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Unformatted text preview: 16.31 Handout #4 Prof. J. P. How September 14, 2007 T.A. TBD Due: September 21, 2007 16.31 Homework Assignment #2 1. The open loop transfer function of a closed-loop control system with unity negative gain feedback is K G ( s ) = s ( s + 2)( s 2 + 6 s + 36) Use Matlab to plot the root locus for this system Determine the closed-loop gain that gives an effective damping ratio of 0.707 for the closed-loop poles closest to the origin. Compare the step response with a second order system with poles that have the same frequency and damping ratio as these closed-loop poles to what extent do you think the response of G cl ( s ) is dominated by the response of these poles? 2. A unity gain negative feedback system has an open-loop transfer function given by K (1 + 5 s ) G ( s ) = s (1 + 10 s )(1 + s ) 2 Use Matlab to draw a Bode diagram for this system and determine the loop gain K required for a phase margin of 20 degs. What is the gain margin?...
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This note was uploaded on 11/07/2011 for the course AERO 16.31 taught by Professor Jonathanhow during the Fall '07 term at MIT.
- Fall '07