lecture18 - Root Locus sketching rules Wednesday Rule 1: #...

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Lecture 18 – Friday, Oct. 19 2.004 Fall ’07 Root Locus sketching rules Wednesday Rule 1: # branches = # poles Rule 2: symmetrical about the real axis Rule 3: real-axis segments are to the left of an odd number of real- axis finite poles/zeros Rule 4: RL begins at poles, ends at zeros Today Rule 5: Asymptotes: angles, real-axis intercept Rule 6: Real-axis break-in and breakaway points Rule 7: Imaginary axis crossings (transition to instability) Next week Using the root locus: analysis and design examples
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Lecture 18 – Friday, Oct. 19 2.004 Fall ’07 Poles and zeros at infinity T ( s )hasa zero at in nity if T ( s →∞ ) 0. T ( s pole at in nity if T ( s ) . Example KG ( s ) H ( s )= K s ( s +1)( s +2) . Clearly, this open—loop transfer function has three poles, 0, 1, 2. It has no nite zeros. For large s ,wecanseethat ( s ) H ( s ) K s 3 . So this open—loop transfer function has three zeros at in nity.
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Lecture 18 – Friday, Oct. 19 2.004 Fall ’07 Root Locus sketching rules Rule 5: Asymptotes: angles and real-axis intercept σ a = P nite poles P nite zeros # nite poles # nite zeros θ a = (2 m +1) π #
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.004 taught by Professor Derekrowell during the Fall '08 term at MIT.

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lecture18 - Root Locus sketching rules Wednesday Rule 1: #...

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