Signal Flow Graph ( control system)
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The document discusses transfer functions, including their definitions, types, and techniques for block diagram reduction. It explains open and closed loop transfer functions, along with methods for reducing block diagrams in series and parallel configurations. Examples and references to control system literature are also provided.
Signal Flow Graph ( control system)
- 1. SIGNAL FLOW GRAPH & BLOCK DIAGRAM REDUCTION Gourab Chandra Ghosh Surendra Institute of Engineering & Management
- 2. CONTENTS: 1. What is Transfer function ? 2. Types of Transfer function 3. Block Diagram Reduction Technique 4. Example 5. Reference 6. Q & A 2
- 3. Transfer Function: Transfer function is defined as the ratio of Laplace transform of output to the of Laplace transform of input (with all initial conditions being zero) r(t) c(t)g R(s) G C(s) T.F.= £{c(t)}/£{r(t)} C(S) / R(s) 3
- 4. Open & Close Loop Transfer Function: 4 R(s) G(s) C(s) R(s) G(s) C(s) H(s) G(s)=C(S) / R(s) C(S) / R(s)= G(s)/(1±G(s) H(s))
- 5. Block Diagram Reduction : Blocks in series: 5 G1 G2 G3 G1 x G2 x G3
- 6. Block Diagram Reduction : Blocks in parallel: 6 G1 G2 G3 G1+G2+G3
- 7. Block Diagram Reduction : Shifting of a summing point behind a block: 7 G G 1/G
- 8. Block Diagram Reduction : Shifting of a summing point beyond a block: 8 G G G
- 9. Block Diagram Reduction : Shifting of a take-off point beyond a block: 9 G G G
- 10. Block Diagram Reduction : Shifting of a take-off point beyond a block: 10 G G 1/G
- 11. Example: 11 G1 H1 G2 H2 C(s) R(s) H3 + - ++ -- We know for C.L.T.F.C(S) / R(s)= G(s)/(1±G(s) H(s))
- 13. Example: 13 G1.G2 (1+ G1.H1) (1+ G2.H2) H3 - R(s) C(s)
- 14. Example: 14 G1.G2 (1+ G1.H1) (1+ G2.H2)+ G1.G2.H3- R(s) C(s)
- 15. Reference: Automatic Control Systems- B.C.KUO Modern Control Engineering- K. OGATA 15