Signal flow graph (sfg)
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This document summarizes key concepts related to signal flow graphs (SFG). It defines the basic elements of an SFG including nodes, branches, input nodes, output nodes, mixed nodes, forward paths, and loops. It explains how to calculate the forward path gain as the product of branch transmittances along a forward path. It also describes Mason's Gain Formula for calculating the transfer function of a system represented by an SFG using determinants based on forward path gains and loop gains. Finally, it outlines the step-by-step process for applying Mason's Gain Formula which involves identifying forward paths and loops, calculating individual and combined loop gains, and determining the numerator and denominator determinants.
![06. The value of ∆ is given by
∆ = 1 - [P11 + P21 + P31 +………..+ Pm1] +[P12 +
P22+ P32 +…………. + Pp2]
- [P13 + P23 + P33 +………..+ Pt3] +[P14
+…………………………+ Pk4]
+..............
07. Find out ∆1, ∆2, ∆3, ∆4.......... ∆n
08.Find out P1∆1, P2∆2, P3∆3,........... Pn∆n
09. Find out Transfer Function :
T.F = P1∆1 + P2∆2 + P3∆3+....../ ∆](https://image.slidesharecdn.com/signalflowgraphsfg-170803234030/85/Signal-flow-graph-sfg-15-320.jpg)
Signal flow graph (sfg)
- 1. Presented By : Dhruv Shah TOPIC : Signal Flow Graph (SFG) Control Engineering
- 2. Comparison of BD and SFG )(sR )(sG )(sC )(sG )(sR )(sC (A) Block Diagram: (B) Signal flow Graph:
- 3. Signal Flow Graph (SFG) :
- 4. (01) NODE: IT IS A POINT REPRESENTING A VARIABLE. X2 = T 12 X1 +T32 X3 X 2 X (02)Branch : A line joining two nodes. In this SFG there are 3 nodes. Definition of terms required in SFG X1 X2 X3 t12 t32
- 5. (03)INPUT NODE : NODE WHICH HAS ONLY OUTGOING BRANCHES. X1 IS INPUT NODE. (04)OUTPUT NODE/ SINK NODE: ONLY INCOMING BRANCHES. (05)MIXED NODES: HAS BOTH INCOMING AND OUTGOING BRANCHES. t12 X1 t23 X3 X4X2 t34 t43
- 6. (06)FORWARD PATH : A PATH WHICH ORIGINATES FROM THE INPUT NODE AND TERMINATES AT THE OUTPUT NODE AND ALONG WHICH NO NODE IS TRAVERSED MORE THAN ONCE. (07)FORWARD PATH GAIN : IT IS THE PRODUCT OF BRANCH TRANSMITTANCES OF A FORWARD PATH. P 1 = G1 G2 G3 G4, P 2 = G5 G6 G7 G8
- 7. (08) Loop : Path that originates and terminates at the same node and along which no other node is traversed more than once. (09)Self loop: Path that originates and terminates at the same node. (10)Loop gain: it is the product of branch transmittances of a loop. (11)Non-touching loops: Loops that don’t have any common node or branch. L 1 = G2 H2 L 2 = H3 L3= G7 H7 Non-touching loops are L1 & L2, L1 & L3, L2 &L3
- 8. SFG terms representation: input node (source) b1x a 2x c 4x d 1 3x 4x mixed node mixed node forward path path loop branch node
- 9. 1a 2a 3a 1a 3a 21S 32S 1 21 32S S 1 1 1 Techniques (1) Series paths 3 21 32 1a S S a 2 21 1 3 32 2 a S a a S a Note that we have removed the node a2.
- 10. 1a 2a 1a 2a aS bS a bS S (2) Parallel paths 2 1 1a ba S a S a 2 1a ba S S a Note that we have combined the two parallel paths.
- 11. Mason’s Gain Formula: • The transfer function, C(s)/R(s), of a system represented by a signal-flow graph is; Where, n = number of forward paths. Pi = the i th forward-path gain. ∆ = Determinant of the system ∆i = Determinant of the ith forward path n i iiP sR sC 1 )( )(
- 12. ∆ = 1- (sum of all individual loop gains) + (sum of the products of gains of all possible Combinations of two non- touching loops) – (sum of the products of gains of all possible Combinations of three non-touching loops) + … and so forth with sums of higher number of non-touching loop gains ∆ i = 1 – (loop-gain which does not touch the forward path) n i iiP sR sC 1 )( )(
- 13. 01. Find out all possible Forward path and hence the corresponding Forward path Gains. P1 =First Forward path, P2 =Second Forward path………….. PN 02. Find out all possible Single (Individual)Loop. P11 = First Single loop, P21 = Second Single loop, P31, P41........... Pm1 Steps
- 14. 03. Find out all possible Combination of two non- touching Loop. P12 = Two non-touching Loop. 04. Find out all possible Combination of three non-touching Loop. P13 = Three non-touching Loop. 05. Find out all possible Combination of four non-touching Loop. & so on. P14 = four non-touching Loop.
- 15. 06. The value of ∆ is given by ∆ = 1 - [P11 + P21 + P31 +………..+ Pm1] +[P12 + P22+ P32 +…………. + Pp2] - [P13 + P23 + P33 +………..+ Pt3] +[P14 +…………………………+ Pk4] +.............. 07. Find out ∆1, ∆2, ∆3, ∆4.......... ∆n 08.Find out P1∆1, P2∆2, P3∆3,........... Pn∆n 09. Find out Transfer Function : T.F = P1∆1 + P2∆2 + P3∆3+....../ ∆
- 16. Thank You !!!!!!