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Unformatted text preview: MAE143B Final Exam – Tuesday December 8, 2009 Start time: 8:00 am, Finish time: 11:00 am. Do not continue to write after the end time. Start each question on a new page. Use one side of the paper only. You may use the reverse side for working, since it will not be read. Staple the solutions together. Put your name and student number on the top right corner of each page. You may use whatever materials you wish except equipment with a communications facility, which latter category includes WiFi or telephone data communications. Question 1: [2 parts, 4 pages] A satellite tracking system with gear backlash is described by the transfer function G ( s ) = s + 2 s ( s + 1) , from motor current to angular position. We are required to construct a feedback controller for the following loop; Requirements are; a stable closedloop system with bandwidth of more than three G ( s ) C ( s ) + r t e t y t Figure 1: Closedloop block diagram of controlled motor. radians per second, phase margin of roughly 20 degrees, and steadystate error to a ramp reference of less than 0.1. The following leadlag control design is submitted. C ( s ) = s + 0 . 1 s + 0 . 02 × s/ 2 . 5 + 1 s/ 25 + 1 . The design used, in time sequence, the following Bode and Nyquist diagrams plus other calculations. Part (i): Identify the lead compensator portion of the controller and the lag compensator portion. On the basis of the figures, explain how the design was performed to meet the specifications. − 40 − 30 − 20 − 10 10 20 30 40 Magnitude (dB) 10 − 1 10 10 1 10 2 90 135 180 225 270 Phase (deg) Bode Diagram Gm = 4.01e − 15 dB (at 1.41 rad/sec) , Pm = 0 deg (at 1.41 rad/sec) Frequency (rad/sec) Figure 2: Question 1: Result of matlab margin command for openloop system G ( s ) ....
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 Fall '09
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 Nyquist plot, Bode Diagram Gm

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