National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 53)

Chapter 5 Root Locus Synthesis
© National Instruments Corporation 5-7 Xmath Interactive Control Design Module
Design
This section gives short descriptions of how the Root Locus window can be
used to design or analyze controllers. This section also provides some
interpretations and describes some uses of the nonstandard contour plots.
Adding a Pole-Zero Pair
Adding a pole-zero pair is a good way to add a little lead or lag action to an
existing controller. When you first add the pole-zero pair, you will not have
changed the controller transfer function. As you grab the zero and drag it
away from the pole, you will induce a smooth change in the controller
transfer function. By dragging the zero a little closer to the origin, you will
add a small amount of lead action to the controller—that is, increase the
controller phase for frequencies between the pole and zero, and increase the
magnitude at frequencies larger than the pole.
Similarly, by dragging the zero away from the origin, you will create some
lag action—that is, decrease the loop phase between the zero and pole, and
increase the gain below the pole frequency.
Deleting Pole-Zero Pairs
Deleting a controller pole-zero pair is a good way to do interactive
controller model reduction. Suppose that you have synthesized a suitable
controller and need to find a lower order controller that has nearly the same
performance. Using the Root Locus window, you want to move (stable)
controller poles or zeros near each other without sacrificing controller
performance. Good candidates are poles and zeros substantially outside the
control system bandwidth, or pairs of nearby poles and zeros. After you
have moved a controller pole or zero (or both) so that they are near each
other—and hopefully, control system performance has not changed too
much—then you can delete the pair without severely affecting the
controller transfer function. You have just reduced the controller order by
one (or two, if you deleted a complex conjugate pair of poles and zeros).