Block Diagram Reduction Techniques and Examples
Explore block diagram reduction techniques with examples like determining open-loop transfer functions, feed-forward transfer functions, control ratios, and more. See how systems are simplified to single transfer functions and obtain closed-loop transfer functions. Gain insights into characteristic equations, poles, and zeros for closed-loop systems.
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Presentation Transcript
PROBLEMS ON BLOCK DIAGRAM REDUCTION TECHNIQUES
Example-8: For the system represented by the following block diagram determine: Open loop transfer function Feed Forward Transfer function control ratio feedback ratio error ratio closed loop transfer function characteristic equation closed loop poles and zeros if K=10. 1. 2. 3. 4. 5. 6. 7. 8.
EXAMPLE-8: CONTINUE First we will reduce the given block diagram to canonical form K + s 1
EXAMPLE-8: CONTINUE K + s 1 K + G s 1 = K + + GH 1 + s 1 s 1
EXAMPLE-8: CONTINUE ( ) B s = ( ) ( ) G s H s 1. Open loop transfer function ( ) E s C ( ) s 2. Feed Forward Transfer function = ( ) G s ( ) E s (s ) G ( ) ( s ) H C s G s =1 3. control ratio + ( ) ( ) ( ) R s G s ( ) ( G ) ( ) B s G + s H s 4. feedback ratio =1 ( ) ( ) ( ) R s s H s (s ) H ( ) E s 1 5. error ratio =1 + ( ) ( ) ( ) R s G s H s ( ) ( s ) H C s G s =1 6. closed loop transfer function + ( ) ( ) ( ) R s G s 7. characteristic equation + = ( ) ( ) G s H s 1 0 8. closed loop poles and zeros if K=10.
Example-9: For the system represented by the following block diagram determine: Open loop transfer function Feed Forward Transfer function control ratio feedback ratio error ratio closed loop transfer function characteristic equation closed loop poles and zeros if K=100. 1. 2. 3. 4. 5. 6. 7. 8.
EXAMPLE-10: REDUCETHESYSTEMTOASINGLE TRANSFERFUNCTION. (FROM NISE:PAGE-243).
EXAMPLE-11: SIMPLIFYTHEBLOCKDIAGRAMTHEN OBTAINTHECLOSE-LOOPTRANSFERFUNCTION C(S)/R(S). (FROM OGATA: PAGE-47)
EXAMPLE-12: REDUCETHE BLOCK DIAGRAM. H 2 C _ R + G G G + ++ _ 3 1 2 H 1
EXAMPLE-12: H 2 G 1 _ C R + G G G + ++ _ 3 1 2 H 1
EXAMPLE-12: H 2 G 1 _ C R + G G 1G + ++ _ 3 2 H 1
EXAMPLE-12: H 2 G 1 C _ R + G G 1G + ++ _ 3 2 H 1
EXAMPLE-12: H 2 G 1 C _ R G G 1 2 + G + _ 1 3 G G H 1 2 1
EXAMPLE-12: H 2 G 1 C _ R G G G 1 G 2 3 H + + _ 1 G 1 2 1
EXAMPLE-12: C R G G G 1 2 + 3 + _ 1 G G H G G H 1 2 1 2 3 2
EXAMPLE-12: C R G + G G 1 2 G 3 H + 1 G G H G G G G 1 2 1 2 3 2 1 2 3
