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

**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 *K*_{2} as a function of *s*.

**(c)** Determine the sensitivity of the closed-loop transfer function to *K*_{2} at dc.

**SOLUTION:(a)**

**(b)**

where

Therefore,

**(c)**

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

**(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 ...

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