l22 - 16.06 Lecture 22 Root Locus Examples Karen Willcox...

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16.06 Lecture 22 Root Locus Examples Karen Willcox October 27, 2003 Today’s Topics 1. Angles of departure 2. Negative gain 3. K crit 4. Root locus examples Reading : 6.4 1
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1 Rule 10 (Continued from L21.) Angles of departure from open-loop poles and angles of arrival at open- loop zeroes are important because aero/astro toys can have complex con- jugate poles and zeroes near the axis. We determine these angles by applying the angle condition to a trial point very close to the pole or zero. Example 1: Example 2: 2
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2 Negative gain 2.1 First-order system C.E. is: 2.2 Second-order system C.E. is: Roots: s 1 and s 2 are 3
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2.3 Third-order system C.E. is: 2.4 General K< 0 case Note that for negative gains, the angles must sum to The entire real axis is 4
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3 K crit At what critical value of K in the third-order case are
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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l22 - 16.06 Lecture 22 Root Locus Examples Karen Willcox...

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