Hw4-S05_Solution - HW 4- SOLUTION ME 304 CONTROL SYSTEMS...

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HW 4- SOLUTION ME 304 Control System Components CONTROL SYSTEMS (01) April 6, 2005 Prof. Dr. Y. Samim Ünlüsoy, Res. Asst. Kemal Çal ı ş kan 1 PROBLEM 1: a) Plunger : Force balance => Mb A S f2 f fF ++ = => .. . MM p AS Mx 2b x f F + += (1) Arm : Torque balance => abk 1 A TTT L f + .. . aa ott a 1 A IbkL f θ+ θ+ θ = (2) Compatibility equations => p 2a xL = θ (3) M1 a = θ (4) e o (t) R, L b p k t , b t pen I o L 2 L 1 M O b p x p M x M F S f b f b f M f a f a θ a T b , T k , T a L 2 L 1
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HW 4- SOLUTION ME 304 Control System Components CONTROL SYSTEMS (01) April 6, 2005 Prof. Dr. Y. Samim Ünlüsoy, Res. Asst. Kemal Çal ı ş kan 2 Solenoid : Pull force => S F =Ki (i is the current flow on the solenoid) (5) Voltage Current Relation => M 0 dx di e =Ri+L +K dt dt (6) Take Laplace transform of (6), 0M E (s)=RI(s)+LsI(s)+KsX (s) => E (s)-KsX (s) I(s)= (R+Ls) Substitute in (5) => 2 S KE (s)-K sX (s) F(s)= (R+Ls) (7) From (1), .. . MM AS p fF M x2 b x =− Insert in (2), .. . .. . aa ott a 1 S p IbkL ( F M x 2 b x ) θ+ θ+ θ = Use (4) to eliminate θ A , .. . .. . 2 M M M 1 S p Ix bx kx L( F Mx 2 bx) ++= −− Re-arrange, .. . 22 2 o1 t 1 p t M 1 S (I L M)x (b 2L b )x k x L F ++ + + = Take Laplace, 2 2 t 1 p tM 1 S L M)s 2L b )s k X (s) L F (s) ⎡⎤ = ⎣⎦ (8) Substitute (7) in (8) 2 2 2 t 1 p 1 KE (s)-K sX (s) L M)s 2L b )s k X (s) L (R+Ls) = Rearrange , 2 2 2
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This note was uploaded on 05/16/2011 for the course ME 304 taught by Professor Samim during the Spring '11 term at Middle East Technical University.

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Hw4-S05_Solution - HW 4- SOLUTION ME 304 CONTROL SYSTEMS...

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