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ps6 - 2.14/2.140 Problem Set 6 Assigned Thurs Due Thurs...

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Unformatted text preview: 2.14/2.140 Problem Set 6 Assigned: Thurs. March 22, 2007 Due: Thurs. April 5, 2007, in class Reading: Nise sections 10.3–10.10; Notes Chapters 4,5,6 Reading for 2.140 students: Ziegler and Nichols paper, and section of Franklin and Powell on Ziegler-Nichols tuning. Both available on course web page. The following problems are assigned to both 2.14 and 2.140 students. Nise Problem 1a Nise Problem 10 a,b Nise Problem 11 a,b Nise Problem 25 Nise Problem 34 Nise Problem 36 Nise Problem 38 Problem 8 Note: The following problem was used as a Doctoral qualifying exam problem in 2005. It is somewhat challenging because the answers are all in terms of the system parameters, as no numeric values are given. Be sure to think about your approach; hand-sketching of the Bode plots is essential. This problem considers the piezoelectric-actuated system shown in Figure 1. Here a massless link pivots without friction as driven by the piezoelectric actuator at a distance l 1 from the pivot. A mass M and spring k 1 are attached at the right-hand end of the link. The spring k 1 is pre-stretched with suﬃcient tension to guarantee that the hemisphere at the end of the piezo remains in contact with the link at all times. The motions x 1 ,x 2 are about the equilibrium established by this preload. All motions are small. Ignore gravity. We further assume that the piezo can be modeled as shown in Figure 2. Here, motion can only occur in the x 1 direction. The force source F p depends upon the applied piezo voltage E...
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ps6 - 2.14/2.140 Problem Set 6 Assigned Thurs Due Thurs...

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