Modern Control System Theory and Design, 2nd Edition

7.3.  MINOR-LOOP FEEDBACK-COMPENSATION TECHNIQUES

Let us consider the general system illustrated in Figure 7.2. The compensating element in this case is the transfer function B(s). In order to have a basis of comparison, we will follow an analysis for minor-loop feedback compensation similar to that performed for the case of phase lead-network cascade compensation.

The minor-loop feedback element B(s) usually represents rate feedback or acceleration feedback. In general, phase-lag, -lead, and/or lag–lead networks may also be cascaded with B(s).

The stabilizing effect of minor-loop feedback compensation can easily be demonstrated for a simple second-order system. We assume that the system illustrated in Figure 7.2 contains simple rate feedback. The specific transfer functions for the system are

The system is redrawn with these transfer functions and shown in Figure 7.14a.

Without any rate feedback, the configuration represents a simple second-order system whose damping ratio is ζ and undamped natural frequency is ω_n. The resulting system transfer function with rate-feedback compensation is given by

Comparing the denominator of Eq. (7.26) with that of Eq. (4.3), we observe that it ...