Synthesis
© National Instruments Corporation 5-3 Xmath Interactive Control Design Module
Edit menu or by typing the accelerators in the Root Locus window.
A more detailed description appears following.
The Root Locus Synthesis window is shown in Figure 5-1 with the standard
(default) 180
° contour. The branches of the locus connect the zeros and
poles of the loop transfer function, which are shown in the plot. The
closed-loop poles, which are on the locus, are also shown.
Opening the Root Locus Synthesis Window
The Root Locus window can accept any type of controller, so it can always
be opened. It simply reads the current controller from ICDM. You then can
use the Root Locus
window to manipulate the controller poles, zeros, and
gain.
After you have changed the controller using the Root Locus window, the
controller loses any special form it may have had—for example, LQG.
It is represented by its transfer function. Thus, you can use the Root Locus
window to change the zeros, poles, and gain of a controller originally
designed using the LQG
window, but you then cannot read the controller
back into the LQG Synthesis window since it is no longer an LQG
controller.
Terminology
The loop transfer function is expressed in the following product form:
where K is called the gain (notice that the gain is high-frequency
normalized), the z
i
values are the zeros of the loop transfer function
and the p
i
values are the poles of the loop transfer function.
Each of these poles and zeros is associated with either the plant or the
controller. The Root Locus
window allows you to change the gain, change
or delete any controller pole or zero, or create new controller poles and
zeros as long as the controller transfer function remains proper—that is, has
finite gain at high frequencies. The Root Locus
window will not allow you
to change or delete any plant pole or zero. The Alternate Plant window can
be used to modify the plant interactively and see the effect on the
closed-loop system performance.
L s ( ) K
s z
1
–
( )… s z
k
–
( )
s p
1
–
( )… s p
1l
–
( )
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