Question

B4b. What is break away and break in point? How to determine them? (around 70 words) (10 marks)

Answer 1

BREAK POINT The point at which two (08) more poles meet is called break point in the root locus BREAKAWAY POINT » If there exists a real axis root Lous branch between two open loop poles, then there will be a breakaway pomt in between two open loop poles location on the real axis Breakaway point is a where the goof locus branches depart or leaver from the real axis Zeroes Nu ។ ** poles BREAKIN POINT > Breakin point is a location location on the real axis cohore the root locus brancher Arrives or enters the real axis

It happens in case of under damped response, where the poles lies on the Imaginary & real asis [complex poles poles Nuo 70 Zeroe. PROCEDURE FOR BREAKIN) BREAKAWAY PONT il calculate (1GH) to get the characteristic equation 11 Df the characteristic equation is provided equate to zego "e; I+GH =0 211) From Equation K= F(s) Apply dk & equate too" [ies de Find the breakaway & breakin pont I consider the roots of dk at only those portions which are at the root Locus Valid points dk zo to Apply ds Vi] Apply this procedure for Linear Time in variant systems

G(S)H(S) = ķ Example s(s+) Characteristic eq" → I+GH=0 Itk sist) s(s+i) tk zo K=-g²-s dk ds -25-1=0 s=-1/2 > Breakaway pomy poles out Niue *7 - 12 Similarly for breakin point poles should be complex for breakin pont