(a) In the unity feedback system in Figure 1, at least how many poles of G(s) must be at the origin for the steady-state error due to the ramp input

is zero? i. 1ii. 2iii. 3iv. 4 100, then the stead-state errors for step and(b) If the static error constant Karamp inputsare \text { i. } e_{\text {step }}(\infty)=0, e_{\text {ramp }}(\infty)=0 \text { ii. } e_{\text {step }}(\infty)=0, e_{\text {ramp }}(\infty)=\infty \text { iii. } e_{\text {step }}(\infty)=\infty, e_{\text {ramp }}(\infty)=0 \text { iv. } e_{\text {step }}(\infty)=\infty, e_{\text {ramp }}(\infty)=\infty (c) If KG(s)H(s) represents the open-loop transfer function of a system, then the gain K and the closed-loop poles of the system satisfy which equation? i. KG(s)H(s) = 1 ji. KG(s)H(s) = -1 iii. KG(s)H(s) = 0 iv. KG(s) = H(s) If the open-loop transfer function is given by \frac{K(s+2)}{s^{4}+2 s+2} how many open-loop zeros are at infinity? i. 1ii. 3iii. 4iv. 0 ) Which of the following statements is incorrect? i. Root-locus is symmetric about x-axis. ii. Root-locus starts at open-loop poles and ends at open-loop zeros. ii. Root-locus graph tracks the closed-loop poles as the gain varies. iv. None.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10

Fig: 11

Fig: 12

Fig: 13

Fig: 14

Fig: 15

Fig: 16

Fig: 17

Fig: 18

Fig: 19

Fig: 20

Fig: 21