Question

Question 2 Figure 2 represents block diagram and signal flow chart which are commonly used in the industry to represent systems. (a) Determine the closed loop transfer function using block reduction method. (8 marks) (8 marks) (b) Using Mason's rule, determine the closed loop transfer function. (c) Comment your results found in part 2a and 2b. (4 marks) R(s) + Vi(s) V2() V3 (8) V4(s) + V:(s) C(s) G(S) Gz() G3(s) V-(8) H2(S) Hz(5) V (5) H (8) Figure 2

Answer 1

Date RCS) y -> > Sonosoby bleek Reductan, Anathedi?. fach CCS Hels) H3(S), 1105) GB (1+62). 1tG313 (1462) 1762 14 (1462) H2 1+ [+G 2)/2 = new bleck diegsamis tas ) 1+G2 . 1+ (1+G2H21 Hits) G1 (1+62) G2(1th2) 1+ (1+G2)H2 11 (1+62/42 1+ G2(1+G2) 41 1+(1+G2H2 G H 1 (1+62) 1+ (1+G2H2 14 (14622 - G2 (1462) G3 1+ (1462) H24 G 2H 2 (1+62) b{1+63 43). R(S) + of = GIG G22G (1 + H2 + H2G2+G2427679242.)(1+G3813)

CCs) = G. G + G₂ G2 G2 Res) lt G3 H3 + H2t G3H2H2 + H2G2+ H 2 G2 G3 Hz th 2 M2 + G2 Hz Garten +G2 G2 H1t G2 G2 H 2 G3 Hz

+1 GI RE) -dz H3 -H1.

> products of two non-touching - (Sum of Jain peoducto G2 G2 G3 + G163 (forward paths) - D= 1- ( sum de Loop, gains of & (Sum of gain all individuals Loops) loops] three non-touching + Loops) D=12 - G3 H3 -G2H2 - Gill -G1 G2 H2 -G] HIGH -G1 G2 H2 -G₂ Hz Hz -G2 G2 G3 H1 H3 . - H3 H 2 G2 G3 Ak= It is that value of a obtained by removing all the loops touching ith forwaal bath -H2

So, (S) RLS) G2 G₂ G2 G2 G3 14 G3H3 + H24 G3H3H2 + C 2 H 2 + G2 H2t GzG3 H3H2 + G2 G2H 1 + G 1 G312 H3 +G₂ G26 3 th Hz. o from both the Results 2a ( block Reduction) & 2b (mason's gain formula) we got the Same trang ber fincheon means whichever Rule is applicable gives the same result.