Modern Control System Theory and Design, 2nd Edition

5.10.  ILLUSTRATIVE PROBLEMS AND SOLUTIONS

This section provides a set of illustrative problems and their solutions to supplement the material presented in Chapter 5.

Figure I5.1

I5.l. The control system of Figure I5.1 contains position and rate feedback:

(a)  Determine the closed-loop transfer function C(s)/R(s).

(b)  Determine the sensitivity of the closed-loop transfer function to K₂ as a function of s.

(c)  Determine the sensitivity of the closed-loop transfer function to K₂ at dc.

SOLUTION:(a)

(b)

where

Therefore,

(c)

I5.2. The sensitivity of the following control systems is to be analyzed:

Figure I5.2

(a)  Determine the overall transfer function, H = C(s)/R(s).

(b)  Determine the sensitivity of the control system’s transfer function, H(s) = C(s)/R(s) with respect to the transfer ...