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controlppt(16.8-25.8)

# controlppt(16.8-25.8) - Disturbance input Disturbance TM TD...

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Disturbance input Disturbance input T T M M - - T T D D = T = T L L T M - T D T L 1 ------------ J L s 2 +B L s θ L +

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Multi input multi output Systems R 1 + E 1 G 1 C 1 - H 1 H 2 G 2 C 2 E 2 + _ R 2 )
To find C 1 / R 1 , assume R 2 = 0 R 1 + E 1 G 1 C 1 - H 1 H 2 G 2 - 1

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C 1 / R 1 = G 1 1 + ( - G 1 G 2 H 1 H 2 )
By signal flow graph. R 1 1 E 1 G 1 C 1 1 C 1 R 2 1 E 2 G 2 C 2 C 2 -H 1 -H 2 1

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C 1 / R 1 forward path gain = G 1 loop gain = G 1 G 2 H 1 H 2 C 1 / R 1 = G 1 1 - G 1 G 2 H 1 H 2
C 2 / R 1 forward path gain = - G 1 G 2 H 1 loop gain = G 1 G 2 H 1 H 2 C 2 / R 1 = 1 - G 1 G 2 H 1 H 2 - G 1 G 2 H 1

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Signal flow graph x G Y x Y G Y = XG
x 4 = -x 3 + x 5 x 1 X 3 1 2 x 2 -1 x 4 1 x 5 x 3 = x 1 + 2x 2

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R + E G C H - Let us take where E = R - CH & C = GE
Equations E = R - CH C = GE Variables R, E, C R E 1 G C - H 1 ?

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Mason’s gain formula (Simplified) Forward path gain = G Loop gain = - GH Forward path gain C/R = ------------------------ 1- loop gain G = ------------------- 1 - ( - GH )
Equations Block diagram Signal flow graph Reduction gain formula Transfer Function

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Δ Δ = K K P R C In general Δ = [1 - ( loop gains) + gain products of non touching loops two taken at a time - etc .]
Forward path gain(P1) = G 1 G 2 G 3 X 1 1 C 1 G 1 X 2 G 2 X 3 G 3 C R - H 1 - H 2 - H 3 Loops - G 1 H 1 - G 2 H 2 - G 3 H 3 ( loop gains) = - G 1 H 1 - G 2 H 2 - G 3 H 3

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controlppt(16.8-25.8) - Disturbance input Disturbance TM TD...

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