MECH 466 - Lecture6-Stability-2009W

1st order polynomial yes no 2nd order polynomial yes

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Unformatted text preview: o Yes / No Higher order polynomial Higher Yes / No Yes / No 2008/09 MECH466 : Automatic Control 25 Why no proof in textbooks? “most undergraduate students are exposed to the Routh–Hurwitz criterion in their first introductory Routh– controls course. This exposure, however, is at the purely algorithmic level in the sense that no attempt is made whatsoever to explain why or how such an algorithm works.” works.” MECH466 : Automatic Control MECH466 : Automatic Control 26 Why no proof in textbooks? (cont’d) An Elementary Derivation of the Routh–Hurwitz Criterion Ming-Tzu Ho, Aniruddha Datta, and S. P. Bhattacharyya IEEE Transactions on Automatic Control vol. 43, no. 3, 1998, pp. 405-409. 2008/09 2008/09 27 “The principal reason for this is that the classical proof of the Routh-Hurwitz criterion relies on the Routhnotion of Cauchy indexes and Sturm’s theorem, Sturm’ both of which are beyond the scope of undergraduate students.” students.” “Routh-Hurwitz criterion has become one of the few Routhresults in control theory that most control engineers are compelled to accept on faith.” faith.” 2008/09 MECH466 : Automatic Control 28 7 Summary and Exercises Stability for LTI systems Stability (BIBO, asymptotically) stable, marginally stable, unstable (BIBO, Stability for G(s) is determined by poles of G. Stability G(s) Routh-Hurwitz stability criterion to determine stability Routhwithout explicitly computing the poles of a system Next, examples of Routh-Hurwitz criterion Next, RouthExercises Exercises Read Sections 6.1 & 6.2. Read Solve Problems 6.1, 6.9 & 6.14. Solve No lecture on next Tuesday (Jan. 27) No 2008/09 MECH466 : Automatic Control 29 8...
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