ece382-fall2011-block-diagram-signal-flow-graph-slides-4-pages3

block diagrams signal flow graphs ece382 21 31 p k pk

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Unformatted text preview: 2 + G1 G4 G3 = 1 - G1 G4 H1 + G1 G4 G2 H2 + G1 G4 G3 H2 Block Diagrams & Signal-Flow Graphs ECE382 22 / 31 C. S. George Lee (Purdue Univ.) Mason's Gain Formula - Example 2 Mason's Gain Formula - Example 3 G3 R(s) + + + C(s) - G1 + H1 G4 G2 R(s) + - G1 + - H3 G2 + G3 G4 C(s) - H1 H2 H2 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 23 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 24 / 31 Mason's Gain Formula - Example 3 Number of (single) closed loops = 3 L1 = -G1 G2 H1 ; L2 = -G3 G4 H2 ; L3 = -G2 G3 H3 Number of two non-touching loops = L1 L2 Number of three non-touching loops = none Determine the determinant of the graph, = 1 - L1 - L2 - L3 + L1 L2 Mason's Gain Formula - Example 4 G4 H2 R(s) + + G1 + G2 G3 + + C(s) = 1 + G1 G2 H1 + G3 G4 H2 + G2 G3 H3 + G1 G2 G3 G4 H1 H2 C. S. George Lee (Purdue Univ.) Number of feedforward path = 1; P1 = G1 G2 G3 G4 ; Determine the cofactor of the k th forward path, k 1 = 1; The overall transfer function, Pk k C(s) P1 1 = k = R(s) Block Diagrams & Signal-Flow Graphs H1 ECE382 25 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 26 / 31 Mason's Gain Formula - Example 4 Number of (single) closed loops = 3 L1 = G1 G2 H1 ; L2 = -G2 H1 ; L3 = -G2 G3 H2 Number of two non-touching loops = none Number of three non-touching loops = none Determine the determinant of the graph, = 1 - L1 - L2 - L3 = 1 - G1 G2 H1 + G2 H1 + G2 G3 H2 Mason's Gain Formula - Algebraic Equation (Example 5) Consider a feedback control described by the following algebraic equations: a11 x1 + a12 x2 + r1 = x1 a21 x1 + a22 x2 + r2 = x2 where x1 and x2 are output variables and r1 and r2 are input variables. Draw a signal flow graph that represents this f...
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