Question

17. Using the Routh-Hurwitz criterion, find out how many closed-loop poles of the system shown in Figure P6.5 lie in the left half-plane, in the right half- plane, and on the jw-axis. R(S) + C(s) 507 $++ 333 + 10s- +30s + 169 S

Answer 1

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o Solution Characterstic eqt- 507 It 54 +353 +105²+305+169 SS+354 + + los?+ 308’+1695 +507 =0 R-H table ss lo ) 69 J s 4 3 30 507 s 0 (12) S3 o (60) s? 15 507 s! -345.6 sº 507 Ausilery ean 3 s" + 305² + So 7 =0 d (4€ :) = 12 s'+603

= 2 are 2 In first column , no. of sign change = 2 so total no w.of booles in Rits. By solving At- S- 3+27); (2-31"); +2+3;) ; 6-2-31) so total boles in Rot-s. Care 4 and in L.H.S. are 2