finalexam_sample - ME 360 Modeling Analysis and Control of...

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ME 360: Modeling, Analysis, and Control of Dynamic Systems Professor Tilbury (Section 2), University of Michigan, Winter 2009 FINAL EXAM: Thursday, April 23, 10:30–12:30pm in different rooms again! Last names A–K 1010 Dow Last names L–Z: 1014 Dow The exam is closed book and closed notes, no calculators are allowed. Two sheets of notes (8.5 × 11), both sides, is allowed. A Laplace transform sheet consisting of pages 19–21, and Figures 10-27, 11-1, and 11-7 from Ogata, will be provided on the exam. 1. (15 points) For each frequency response (as shown in the three Bode plots), choose the transfer function that it corresponds to (one of H 1 ( s ) , . . . , H 9 ( s )). -20 -15 -10 -5 0 5 10 15 20 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 -90 -45 0 Phase (deg) Bode Diagram Frequency (rad/sec) -100 -80 -60 -40 -20 0 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 10 3 -180 -135 -90 -45 0 Phase (deg) Bode Diagram Frequency (rad/sec) -20 -15 -10 -5 0 5 10 15 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 -90 -45 0 45 Phase (deg) Bode Diagram Frequency (rad/sec) H 1 ( s ) = 1 s + 1 H 4 ( s ) = 10 s 2 + 2 s + 10 H 6 ( s ) = 10 ( s + 1) 2 H 2 ( s ) = 10 s + 1 H 5 ( s ) = 10( s + 1) s 2 + 2 s + 10 H 8 ( s ) = s + 1 s + 10 H 3 ( s ) = 1 s + 10 H 6 ( s ) = 10( s + 1) s 2 + 10 s + 75 H 9 ( s ) = 10 ( s + 1)( s + 10) 2. (15 points) Consider an armature controlled DC-motor as shown in the figure below. The armature voltage V A (and hence the armature current i A
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