If the DC gain is 5 and GGc(s) has One poles at the origin then, the steady stat

Question

If the DC gain is 5 and GGc(s) has One poles at the origin then, the steady state error will be around (A) 10% (B) 5% (C) 50% (D)20% (E) 25 If G(s) and G(s) = 1/s(s + 4) and Gc(s) = K, it is required to force the system to have zeta = 0.5, then the gain K will have the following value (A) K = 10 (B) K = 16 (C) K = 18 (D) K = 20 (E) Kd = 23 If the G(s) has no poles at the origin and the steady state error due to step input is 40%, . It is required to reduce the error to 5% by adding a phase lag with unity DC gain, the ratio between its pole and zero is approximately (A) 10 (B) 12 (C) 14 (D) 16 (E) 19

Explanation / Answer

8) Solution:

DC gain = Kp = 5 and Gc(s) = 1 / s

then G(s) = Kp / s   

now , Steady state error is given by = ess  = 1 / [ lims->0  s*Kp*Gc(s) ] .. for the system having pole at the origin

ess  = 1 / [ lims->0  s Kp / s ]

ess = (1 / 5)*100 = 20 %

hence the answer is (D)

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