W . R . Evans – 1948 Analysis of Control Systems To achieve desired system performances Open Loop Transfer Function K = 0 The roots are given by open loop poles K= ∞ The roots are given by open loop zeros The path taken 0 to ∞ is called ROOT LOCUS or ROOT LOCI

1. Root Locus Techniques
By
Priyanga KR,
Assistant Professor,
Avinashilingam Institute.

2. Root Locus Techniques
 W . R . Evans – 1948
 Analysis of Control Systems
 To achieve desired system performances
 Open Loop Transfer Function
p = poles z = zeros

3. Closed Loop Transfer Function

4. Contd…
 K = 0 The roots are given by open loop poles
 K= ∞ The roots are given by open loop zeros
 The path taken 0 to ∞ is called ROOT LOCUS or ROOT LOCI

5. Transfer function
For Single Loop System,

6. Under Evans Condition
Magnitude Criterion
Angle Criterion

7. Magnitude Criterion

8. Magnitude Criterion

9. Angle Criterion

10. Rules – Root Locus
 Symmetrical about the real axis
 K =0 and K = ∞
 Segments of the real axis
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11. Rules – Root Locus
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 K at any point

12. Thank You