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Unformatted text preview: Problem Set #3 16.30: Estimation and Control of Aerospace Systems Posted: Mar 1, Due: Mar 7 Note: this problem set is very short, because you will be required to do a prelab assignment as well, coming up shortly 1 Problem 4.5 in DFT. (Upper and lower gain margins are the factors by which you can multiply or divide the gain while maintaining closedloop stability.) Probably the easiest approach to solve this problem is based on the Nyquist plot. There are two main cases to be analyzed, summarized in the following figure. 1 Re( s ) Im( s ) 2 1 Re( s ) 3 Re( s ) Im( s ) 2 1 Figure 1: The Nyquist plots in the two main cases cases: > 0 (left), < 0 (right). The numbers on the real axis represent the number of unstable closedloop poles should the 1 point fall within those ranges. From the analysis of the Nyquist plots, one can conclude that the only case in which the closed loop is positive is when is positive, and the gain is positive and small. Since the gain is specifiedis positive, and the gain is positive and small....
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This note was uploaded on 03/17/2008 for the course COURSE 16.30 taught by Professor Frazzolli during the Spring '07 term at MIT.
 Spring '07
 Frazzolli

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