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Reinforcement Problem #1 (20 pts.) A) Glven For a feedback control system with an open-loop process and negative feedback des
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RS Gry se (5) EB)(049) [+0) K G(S) = 2, Glo(872 I (8)21 125 5+1 stepo open loop Transfer function Gids) Gip(s) tts) GCG) = 2Hirit giG(S) 8.2 S 125 stl 0 +1 kv = 0 ka= Lt Š GG) Sto - z Lt. § 2 sto g5st OX2 THE o+1 ka static error Coefficients ko= 2 kstep from the Diagram, c(s) a. forward Path gain I loop gain RS) - Gno(sGap(s) - Hels) Gps) 463 = 2 (ikssto) % 1 + 21 425 5+1Els) 125 5+ !!! 1255+ i + 2, Els 125 St1 R(S) 125 St3. from ev t = utt) Apply Laplace Transform R69725 C(52 R(S). 2 125 S+3 (By partial fractions C(5)2 A EB Was is +37125 129 |(5+3) Iszo 82 125 Pins a ns = } s s =-3 +3 / 126 (15) 2 2 2 3 3 2 2 5+3/15from ear ES 2 125 st R(S) RIS) (1255 +3) EB) 2 125 s+Yus) 1254s+ 1) r(t) tt) Apply Laplate Transform R(S)= E(S) 2 (sties) i (+3 1 (5) + 아 Apply Inverse Laplace Transform piti -3/125 ett) = 1 +3 st 1 ) (1) - c代) Sa ult) | wlee ut) - 를 4) + stat) - (t)

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