Page 647 - Mechanical Engineers' Handbook (Volume 2)

638 Controller Design

Figure 16 Effects of variations in forward-loop poles on stability of a lead-compensated loop: (a) root
locus; (b) open-loop frequency response.

the use of notch filters. The notch is intended to attenuate the resonant peak, without the
bandwidth boost of the lead compensator described in the present example ( , instead
cz
cp
of 3 ).
cz
However, it is possible to design a compensator that will improve the damping of these
poles. To accomplish this, it is useful to recall that for any system in which the number of
poles exceeds the number of zeros by two or more, the sum of the real parts of all the poles
is not changed when the loop is closed. In this case, closing the loop will cause some roots
1
to become more stable and others to become less stable (usually those that were poorly