Root Locus short-cut important rules

1. Root Locus
Prajakta J Pardeshi
Assistant Professor
MITCOE

2. Construction Rules For Root Locus
1. find The open-loop pole, open-loop zeros, & no.
of branches.
2. Draw pole-zero plot; find the pts on real axis
where root locus exists.
3. Calculate angle of asymptotes;
4. Find the co-ordinates of Centroid
5. Find breakaway point, & check their validity
6. Find the intercepts on jw-axis
7. Find the angle of departure for complex roots
8. Draw final sketch
9. Predict/ comment on stability of the system

3. Rule 5: Breakaway Point
1. Form the CE
2. Rearrange the above equation in the form of
K=f(s)
3. Differentiate k w.r.t s & make it equal to zero
Roots of dK/ds=0; gives the valid & invalid
breakpoint
For Valid Brk pt:-
1. K should be positive
2. OR it should lie on Root Locus

4. Rule 4: Finding Asymptotes & Centroid

5. 1. Use Routh’s Criteria
2. Substitute K=Kmar
3. Find out Auxiliary polynomial roots of A(s)=0
(these are the intersection points on jw axis)
Rule 6: Finding Intersection Procedure

7. Rule 7:Angle of Arrival & Departure

9. • Ex: Range of K: 0<K<2; Kmar=+2
1. For 0<K<2 : All roots are in left half of s-palne,
system is absolutely stable.
2. At Kmar= +2 : Dominant Roots are on imaginary
axis. System is marginally stable which oscillates
at 2 rad/s
3. For K>2 : Dominant Roots are in RHS, System is
unstable in nature
Prediction about Stability