Question

R(s) C(s) G(s) Figure P3 where G(S) = K(S2 – 2s + 2) S(S + 1) (3 + 2)

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Answer 1

1 sol, Crinen I page 1 + GC) Rre) C($) figure P3 where G(S) - K(8²28+2) s(s+1)/8+2) (a) closed cloop transfer function: a(s) K( 8² 2512) C(S) -T(S) - 8(841)(1+2 It als It K(8²28+2) 8(3+1)(3+2) K( 8² 28+2) & TS) = s(841) (S+2)+K (8²28+2) R(8) any pole at Here, there is no Origin Here, this system is type-o system. pole 3 put Denominator of T(8) 20 S(8² 38+2) + k ( 1228 +2)=0 +42(3 tk) + 8 (2-2) +2kzo 13 Roots sto

(b) Cinen, maximum overshoot 210%. k=0.24 G(s) = (0.24) (8² 28+2) 1 where, error s(s+1)(8+2) 4 steady state enor (es): itke (for unit step input) Kp = positional constant ka It GCS) t 0.24 (8²2872) S (3+1)(4+2) kpzool sto 24 sro esz (C) steady state entor for ramp input: where ku= velocity error constant essa Ку Its als sto

tal - ku= lt & sto ko z eu-I = 4.166 where, G(S) = K (S²2 8+2) 0.24182_2642) (page 3 Ms+1(8+2) 0.24 (2) 20.24 182 0.24 d GOLD Ears S(1+1)(1+2) ㅗ (1) = + Sta) ST; + $(0.2) s (10) cs (3) Goss) = k (it 4 (1) 1 (1+ 1 * G46N = /25 + 105+1) To find poles, put denominator of Goods/20 So pole To find zero, put nominator of apsf)=0 72 +11+120