hw2sol_F2009 - MAE170 Homework 2 Solution Fall 2009 E2.20...

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Unformatted text preview: MAE170 Homework 2 Solution Fall 2009 E2.20 The equation of motion for the high-precision positioning slide is m c ¨ x p + ( b d + b s ) ˙ x p + k d x p = b d ˙ x in + k d x in . Taking the Laplace transform with zero initial conditions yields [ m c s 2 + ( b d + b s ) s + k d ] X p ( s ) = [ b d s + k d ] X in ( s ) . So, the transfer function is X p ( s ) X in ( s ) = b d s + k d m c s 2 + ( b d + b s ) s + k d = . 7 s + 2 s 2 + 2 . 8 s + 2 . 1 P2.34 Using block diagram transformations, we successively obtain: 2 3 4 Next, we solve the problem using equations. Let E 1 ( s ), E 2 ( s ), and E 3 ( s ) be the Laplace transforms of the signals that feed into blocks G 1 ( s ), K 6 ( s ), and G 3 ( s ) respectively (the outputs of the summing nodes in the original block diagram.) Then (omitting dependence on s ), we have the following equations: E 1 = R- H 2 Y- K 4 Y (1) E 2 = K 5 G 1 E 1 + Y (2) E 3 = G 2 G 1 E 1 + K 6 E 2 + H 1 Y (3) Y = G 3 E 3 . (4) Substitute(1) in (2) to get: E 2 = K 5 G 1 R- K 5 G 1 H 2 Y...
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hw2sol_F2009 - MAE170 Homework 2 Solution Fall 2009 E2.20...

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