This question was previously asked in

UPRVUNL AE EC 2014 Official Paper

Option 1 :

Product of length of vectors from poles / Product of length of vectors from zeros

CT 1: Determinants and Matrices

2850

10 Questions
10 Marks
12 Mins

In the root locus method, the value of K is obtained as:

\(k=\frac{Product of the length of vectors from poles}{Product of length of vectors from zeros}\)

1) Every branch of a root locus diagram starts at a pole (K = 0) and terminates at a zero (K = ∞) of the open-loop transfer function.

2) The root locus diagram is symmetrical with respect to the real axis.

3. The number of branches of the root locus diagram are:

N = P if P ≥ Z

= Z, if P ≤ Z

4) Number of asymptotes in a root locus diagram = |P – Z|

5) Centroid: It is the intersection of the asymptotes and always lies on the real axis. It is denoted by σ.

\(\sigma = \frac{{\sum {P_i} - \sum {Z_i}}}{{\left| {P - Z} \right|}}\)

ΣPi is the sum of real parts of finite poles of G(s)H(s)

ΣZi is the sum of real parts of finite zeros of G(s)H(s)

6) The angle of asymptotes:

l = 0, 1, 2, … |P – Z| – 1

7) On the real axis to the right side of any section, if the sum of the total number of poles and zeros are odd, the root locus diagram exists in that section.

8) Break-in/away points: These exist when there are multiple roots on the root locus diagram.

At the breakpoints gain K is either maximum and/or minimum.

So, the roots of \(\frac{{dK}}{{ds}}\) are the breakpoints.