MechanicalSystem

MechanicalSystem - WRITING A TRANSFER FUNCTION FOR A...

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http://www.teicontrols.com/notes tomzap@eden.com MechanicalSystem.pdf page 1 of 2 WRITING A TRANSFER FUNCTION FOR A MECHANICAL SYSTEM The following example illustrates how to write a transfer function to describe a mechanical system. THE PROBLEM Given the mechanical system ( ) t f 1 1 2 Dashpot (mechanica resistance) Mass (output) 2 2 M K 3 2 K 2 B M K 2 2 3 1 B x 2 x 0 Input force 2 1 B 0 K 2 B Spring find the transfer function G ( s ) for the system F ( ) s ( ) s G ( ) s X 2 LIST THE FORCES ON EACH MASS WRITE THE DIFFERENTIAL EQUATIONS FOR EACH MASS ( 29 ( 29 ( 29 1 1 1 1 1 1 3 2 1 3 21 M x K x B x Kxx Bxx ft = -- + - + -+ & & & && ( 29 ( 29 2 2 2 2 2 2 3 2 1 3 M x K x B = - - & & & Forces on M 1 : 11 Kx - ( 29 3 Kxx - ( 29 Bx - & ( 29 3 - Forces on M 2 : 22 - ( 29 3 - & ( 29 3
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http://www.teicontrols.com/notes tomzap@eden.com MechanicalSystem.pdf page 2 of 2 CONVERT TO THE S -DOMAIN ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 1 1 1 3 21 1 1 3 MsX s KX s KXs X s B s X s B s Xs s X s Fs = - + - - + -+   ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 3 3 s s Xs KXs X s B s s = --- - --  
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This note was uploaded on 09/26/2011 for the course 332 373 taught by Professor Shoane during the Spring '09 term at Rutgers.

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MechanicalSystem - WRITING A TRANSFER FUNCTION FOR A...

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