Question

1 GH(s) (s24s3s2 + 10s 24) sketch the root locus and find the following: [Section: 8.5 a. The breakaway and break-in points b. The jo-axis crossing c. The range of gain to keep the system stable d. The value of K to yield a stable system with second-order complex poles, with a damping ratio of 0.5

Answer 1

Answen Crfven thar CrHis) ist1)st3) 1StyI1t6) yt)103t2v) Root L0006 toop poles Yo pen Thene ane betocen -E-3 fi, The to cu6 exists berween-yand-6 and C--6) 1,-3) angic at 1OCus between The asy m ptots peini- move alon g the brear A) 1NOC2KH no.ot POLES A= 10201 Ma no. of zenos n-m 225 815 adympto es i's ' Z re a l posnE pOLes- 2 Real pofnt openas 1 The cenrofd CaA t3t9t 6-0 L 3.5 4-0 vi pofnts dve ane fren dy The brealt =0 dd cstIlst3) sty ) st6) Ot the roor 6 on Quare above The 6-5.3,-d. S, -I69 -,- 8Y-6) the 5 be toeen LOC05 &in ce Phe S2-5.8 - 1,64 ane pofnro rcalc vii ihe o' eredsPny rabfuiry chon iesrrc roae fe-tn Sth e ETie fven by ro 0 equatr on 1tl hts) O One amon

Rorh tivdt 1263 t3) fiC o 67 424K Tab sydtm Por 12.6 C 63 K 450 heasing pofnt fs The Jo 3 66rafne by sustkf nafnfng e 5 d 6 56s++2+EzO Cor) 6 181 5&x9-4- the lows Cre ses He at Juo-3 aux The =0.5 10106 86 draon vi beloo Th e 53 thure by heomety 60 th fmagin un aS efn he point a bove pfs the ain Pprantmartay p ps Fan60k J 0. b P On red ars He value PA XPBAPCX PD PA 1-43 1-73 : 2,644 Po- S133'25 5. 2 q0 -4- lp ad240d d. y68 1t .6Y y4 .823