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

X2 where x1 and x2 are output variables and r1 and r2

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Unformatted text preview: eedback control system. Find the following transfer functions from your signal flow graph: x1 (s) x1 (s) x2 (s) x2 (s) , , , r1 (s) r2 =0 r2 (s) r1 =0 r1 (s) r2 =0 r2 (s) r1 =0 Block Diagrams & Signal-Flow Graphs ECE382 C. S. George Lee (Purdue Univ.) Number of feedforward path = 2; P1 = G1 G2 G3 ; P2 = G4 Determine the cofactor of the k th forward path, k 1 = 1; 2 = 1 - L2 - L3 The overall transfer function, Pk k C(s) P1 1 + P2 2 = k = R(s) Block Diagrams & Signal-Flow Graphs ECE382 27 / 31 C. S. George Lee (Purdue Univ.) 28 / 31 Mason's Gain Formula - Example 5 - Signal Flow Graph r1 1 a11 x1 Mason's Gain Formula - Example 5 For : 3 loops: L1 = a11 ; L2 = a22 ; L3 = a12 a21 Two non-touching loop = L1 L2 = a11 a22 = 1 - L1 - L2 - L3 + L1 L2 = 1 - a11 - a22 - a12 a21 + a11 a22 x1 (s) For : P1 = 1; 1 = 1 - L2 r1 (s) r2 =0 x1 (s) P1 1 1 - a22 = = r1 (s) r2 =0 1 - a11 - a22 - a12 a21 + a11 a22 x1 (s) For : P1 = a12 ; 1 = 1 r2 (s) r1 =0 x1 (s) P1 1 a12 = = r2 (s) r1 =0 1 - a11 - a22 - a12 a21 + a11 a22 Block Diagrams & Signal-Flow Graphs a21 1 r2 a22 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs a12 x2 ECE382 29 / 31 C. S. George Lee (Purdue Univ.) ECE382 30 / 31 Mason's Gain Formula - Example 5 x2 (s) For : P1 = a21 ; 1 = 1 r1 (s) r2 =0 x2 (s) P1 1 a21 = = r1 (s) r2 =0 1 - a11 - a22 - a12 a21 + a11 a22 x2 (s) For : P1 = 1; 1 = 1 - L1 r2 (s) r1 =0 x2 (s) P1 1 1 - a11 = = r2 (s) r1 =0 1 - a11 - a22 - a12 a21 + a11 a22 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 31 / 31...
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