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Assignment_4_2007_Solutions

# When the value of k is around 51 it is exact ly at

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Unformatted text preview: s, 0.5 s 2 + (5.1 - 0.1k c ) s + (1 + k c ) = 0 For the Routh’s criterion, all coefficients in the characterist ic po lyno mial need to be posit ive. Since k is posit ive, the condit ion for stability, then, beco mes c ( 5.1 - 0.1kc ) > 0 Or, we can show that, kc < 5.1 / 0.1 = 51 Figures 6 and 7 illustrate the Root­Locus diagrams for two values o f the controller gain, 10 and 50.5. As the value o f the controller gain is increased, the locat ion of the roots (indicated by the squares in the plot) moves towards the imaginary axis. When the value of k is around 51, it is exact ly at the crossing po int reaching the crit ical stabilit y value, c which is consistent with the results provided by the Routh’s Criterion. Figure 6: Root­Locus for the blending process, squares show the root location when k c = 10 . Figure 7: Root­Locus for the blending process, squares show the root location when k c = 50.5 . The stabilit y analysis for this process was studied before and the limit ing value for the controller gain...
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