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By Prof. Hitesh Dholakiya
Signal Flow Graph
Examples
Control Engineering
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Engineering Funda Android App Control System YT Playlist
Steps to find transfer function from Signal flow graph
? Find Forward paths. (E.g. ??, ??, ¡­ ¡­ , ??)
? Find Single Loops. (E.g. ??, ??, ¡­ ¡­ , ??)
? Find Two Non-Touching Loops (E.g. ??
¡ä
= ?? ¡Á ??)
? Find ?
?= ? ? ? ?????? ????? + ? ??? ??? ???????? ????? ? ¡­ ¡­ ¡­ ¡­
? Find ??, ??, ¡­ ¡­ , ?? based on forward path
??= ? ? ? ?????? ????? ??? ???????? ???? ??
??= ? ? ? ?????? ????? ??? ???????? ???? ??
? Transfer Function
?(?)
?(?)
=
???? + ???? + ¡­ ¡­ + ????
?
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R C
-1
-1 -1
1 1
?1 ?2 ?3
?4 ?5
?6
?1 = 1 ¡Á ?1 ¡Á ?2 ¡Á ?3 ¡Á 1 = ?1?2?3
Find Forward Path
?2 = 1 ¡Á ?4 ¡Á ?5 ¡Á 1 = ?4?5
Find Single Loops
?1 = ?1 ¡Á ?2 ¡Á ?3 ¡Á ?1 = ??1?2?3
?2 = ?2 ¡Á ?1 = ??2
?3 = ?3 ¡Á ?1 = ??3
?4 = ?6
?5 = ?4 ¡Á ?5 ¡Á ?1 = ??4?5
Find Two Non Touching Loops
?1
¡ä
= ?1 ¡Á ?4 = ??1?2?3 ¡Á ?6 = ??1?2?3?6
?2
¡ä
= ?2 ¡Á ?4 = ??2 ¡Á ?6 = ??2?6
?3
¡ä
= ?2 ¡Á ?5 = ??2 ¡Á ??4?5 = ?2?4?5
?4
¡ä
= ?3 ¡Á ?4 = ??3 ¡Á ?6 = ??3?6
Find ?
?= 1 ? ? ?????? ????? + ? ??? ??? ???????? ?????
?= 1 ? ??1?2?3 ? ?2 ? ?3 + ?6 ? ?4?5 + (??1?2?3?6 ? ?2?6 + ?2?4?5 ? ?3?6)
Find ??
??= ? ? ? ?????? ????? ??? ???????? ???? ??
??= ? ? ??
??= ? ? ? ?????? ????? ??? ???????? ???? ??
??= ? + ??
?(?)
?(?)
=
???? + ????
?
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R C
1 1 1
?1 ?2 ?3
?4
?1
??1
??2
Find Forward Path
?1 = 1 ¡Á ?1 ¡Á ?2 ¡Á ?3 ¡Á 1 ¡Á 1 = ?1?2?3
?2 = ?4 ¡Á 1 = ?4
Find Single Loops
?1 = ?1 ¡Á ?2 ¡Á ?1 = ?1?2?1
?2 = ?2 ¡Á ??1 = ??2?1
?3 = ?2 ¡Á ?3 ¡Á ??2 = ??2?3?2
No Two Non Touching Loops
Find ?
?= ? ? ? ?????? ????? + ? ??? ??? ???????? ?????
?= ? ? ?????? ? ???? ? ??????
Find ??
??= ? ? ? ?????? ????? ??? ???????? ???? ?? = ?
??= ? ? ? ?????? ????? ??? ???????? ???? ?? = ? + ?????? + ???? ? ??????
?(?)
?(?)
=
???? + ????
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Signal Flow Graph Examples

  • 1. By Prof. Hitesh Dholakiya Signal Flow Graph Examples Control Engineering E n g i n e e r i n g F u n d a Engineering Funda Android App Control System YT Playlist
  • 2. Steps to find transfer function from Signal flow graph ? Find Forward paths. (E.g. ??, ??, ¡­ ¡­ , ??) ? Find Single Loops. (E.g. ??, ??, ¡­ ¡­ , ??) ? Find Two Non-Touching Loops (E.g. ?? ¡ä = ?? ¡Á ??) ? Find ? ?= ? ? ? ?????? ????? + ? ??? ??? ???????? ????? ? ¡­ ¡­ ¡­ ¡­ ? Find ??, ??, ¡­ ¡­ , ?? based on forward path ??= ? ? ? ?????? ????? ??? ???????? ???? ?? ??= ? ? ? ?????? ????? ??? ???????? ???? ?? ? Transfer Function ?(?) ?(?) = ???? + ???? + ¡­ ¡­ + ???? ? E n g i n e e r i n g F u n d a Engineering Funda Android App Control System YT Playlist
  • 3. R C -1 -1 -1 1 1 ?1 ?2 ?3 ?4 ?5 ?6 ?1 = 1 ¡Á ?1 ¡Á ?2 ¡Á ?3 ¡Á 1 = ?1?2?3 Find Forward Path ?2 = 1 ¡Á ?4 ¡Á ?5 ¡Á 1 = ?4?5 Find Single Loops ?1 = ?1 ¡Á ?2 ¡Á ?3 ¡Á ?1 = ??1?2?3 ?2 = ?2 ¡Á ?1 = ??2 ?3 = ?3 ¡Á ?1 = ??3 ?4 = ?6 ?5 = ?4 ¡Á ?5 ¡Á ?1 = ??4?5 Find Two Non Touching Loops ?1 ¡ä = ?1 ¡Á ?4 = ??1?2?3 ¡Á ?6 = ??1?2?3?6 ?2 ¡ä = ?2 ¡Á ?4 = ??2 ¡Á ?6 = ??2?6 ?3 ¡ä = ?2 ¡Á ?5 = ??2 ¡Á ??4?5 = ?2?4?5 ?4 ¡ä = ?3 ¡Á ?4 = ??3 ¡Á ?6 = ??3?6 Find ? ?= 1 ? ? ?????? ????? + ? ??? ??? ???????? ????? ?= 1 ? ??1?2?3 ? ?2 ? ?3 + ?6 ? ?4?5 + (??1?2?3?6 ? ?2?6 + ?2?4?5 ? ?3?6) Find ?? ??= ? ? ? ?????? ????? ??? ???????? ???? ?? ??= ? ? ?? ??= ? ? ? ?????? ????? ??? ???????? ???? ?? ??= ? + ?? ?(?) ?(?) = ???? + ???? ? E n g i n e e r i n g F u n d a
  • 4. R C 1 1 1 ?1 ?2 ?3 ?4 ?1 ??1 ??2 Find Forward Path ?1 = 1 ¡Á ?1 ¡Á ?2 ¡Á ?3 ¡Á 1 ¡Á 1 = ?1?2?3 ?2 = ?4 ¡Á 1 = ?4 Find Single Loops ?1 = ?1 ¡Á ?2 ¡Á ?1 = ?1?2?1 ?2 = ?2 ¡Á ??1 = ??2?1 ?3 = ?2 ¡Á ?3 ¡Á ??2 = ??2?3?2 No Two Non Touching Loops Find ? ?= ? ? ? ?????? ????? + ? ??? ??? ???????? ????? ?= ? ? ?????? ? ???? ? ?????? Find ?? ??= ? ? ? ?????? ????? ??? ???????? ???? ?? = ? ??= ? ? ? ?????? ????? ??? ???????? ???? ?? = ? + ?????? + ???? ? ?????? ?(?) ?(?) = ???? + ???? ? E n g i n e e r i n g F u n d a Engineering Funda Android App Control System YT Playlist