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# ps7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 7 Due: 11/6/2003 Important Reminder: Do Lab 2! Complete your preliminary controller design and lab work by Friday, November 7. Your lab writeup will then be due the following week. This problem set is a bit shorter than normal so that you will have more time for the lab. Problem 1: Root Locus Sketches for Positive and Negative Gain Sketch (by hand) the root loci for the following pole-zero plots, for both K > 0 and K < 0. (The last one is tricky...) 2 2 (1) (2) (3) (4) Problem 2: Root Locus Sketches with Calculations Sketch (by hand) the loci of the closed-loop poles for K > 0 for systems with the following open-loop transfer functions: K 1. G ( s ) = ( s +1) 2 ( s +2) K ( s +2) 2. G ( s ) = s ( s +1)( s +3)( s +4) K ( s +3) 3. G ( s ) = s ( s +2)( s 2 +2 s +2) K ( s +1)( s +3) 4. G ( s ) = ( s +2)( s 2 +4 s +8) K ( s +2) 2 5. G ( s ) = s 2 ( s 2 +2 s +2) For each, indicate: The number and direction of asymptotes.

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ps7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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