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Unformatted text preview: 16.30/31 Handout #1 Prof. J. P. How and Prof. E. Frazzoli September 10, 2010 T.A. B. Luders Due: September 17, 2010 16.30/31 Homework Assignment #1 Goals: Refresh skills for Matlab and classical analysis. 1. Sketch the root locus for the following systems, using the rules discussed in class and the lecture notes. (Concentrate on the real axis and the asymptotes/centroids.) K (a) G c G p ( s ) = ( s 2 +6 s +8)( s 2 +2 s +5) (b) G c G p ( s ) = K ( s 2 2 s +2) s ( s +2) K ( s +3) (c) G c G p ( s ) = s 4 s 4 2 (d) After completing these sketches, verify the results using Matlab. How closely do your sketches resemble the actual plots (we would not expect them to be exact)? 2. (adapted from FPE 4.10, page 215) Consider the DC motor control system with rate feedback shown in Figure 1(a). Figure 1: DC motor control system (a) Find values for K and k t so that the system of Figure 1(b) has the same transfer function as the system of Figure 1(a). Your answers should be in terms of K p ,...
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- Fall '04