Question

1. Find the following transfer function Io(t) and Is(t) are output and input respectively. transfer function H(s) n+ 1 (0.1*n+0.2) L + + vs ☺ 0.5 F n+ 2 s 1 a) Find Transfer function (assuming initial conditions are zero) H(s) = 1(s)/V; (s) b) Explain the system stability

Answer 1

h s domain inductor - Sh - S 6.10 +0:2) capacitor - 15 16 = 33. @ equivalent circuit in s-Somain is mit V6) (610+0-2) m It Ento vs@ LG To o Apply notal Analysis at note VG). (6) - V VS) Vol n+1 + 2 + - S 6. Into 2 S + na - and set 16 - V0) Co.In +0.2)S+n+2 V +0.25 +0+2] Ios) 0 = V(s). La 17 V V). I nti VS) - nt n + 6.11 +0.25 +0+2 substitute above values of Jo (3), vol here [0.10+ 0.2 5) + N43] ). [1 ] - Vs + Io (8) = 0. 30.) (6.11 +0.25) + N +9) ( 11 ) + 1] - Vs=o.

( 2 (0+1) 10. 56.10 +0.25 +n+ 2) (2 - Sam - 1) = vs 30.) (11 +0.25 + 2) (2 - 51-5) + 1] = vs. for H (1-10 +0-25+ 2) (2-50-) + 2 (+1) 2(6+1) J & 30 ( 2.20 - 10 10²S-lins+0045200205² -0.252 Tu-ans-25 2 (n+1) - Us of (-0.20-0.9) 5² + s(-11 112 11 +04-20-2) + (2. 2074 2 (41) & Io. [ -0.2 (N+1) 5²+ (-11n 2 23.10-1.96) 5+ (4 +2:20) g(n1) Ion 2 (N+1). -0.9 (141) 5+ E (1.133.10+199] 5+4 +226) 3 - Transrer schon is HO) = 50 - 9 at 1) -0.2 (N+1) 5² (1.107 3.10+1196)5+ (4+2.20)

6 Stability of system: fom chad Thanreg runchon chara desishe egration of above system is Denominator =o) - - 0.2 (N+1) 5² (1.10²+3.10+ 1.96) + (4 + 2 2 ) = 0. > using Rowth - Hurwitz (RM) Criteria in order to be a system to be stable, all terms in charaderista must have same sign. by alsson in order to have same sign, constant term in above equation (4+ 2.20 must te negative. » 4+2.2n <0 ) 2.20 <- 4 an 2.2 I n -1.8 ntk - 1.8t 1 & N+1 <-0.8 & Resistme vabe in given circuit- So forn to be 1.8 Resistonle has & negative value, which is impractical. so the system is always Als un state. The system is alcrays unstable