Question

4)Convert the following block diagram into signal flow graph (15 marks) R(s) X (s) U(s) H.(s) D(s) G(s) Xx(s) Hz(s) 5) Using Mason's gain formula, find the transfer function of the following systems (40 marks).

Answer 1

0 Given Block diagram 02 4,(s)/ 2 ECDs) US) G ( 34) RIS) (S) * Assume nodes at the input, output, at every summing Point, at everry branch point and between cascaded blocks & Numbering the nodes. * from the given block diagram find the gain between each nodes in the main froward path and connect the all Comesponding nodes and mark the gains respective an the branches. sepetlike

HS), DS) 745 G(S) 3 4 ) feedback * Draw the fede bord paths between varios nodes and mask the gain of the feedback forward paths along with the signs. given in the block diagram. feed back Al Hils) xq d(s) x3 - #25

x2 G14 G14 X5 04 wut 142 By Massians gain formula Far Word path gains - nontouching loopgainst two nontochingloop from the above signal flow graph Forward paths are 0 R X2 X3xy xgtc. ③ R xz 3 y 5 C for the first forward path gain pi= GIG4G2. for the Second Forwardpath gain P2 = G, GG G3 loops are 3 x₂x3 x2 loop gaine, G. Gy Hi x2 3x4 x5 x2 loop gainda - G, GG G2 H2 x3 x4 x5 x2 loopgain lz= - Gi Gy Grz H2 x

By the Masson's gain formula CC) - R(S) P + P2 Tle-le-dz = G, G2 G2+ G, Gy G3 1 - G, G44,-EGY GY G3 Hz) 4G, GU G2H2) Siz G, Gu [G2+G3] -G, Gyti + G G4 G3 H₂+G, Gu G₂ H2 ez Go Gy ( 622+G3] It Go Gry [3 +2+G2 H2 – Hty] -13 GL / GZ Here Forward paths are two GRI 2 3 4 5 6 Forward path gaine, G, G2 G3.

Forward path RI6c Forward path gain. &z= G4. loop sare 3' loop 344 3 loop gain loop gain I -G2 Hi - Gi Gatt, 1001 273 7442 100p 3 4 → +3 loop gain dz-G2 G3 Hz. In fooword. By massione gain formula e Sumoborow and pats gain {1- nontoching loop gainst two hon fouching) loopgains 1- nontoching loop gainst two hontoching loop gains $ - $ Pro; e Pi +Pz [9-01-22-ds] - denda - dz.

E = G G2 G3 + G4 [!+G2 H, 4 G2G1, 41+ G12 G13 Hz] [[+ G12 #+612 G, Hi +G2 G3 H3.] & = G, G12 G13 +Guy$1+ G2 [Hi+G, 4h+6343] It G2[Hit Gi Hj + G3 H3]