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, wn
o damping constant, σ → first‐order modes
o Consider how these roots change as the loop gain is varied from 0 to ∞
