Question

Find the transfer function for the following system using Signal Flow Diagram.

Can you please write clear and do it step by step. Thanks

Answer 1

Answer Кл As per the block diagram of figure the corresponding signal flow graph is shown in ligure below i ļ Q -KM the one forward Pathare Pi Pi 5 ' SHI) Ke Liś and the 2 in dividual Joop is Li = Tekin, 12 = - Kodit The closed loop touches both the forward Paths therefore Path factor are Aiz

"The graph determinant is As 1-(41 +L4) 4 = 1-6 weken - The S+ SC +1S+10) ja = It is the + S&S +) CS +18) Applying masons gan formula the closed loop transfer function is determined below = 24 ( = S (5+1)(8+10) 1+ Кл (5+) Ко SGS+1) CS+10) 7** S(S+1) (S+10) + Ky S(S+19)+ ka i Ka + K +R Silot ka S? +11 32+10 Ka Qc - 153 +K +11)32 + (10K 3+10)3 + ka)

Mason's Grain formula T = 1 = Px Ak K=1 Where To overall gain of the system Pk = Path gain of 4th forulard Path A is called the eignal flow graph determinant the A= 1- (sum of doop gain of all individual boop) + +(sum of gain product of all possible combination of two non touching loop) - (Sum of gain product of all possible combination of this non-touching loopt-. A = the value of a dor the part of the graph nout touching with Kath forward Path