EE350_Quiz-1Solution

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EE350 Control Systems Quiz-I Solution Marks-10 Q.N.1 (a) Signal Flow Graph (b) Forward Path Gains P 1 = G 2 G 5 G 6 P2 = G 4 G 6 P3 = G 3 G 5 G 6 Loop Gains L 1 = -G 1 G 2 L 2 = -G 6 L 3 = -G 2 G 5 G 6 G 7 L 4 = -G 3 G 5 G 6 G 7 L 5 = -G 4 G 6 G 7 L 6 = -G 1 G 3 Two Non- touching loop gains L 1 L 2 = (-G 1 G 2 )(-G 6 ) = G 1 G 2 G 6 L 2 L 6 = (-G 6 )(-G 1 G 3 ) = G 1 G 3 G 6 Determinant ° = 1- (L 1 +L 2 +L 3 +L 4 +L 5 +L 6 ) + (L 1 L 2 +L 2 L 6 ) = 1- (-G 1 G 2 -G 6 -G 2 G 5 G 6 G 7 -G 3 G 5 G 6 G 7 -G 4 G 6 G 7 -G 1 G 3 ) + (G 1 G 2 G 6 + G 1 G 3 G 6 ) = 1 + G 1 G 2 +G 6 +G 2 G 5 G 6 G 7 +G 3 G 5 G 6 G 7 +G 4 G 6 G 7 +G 1 G 3 + G 1 G 2 G 6 + G 1 G 3 G 6 ° 1 = 1 ° 2 = 1 ° 3 = 1 ( ) ( ) 1 1 2 2 3 3 2 5 6 4 6 3 5 6 1 2 6 2 5 6 7 3 5 6 7 4 6 7 1 3 1 2 6 1 3 6 Y s P ° +P ° +P ° R s ° G G G +G G +G G G 1+G G +G +G G G G +G G G G +G G G +G G +G G G +G G G = =
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Q.N.2 Transfer Function ( ) ( ) 2 o n 2 2 2 i n n 1 V s ± LC = = R 1 V s s +2
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