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Control ENG HW_Part_64

# Control ENG HW_Part_64 - 1 0.5t L1 = e(Cos 0.5t Sin 0.5t...

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) 5 . 0 5 . 0 ( ) 5 . 0 5 . 0 ( 1 5 . 0 1 t Sin t Cos e i s L t + = + - - 14.8 For the output C to be stable, we analyze the characteristic equation of the system 0 ) 1 ( ) 1 )( 1 ( 1 1 1 3 2 1 = + × + + + s s s s I τ τ τ τ 0 1 ) ( ) ( 0 1 ) 1 ( 3 2 2 1 3 2 1 3 2 1 2 2 1 = + + + + + = + + + + + s s s s s s s s I I I I τ τ τ τ τ τ τ τ τ τ τ τ τ τ Routh Array 1 0 1 ) ( 0 2 1 2 3 2 1 3 s s s s I I I α τ τ τ τ τ τ τ τ + + ) ( ) )( ( 2 1 2 1 3 2 1 τ τ τ τ τ τ τ τ τ τ τ α + - + + = I I I I Now 0 ) 1 ( 1 2 > τ τ τ I Since 2 1 & τ τ are process time constant they are definitely +ve 0 ; 0 2 1 > > τ τ (2) 0 ) ( 2 1 > + τ τ τ I (3) 2 1 3 2 1 ) )( ( 0 τ τ τ τ τ τ τ τ α I I I > + + >

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0 ) ( ) ( 0 3 2 1 2 1 2 1 3 2 1 2 1 2 1 3 2 2 3 1 1 > - + > + - > + > - + + + I I I I I also τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ 14.9 In the control system shown in fig find the value of Kc for which the system is on the verge of the instability. The controller is
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Control ENG HW_Part_64 - 1 0.5t L1 = e(Cos 0.5t Sin 0.5t...

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