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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 closedloop 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 closedloop gain that gives an effective damping ratio of 0.707 for the closedloop 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 closedloop 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 openloop 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
 jonathanhow

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