Page 663 - Mechanical Engineers' Handbook (Volume 2)

654 Controller Design

the variations in forward-loop characteristics are large, it may be necessary to use inner
feedback loops to minimize the variations in closed-loop response, as explained in Section
4.1.

5.3 Feedforward
As explained in Section 5.2, the effectiveness of lead prefilters is limited by the fact that the
command signal must be differentiated. In a system whose forward loop contains electronic
lags, the number of command differentiations can often be reduced by the use of feedforward
techniques. Feedforward can also be used to reduce the following errors associated with a
steady rate of change of the command signal. However, these techniques must be carefully
applied to prevent adverse effects on system dynamic response.
The principles of feedforward are illustrated in Fig. 31a. If the electronic shaping in the
feedforward path approximates the reciprocal of the nonelectronic forward-loop elements,
the command signal will nominally be reproduced at the output. Follow-up by the feedback
loop will then try to minimize the effects of inaccuracies in the feedforward signal. The use
of a prefilter matched to the feedback path further improves the overall response to com-
mands. The net effect of the feedforward configuration can be seen by rearranging the block
diagram into an equivalent one that has only a prefilter, as shown in Fig. 31b. From this
figure, the system response can be written

Figure 31 Idealized use of feedforward: (a) feedforward model; (b) equivalent prefilter model.