What is root locus technique and root locus analysis ?

1.	What is root locus technique and root locus analysis ?
Answer» Root locus Technique: • Introduced by W. R. Evans in 1948 • Graphical method, in which movement of poles in the s‐plane is sketched when some parameter is varied • The path taken by the roots of the characteristic equation when open loop gain K is varied from 0 to ∞ are called root loci • Direct Root Locus = 0 < k < ∞ • Inverse Root Locus = ‐ ∞ < k < 0 Root Locus Analysis: • The roots of the closed‐loop characteristic equation define the system characteristic responses • Their location in the complex s‐plane lead to prediction of the characteristics of the time domain responses in terms of: o damping ratio, ζ o natural frequency, w_n o damping constant, σ → first‐order modes o Consider how these roots change as the loop gain is varied from 0 to ∞

Answer»

Root locus Technique:

• Introduced by W. R. Evans in 1948

• Graphical method, in which movement of poles in the s‐plane is sketched when some parameter is varied

• The path taken by the roots of the characteristic equation when open loop gain K is varied from 0 to ∞ are called root loci

• Direct Root Locus = 0 < k < ∞

• Inverse Root Locus = ‐ ∞ < k < 0

Root Locus Analysis:

• The roots of the closed‐loop characteristic equation define the system characteristic responses

• Their location in the complex s‐plane lead to prediction of the characteristics of the time domain responses in terms of:

o damping ratio, ζ

o natural frequency, w_n

o damping constant, σ → first‐order modes

o Consider how these roots change as the loop gain is varied from 0 to ∞

Discussion

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