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Modern Control System Theory and Design, 2nd Edition by Stanley M. Shinners

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PROBLEMS

5.1. Assume that the system shown in Figure P5.1 has the following characteristics:

Image

Figure P5.1

K1 = 10 V/rad,K2 = 10 V/rad,G(s) = Image

(a)  Determine the sensitivity of the system’s transfer function H(s) with respect to the input transducer, K1.

(b)  Determine the sensitivity of the system’s transfer function H(s) with respect to the feedback transducer, K2.

(c)  Determine the sensitivity of the system’s transfer function H(s) with respect to G(s)

(d)  Indicate qualitatively the frequency dependency of Image

5.2. For the system in Figure P5.2, assume the following characteristics:

Image

Figure P5.2

Image

(a)  Determine the sensitivity of the system’s transfer function H(s) with respect to G1(s) at ω = 1 rad/sec.

(b)  Determine the sensitivity of the system’s transfer function H(s) with respect to G2(s) at ω = 1 rad/sec.

(c)  Determine the sensitivity of the system’s transfer function H(s) with respect to H2(s) at ω = 1 rad/sec.

(d)  Determine the sensitivity of the system’s transfer function

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