Question

Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 112 M M w + + Vilt) 1 H sooo 1 H nooo 1F vo(t) Figure 1

Answer 1

hare A Full 113 13 -23 213 113 -2b B =[-1 o o] Transfer function from state space matrices CCSI-AJTB CEST-AJTB TF +D. ST-A Istul lly Ilz tis S+213 -2/3 +213 Stllz let CS-A). e + n -- 9 TE b с o d + 30 0 9 n 600(3) -69] csccwadi CC

be c * B1-A)! 1 f ISI-AU d e 1 9 adj A. if A= Aiz 913 192, 923 (913 912 jaizao 083 Os 22 de land 1032 033 021 Azz (123 1. At Qap 221 IAT 031 032 aga Orz azz 913 912 912 913 032 033 033 03 022 023 JAI 911 913 a 13 au 1923 A21 ja33 azi 031 ag 023 021 021 0221 912 ani all 012 031 03 a32 931 021 022 As s Al2 an -13 to find g in Ishall 091 023 022 S+213 -213 012 03 +213 84113 9 1921 O22 - S+413 +113 (31-A)- 13 0913 lally S+213 listas -29-1-1)(+213) = 113 [X3 + S+213 S18 191–6) = (3:41) S+8+21q #419) -1bf-115-19 - GEA8 A31 Azz +213 - انہ) Bla72/3 -2

{M (6+༥） (སs + 33) + [ ] - ༢ ལྟུs+y+c+ S3+2S +། 9 - 313 = -9 = -1₂ s s3++2 +/ s3+s+༡༤ +| RLC Circent is . Transfer function of given - 1₂8 ITF = Vors) vics) 33,ཤུ༡S 4། CS Scanned with Camdannes

Given Chocuit: J4+212 TL Ilgt Ic here no. of state variables=3. Ma BIN Volt) - Vitti. 1 Voltl= Volth=;V (g = V., -IL-Tc Ic = VLgYC = -2,-2 Jcve Ic = VL-ve +31c = Tu-Bi-vc VLI= Iu -Il-Tc * Je = '13 I, -213 IL-VC / 3 VL2=Q4 - I 1₂ -Ic-The-Te Ic = edve covo duo dt म at General form of state variable representation, diu at iz 6:1-4) dre dt Vc 3x1 nxp 3x3 nxn ] Volt-[ 14 t 183 9x VilH. ve 11 Ic= VL₂-Volt

Vilt = Je, 4 In + TC AVL, ; that the Big Thomas ali su se zaustavi 1 & Vilt) = 412Tht tvu diu at -A,Pu - 4 pin + 1\, Ve - vtt) & Vi= 1 1 1 1 1 2 -1c - Ilc 1-1-212-BTC put Ic= T1 - 2 1 - 3 Tuth Tig + 2 ve Indy - 2 I clo Me 13 I 2 I 2 + 2 vc dt IL - Vc dve at Volta volt. writing it ies state space representation diy alla at ใน 3 -1 follo 21 + -2/3 vitt) dice dt duc dit 113 -213 -- Vc واة 2 [ Volth = & [ o ] Vilts VC