Page 657 - Mechanical Engineers' Handbook (Volume 2)

648 Controller Design

Figure 23 Effects of derivative feedback on
closed-loop roots.

Note, however, that the practical implementation of Fig. 25 requires one less transducer than
Fig. 22a.
Another way in which derivative feedback can be useful is to provide very smooth and
repeatable dynamic response and high static accuracy when the primary control loop has an
inherent integration. This is particularly useful when closed-loop bandwidth is not a major
concern. The technique involves closing a tight integrating loop around the first derivative
of the controlled variable, as illustrated in Fig. 26. This loop submerges the effects of
forward-loop gain variations, static offsets, and external disturbances. The primary control
loop gain can then be set at relatively low levels to ensure smooth, repeatable dynamic

Figure 24 Effects of derivative feedback on closed-loop frequency reqponse of U 2 /U c .