Control ENG HW_Part_56 - K C(1 D s(1 m s C = 2 R 1 m s 1 m...

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) 1 ( ) ( ) 1 )( 1 ( 1 2 1 + + + + + + + = C D C m m m D C K s K s s s K R C τ τ τ τ τ τ τ = 1 1 2 + = C m K τ τ τ 1 1 + = C m K τ τ τ ) 1 ( 2 1 1 1 + + + = C m D C m k k τ τ τ τ τ ξ b) 7 . 0 ; 10 min; 1 1 = = = ξ τ τ s m 1) ) 1 ( 600 70 2 1 7 . 0 0 + × = = C D k τ k c =3.167 2) 255 . 5 ) 1 ( 600 3 70 2 1 7 . 0 3 = + + × = = C C C D k k k s τ c)for 1 ) ( ; 1 + = = C C k k c s R
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period s period s for period period for offset C s for offset C For D D D D = = - = = = = - × = = = = = = = = 17 . 86 ) 7 . 0 ( 1 255 . 6 600 2 ; 3 57 . 105 1 167 . 4 600 2 ; 0 16 . 0 ; 84 . 0 ) ( ; 3 24 . 0 ; 76 . 0 ) ( ; 0 2 2 π τ ξ π τ τ τ Comments: Advantage of adding derivative mode is lesser offset lesser period 13.6The thermal system shown in fig P 13.6 is controlled by PD controller. Data ; w = 250 lb/min; ρ = 62.5 lb/ft 3 ; V 1 = 4 ft 3 ,V 2 =5 ft 3 ; V 3 =6ft 3 ; C = 1 Btu/(lb)( ° F) Change of 1 psi from the controller changes the flow rate of heat of by 500 Btu/min. the temperature of the inlet stream may vary. There is no lag in the
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