Modern Control System Theory and Design, 2nd Edition

PROBLEMS

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

Figure P5.1

K₁ = 10 V/rad,K₂ = 10 V/rad,G(s) =

(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

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

Figure P5.2

(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