MAE 340 Lecture 6: 6-Root_Locus

• School: University at Buffalo
• Department: Mechanical & Aerospace Engr
• Course: MAE 340
• Professor: J.Mook

Document Summary

+ powerful technique to determine how many roots of a given polynomial have real parts larger than a speci ed value. + useful to nd conditions on unknown parameters that must be met in order to ensure system stability and/or a speci ed settling time. + can be used with any number of unknown parameters. Does not tell us anything about imaginary parts of roots: root locus. + shows the actual values of roots for a range of unknown parameter. Is limited to a single unknown parameter. Consider the nth-order characteristic equation: an n + an 1 n 1 + + a1 + a0 + k (bm m + bm 1 m 1 + + b1 + b0) = 0 (1) where. 1, 2, n are the roots a0 , a1 , an known, real constants b0 , b1 , bm known, real constants m n.