hw1solnf2009

# hw1solnf2009 - MAE170 Homework 1 Solution Fall 2009 P1.11...

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MAE170 Homework 1 Solution Fall 2009 P1.11 The accuracy of the clock is dependent upon a constant ﬂow from the oriﬁce. The ﬂow is dependent upon the height of the water in the ﬂoat tank. The height of the water is controlled by the ﬂoat. The control system controls only the height of the water. Any errors due to enlargement of the oriﬁce or evapo- ration of the water in the lower tank is not accounted for. The control system is shown in Figure 1 on the next page. E2.21 The rotational velocity is ω ( s ) = 2 . 5( s + 2) ( s + 5)( s + 1) 2 1 4 s Apply the partial fraction expansion method. 2 . 5( s + 2) 4 s ( s + 5)( s + 1) 2 = A s + B s + 5 + C s + 1 + D ( s + 1) 2 0 . 625( s +2) = A ( s 3 +7 s 2 +11 s +5)+ B ( s 3 +2 s 2 + s )+ C ( s 3 +6 s 2 +5 s )+ D ( s 2 +5 s ) and by comparing coeﬃcients of equal powers of s on both sides, we obtain a system of 4 linear equations in the 4 unknowns. A

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## This note was uploaded on 08/31/2010 for the course ENGRMAE 170 taught by Professor Staff during the Fall '08 term at UC Irvine.

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hw1solnf2009 - MAE170 Homework 1 Solution Fall 2009 P1.11...

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