Question

2nd. In the control system below; w(s) + R(s) E(s) Y(s) Ko+Kp.s s(s+1) Sistem a. The damping factor is & = 0.5 and the complex conjugate poles of the closed loop system K for real part to be -2p and Ko Calculate the values that should be taken. ( 10p) b. Find the absolute value of the continuous regime error against the unit step-breaking effect. This error how to minimize. (20p) c. K to PD, When s is added; K in a PA and Ko system unstable using values the biggest K that won't do. Find the value. (20p)

Answer 1

Solution co(s) E(s) TY(s) + + kp tkos scéan SCS+) RCS) System GC) (ket kos) s(s+1) .. Close loop transfer function.i.e Y(3) G(s) il R(s) + GCS), H(S) Kptkos s(s+1) + kp tkos

ys) t Now the equation with des (ket kos) RCS) s +s+IDS +hp) Charecterstic equation + 2 & wnst won 2ę wn Citko) and who=kp &r=0.5 (Given) 2x 1 x Wn Citkn) Wn=lt ko (wn's kp) = and also, it is that poles whose real part is of CLIF given from is in complex Conjugate a (Given) (real -a (Given)) 9,- -3+jo Sa. -a-jo part is

Š + : (848+j) (+2–j® ) - s(ltko) + kp (sta} ta ŠAS(tko) tkp Štusty to 8 +5(ltkp) tep Comparing the Coefficients I Kp 4 and We know that Ko=3 Wn- Citro) ::wr (1+3) (n=4 and wr=kp uto=kp and kp= 16 &=(xp-4) a = (16-4) Answer 8=12 no burma all the Values

Y(s) 16+35 = 38+16) R(s) (stus+ 16) (34) tha (6) G (6) Kpt kos (ts) G(s) \+st (14)s Since this is a type-l system $ ess =ay arzum Velocity Coror Coefficient ku= lim SG(s) sto 38 +16 s(s+1)] i. Ko=16

ssa'' = ku 이 essa SAswer 16 (c) Now, is also added, . G(s) (ket tt say (fy 's G(s) 35+16+KI) (+1) G(S) = (35 +16stk) Šf6+1) H(S)-1 G(s) = e. CLTF It G(3) H(s)

3 = + 16S +KI) § (st) + 35 tisst ka qr(s) Characteristic equation is (s+) +33 +168 +1] Š438+16stk (s) = [3+45 +168 +KI] Now, By R-H (Rowth q(s) [s + q(s) t Hur unty) Criteria is 16 $ IN s ' G4-KI so RI

for there should you be Stability any sign Column Change in the first (64-ki) o Kazo :.64 Кт of KI < 64 N stability Conduction 1 GY kamay Answer
Note:plzz don't give dislike .......plzzz comment if you have any problem i will try to solve your problem...... plzz give thumbs up i am in need......