Question

please help to solve this . Thank you

B2. Determine the range of k for stability using Routh's criterion. K 1.0.5s 1.10s B3. Sketch the root locus of the control system shown in the figure below K $(82 +65 +25)

Answer 1

> Range of k 1+0.55 ac Itlos St d-1 K(1+0.55) ay It los 1 sti i formula G(s) H () GCS) If= It Gos) #Cs) K (170.55) (It los) So Yus) ris) (KC1+0.55) It S) S+I Scr

F = y(s) ris) K(1+0.55) (S-1) (14) (4-1) + K ( 0.5 )(+) K cito.5s) (0-1) 5-1 +105-108 + KC 3+1+0.58 +*) K (1+0.55 ) (1-1) los"_95-1+ K (0.5577.58+ k) K (8-1) (170.55) T. F ST(0.5 k +10) + 5 (1.5K9)+(K-P De nominator is charatistic Equation C.E : SIN CO.SK +1) +5(1.5K-9) +-1) SN 6.5k +10) (K-1) امی (1.5k-9) so K-1

According to stability Sign Chansel the first Column of RH Critiria is? always positive 0.5k + 100 1.5k-900 K-1 70 o.sk 7 - 10 i.sk >q kal K> 9 K> 10 0.5 1-5 k>6 kol K) -20 Resultant K>-20 K>6 Resultant K>6 tho Range of k K76

Root locus K SCS"+65425 Gls) H(s) = SCS 65+25) К. €) (5+3+48)65+3+11) K 615) H (3) s(5+3 = 4i) ($+3+41) 4). No of Branches (Separete brametes NE Z =3, order of the System is ,'3' 2) Centroin ({pour szendbor Geel HO (p-z) 0-3-3 3

oló 6 5-2 © A sympa totes (20+) P-z id, -0,1,21 1-0 TT 3 60 P=1 -) 30 180 3 300 l:2 =) 571 3 (-3+47) -37-8 kow Centrinco (-3-4;)