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Understanding Mason's Gain Rule in Automatic Control with Signal Flow Graphs

Learn how to apply Mason's Gain Rule in automatic control using signal flow graphs to analyze system transfer functions. Discover how to compute loop gains and nontouching loops to determine system stability.

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Understanding Mason's Gain Rule in Automatic Control with Signal Flow Graphs

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  1. Block diagrams & Signal flow graphs

  2. Automatic control block pickoff point summer GWCET, NGP

  3. Automatic control GWCET, NGP

  4. Automatic control GWCET, NGP

  5. Automatic control GWCET, NGP

  6. original equivalent GWCET, NGP

  7. G G G original equivalent G G GWCET, NGP

  8. G G G original equivalent G G GWCET, NGP

  9. Automatic control Example 1 GWCET, NGP

  10. Automatic control Example 2 GWCET, NGP

  11. Signal flow graphs Automatic control GWCET, NGP

  12. Automatic control GWCET, NGP

  13. Automatic control Mason’s Rule Mason’s gain rule is as follows: the transfer function of a system with signal-input, signal-output flow graphs is Δ=1-(sum of all loop gains)+(sum of products of gains of all combinations if 2 nontouching loops)- (sum of products of gains of all combinations if 3 nontouching loops)+… A path is any succession of branches, from input to output, in the direction of the arrows, that does not pass any node more than once. A loop is any closed succession of branches in the direction of the arrows that does not pass any node more than once. GWCET, NGP

  14. Automatic control Example 3 GWCET, NGP

  15. Example 4 find GWCET, NGP

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