Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic : Models for Control System

Difficulty : High

Marks : 5M

The Masson's gain formula is used to determine the Transfer function of the system from the signal flow graph of the system.

Let, R(s) = Input to the system

C(s) = Output of the system

Now, Transfer function of the system

$T(s) = \frac{C(s)}{R(s)}$ -------(1)

Masson's gain formula states the overall gain of the system as follows,

overall gain, T = $\frac{1}{\Delta} \sum_{k} p_k \Delta_k$

Where, T = T(s) = Transfer function of the system

$P_K$ = Forward path gain of $K^{th}$ forward path.

K = Number of forward path in the signal flow graph.

$\Delta$ = 1 - (Sum of Individual loop gain) + (sum of gain products of all possible combinations of two non-touching loops) - (sum of gain products of all possible combinations of three non-touching loops) + _ _ _

$\Delta_K$ = $\Delta$ for that part of the graph which is not touching $K^{th}$ forward path

i.e. (1 - All the loops that do not touch the $K^{th}$ forward path)