stability6

# stability6 - • Finish the array Slide 4 ME 475 Session 6...

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Slide 1 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases Case 1: Single zero in column 1 with at least one nonzero element in that row. Procedure: Replace zero with small positive number F , complete the array, then take the limit as F 0.

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Slide 2 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases Case 1 Example: D(s) = s 4 + s 3 + s 2 + s + K
Slide 3 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases Case 2: Entire row of zeroes. Procedure: • Call the row above the row of zeroes the auxiliary polynomial P(s). • Replace the row of zeroes with dP/ds.

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Unformatted text preview: • Finish the array. Slide 4 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases Case 2 Ex.: D(s) = s 5 + 2s 4 + 6s 3 + 10s 2 + 8s + 12 Slide 5 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases The auxiliary polynomial represents a factor of the original polynomial and will typically be purely even (i.e., it has nonzero coefficients for only even powers of s). Even polynomials only have roots that are symmetrical about the origin. Slide 6 ME 475 Session 6: Routh-Hurwitz Stability Galen King Purdue University Routh-Hurwitz Special Cases Example:...
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stability6 - • Finish the array Slide 4 ME 475 Session 6...

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