Question

N R(s) c(s) 7 23 2 3 2 2 N

If the gain formula is applied for the signal flow diagram given in Figure 1 what is the relationship between entry and exit?

Answer 1

firstly deduct the block diagram and than draw the signal flow graph, and than by using mason's gain formula we can calculate the gain between the input and output.
Quey first and we will deduct the given block diagram sigual flow graph for given system, than the drow the 2 + cas ) Ris) f 7 per parlar X 2k 2 al Now, so in Connected both are path I. added, gived block 2 are both Next, here from the top gain of 2 with a unit parallel will they and block with gain gain of again parallel and gives will the bottom At also be and connected en 4 block of they will of gein gain with 4 a added be . So block diagram of ((s) Ris) a tepla 2 uk

Now, let's draw the sigual flow graph, RS) 23 CS) 2 3 4 Kle New according Mason's Gain formula, Cos) hs - kal Pk Ak A Ris) Pk forward paths determinant for forward path of graph al touching loops gain that are path Determinant L Dk = 1- sum all non not touching kth forward 1- Sum of all individual loop gain So, here, Prz FX23X 2x3 Ak = 1 P, = 96 one forward path) Žias no mon- touching loops present? Liz-:(+423) = -16) A loops, - = 24 L2= (2x3x4) L3= 2342 246 Lu 7x23x 2 X3x (-18) = -120.75 -

s ) do [{1+ 22 +23+4 1-[-161 +24+46 - 120.75] 1-[- 211.75] - 1 212.75 = cis) Ris) AMS Pk Ak A Cis) RIS) 966X1 212.75 4.54 C(s) Ris)