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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 pre-lab 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 closed-loop 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 closed-loop 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