Hw5Soln - ME 375 Homework 5 : Solution October 5, 2009...

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ME 375 Homework 5 : Solution October 5, 2009 Problem 1 Problems 3.18 (a), (d) and (e) in Palm textbook, page 152. Determine poles and zeros of each transfer function, and comment on stability. Note that ”characteristic roots” and ”poles”are the same. Part A Given: x +7 x =15 f ( t ) Solution: The Laplace-transformation of equation :5 ˙ x +7 x =15 f ( t )is 5 sX ( s )+7 X ( s )=15 F ( s ) The transfer function is : X ( s ) F ( s ) = 15 5 s +7 (1) Poles and Zeros: The zeros are determined from the numerator: from this transfer function there are no zeros. The poles are determined from the denominator. The open loop characteristic equation: 5 s +7=0 1
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The pole is s = - 7 5 . Stability: All the poles are on the left half plane (LHP), therefore our system is stable. Part B Given: ¨ x +14˙ x +49 x =7 f ( t ) Solution: s 2 X ( s )+14 sX ( s )+49 X ( s )=7 F ( s ) X ( s ) F ( s ) = 7 s 2 +14 s +49 The transfer function is: X ( s ) F ( s ) = 7 ( s +7) 2 (2) Poles and Zeros: The zeros are determined from the numerator: from this transfer function there are no zeros. The poles are determined from the denominator. The open loop characteristic equation:
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This note was uploaded on 12/22/2011 for the course ME 375 taught by Professor Meckle during the Fall '10 term at Purdue University-West Lafayette.

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Hw5Soln - ME 375 Homework 5 : Solution October 5, 2009...

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