PSet3Solutions - Problem Set#3 16.30 Estimation and Control...

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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 ) 0 2 1 ω Re( s ) 3 Re( s ) Im( s ) 2 1 ω Figure 1: The Nyquist plots in the two main cases cases: α > 0 (left), α < 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 α is positive, and the gain is positive and “small.” Since the gain is specified
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