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Unformatted text preview: 2.171 Problem Set 6 Assigned: Wed. Nov 1, 2006 Due: Wed. Nov 8, 2006, in class Problem 1 Suppose we have a plant with the transfer function G p ( z ) = ( z 1) 3 ( z . 999) 3 ( z . 99) 2 Assume that this plant is in the forward path of a unitynegativefeedback loop, with a controller transfer function G c ( z ) preceeding the plant. The objective of this problem is to design a controller which stabilizes this plant with as wide a bandwidth as possible. a) Sketch the Bode plot of this plant. Use Matlab to confirm your sketch. b) Design a controller G c ( z ) which stabilizes this plant with as wide a bandwidth as possible. Clearly explain your design thinking. Use a Nyquist analysis to indicate the stability issues and to show that your design results in a stable system. c) For your chosen controller, sketch a root locus as a function of loop gain. Use Matlab to confirm your sketch. Problem 2 FPW 7.13 ac only. Problem 3 This problem looks at the diculties associated with the design in Problem 2. Specif ically, we will see that the sample rate of 50 Hz specified in the problem is too low to allow a robust design. Also, we will see that the rise time spec in Problem 2 is too long to guarantee a suciently robust design. a) Plot the response of your system in x and i to an initial position error in x of 1 mm. Comment on the features of this response with respect to the designed damping and natural frequency....
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 Fall '06
 DavidTrumper

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