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By N C Jagan

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Input node: It is a node at which only outgoing branches are present. In Fig. 37 node Xl is an input node. It is also called as source node. Xl a l2 o-__~__~__~__~__~~~~__~__~X5 Fig. 37 An example of a signal flow graph 43 Mathematical Modelling of Physical Systems 5. Output node: It is a node at which only incoming signals are present. Node Xs is an output node. In some signal flow graphs, this condition may not be satisfied by any of the nodes. We can make any variable, represented by a node, as an output variable.

34 (d). ' Finally the closed loop in Fig. --- C(s) Fig. 11 C(s) Reduce the block diagram and obtain R(s) in Fig. 35 (a). , Fig. 35 (a) Block diagram of a system for Ex. 11 I---r-- C(s) 41 Mathematical Modelling of Physical Systems Solution: Step 1 : Move pick off point (2) to left of G2 and combine G2 G 3 in cascade. Further G2 G 3 and G4 have same inputs and the outputs are added at summer III. Hence they can be added and represented by a single block as shown in Fig. 35 (b). C(s) R(s) Fig. --C(S) G G +G 2 3 4 Fig.

We can make any variable, represented by a node, as an output variable. To do this, we can introduce a branch with unit gain, going away from this node. The node at the end of this branch satisfies the requirement of an output node. In the example of Fig. 37, if the variable x 4 is to be made an output variable, a branch is drawn at node x 4 as shown by the dotted line in Fig. 37) to create a node x 6. Now node x6 has only incoming branch and its gain is a46 = 1. Therefore x6 is an output variable and since x 4 = x 6' x 4 is also an output variable.

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