48094_q2spr03soln - Massachusetts Institute of Technology...

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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.011: Introduction to Communication, Control and Signal Processing QUIZ 2, Spring 2003 Solutions • This quiz is closed book , but two “crib” sheets are allowed. • Put your name on each sheet of the answer booklet, and your recitation instructor’s name and time on the cover page of that booklet. • Only the answer booklet will be considered in the grading; no additional answer or solution written elsewhere will be considered. Absolutely no exceptions! • Neat work and clear explanations count; show all relevant work and reasoning! You may want to first work things through on scratch paper and then neatly transfer to the answer booklet the work you would like us to look at. Let us know if you need additional scratch paper. • The quiz will be graded out of 50 points . The three problems are nominally weighted as indicated (but our legal department wishes to let you know that we reserve the right to modify the weighting slightly when we grade, if your collective answers and common errors end up suggesting that a modified weighting would be more appropriate). 1 6.011 Quiz 2, April 23, 2003 Problem 1 (36 points) (a) (i) Using the usual notation for state space model, we have H ( s ) = c T ( sI − A ) − 1 b + d . cb For the forst order case, this reduces to H ( s ) = s − a + d . Comparing with H 1 ( s ) = 1 + 1. We find that s − 1 q ˙ 1 ( t ) = q 1 ( t ) + x 1 ( t ) y ( t ) = q 1 ( t ) + x 1 ( t ) (ii) Is your state-space model for System 1: • reachable? Yes. The first order system is in modal form and β = 1. Alternatively there is no hidden mode....
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48094_q2spr03soln - Massachusetts Institute of Technology...

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