Control ENG HW_Part_6

# Control ENG HW_Part_6 - X L 2 1 2 1-= = = b 2 2 = = x x dt...

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2 3 3 3 ) 4 3 4 ( ) 3 4 6 ( ) 3 4 2 ( ) 4 3 ( ) ( 2 3 4 5 = + + + + + + + + + + + + + + + + + + + + + + + = F E AC A F E B C A s C B C A s B C B A s F B C A s F B A s A+B+F=0 -3A+C+4B+F=0 2A+B+4C+3B=0 6A+C+4B+3C=0 A+4C+3B+3D+4E+F=0 3A+3C+3E+F=2 by solving above 6 equations, we can get the values of A,B,C,D,E and 3 3 ) 3 ( ) 1 )( 1 ( 1 ) ( + + + = s s s s s X . 3 2 3 2 ) 3 ( ) 3 ( 3 2 1 ) ( + + + + + + + + + + + + = s H s G s F s E s D s C s B s A s X by comparing powers of s we can evaluate A,B,C,D,E,F,G and H. c) ) 4 ( ) 3 )( 2 ( 1 ) ( + + + = s s s s s X 4 3 2 1 ) ( + + + + + + + = s D s C s B s A s X by comparing powers of s we can evaluate A,B,C,D 3.5 a) ) 1 5 . 0 )( 1 ( 1 ) ( + + = s s s s X ) 1 5 . 0 ( 1 ) 1 5 . 0 )( 1 ( 1 + + + + = + + s C s B s A s s s Let 1 ) ( 2 1 2 3 2 2 2 2 = + + + + + + = s s C s s B s s A A=1 2 1 2 0 2 2 - = + = = + + C B C B A 2 3 0 2 3 - = + = = + + C B C B A

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B/2=1/2 *-3/2=-1; B=-2; C= -3/2+2=1/2 + + + - = 1 5 . 0 1 2 1 1 2 1 ) ( s s s s X t t e e t x s
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Unformatted text preview: X L 2 1 2 1 ) ( )) ( (---+-= = = b) ) ( ; 2 2 = = + x x dt dx Applying laplace trafsorms s s X x s sX / 2 ) ( 2 ) ( ) ( = +-) 2 ( 2 )) ( ( 1 + =-s s s X L + =--) 2 ( 2 2 )) ( ( 1 1 s s L s X L = +-=--2 2 / 1 2 / 1 2 )) ( ( 1 1 s s L s X L = t e 2 1--3.6 a) 5 2 1 ) ( 2 + + + = s s s s Y...
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Control ENG HW_Part_6 - X L 2 1 2 1-= = = b 2 2 = = x x dt...

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