1

GATE EE 2002

Subjective

+5

-0

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = {{2\left( {s + \alpha } \right)} \over {s\left( {s + 2} \right)\left( {s + 10} \right)}}.$$ Sketch the root locus as $$\alpha $$ varies from $$0$$ to $$\infty $$. Find the angle and real axis intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any

2

GATE EE 2001

Subjective

+5

-0

Given the characteristic equation $${s^3} + 2{s^2} + Ks + K = 0.$$ Sketch the root focus as $$K$$ varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, break-away / break-in points, and imaginary axis crossing points, if any

3

GATE EE 2000

Subjective

+5

-0

A unity feedback system has open loop transfer function $$G\left( s \right) = {{K\left( {s + 5} \right)} \over {s\left( {s + 2} \right)}};K \ge 0$$

(a) Draw a rough sketch of the root locus plot; given that the complex roots ofthe characteristic equation move along a circle.

(b) As K increases, does the system become less stable? Justify your answer.

(c) Find the value of $$K$$ (if it exists) so that the damping $$\xi $$ of the complex closed loop poles is $$0.3.$$

(a) Draw a rough sketch of the root locus plot; given that the complex roots ofthe characteristic equation move along a circle.

(b) As K increases, does the system become less stable? Justify your answer.

(c) Find the value of $$K$$ (if it exists) so that the damping $$\xi $$ of the complex closed loop poles is $$0.3.$$

4

GATE EE 1991

Subjective

+5

-0

A unity feedback system has the forward loop transfer function $$G\left( s \right) = {{K{{\left( {s + 2} \right)}^2}} \over {{s^2}\left( {s - 1} \right)}}$$

(a) Determine the range of $$K$$ for stable operation

(b) Determine the imaginary axis crossover points

(c) Without calculating the real axis break - away points, sketch the form of root loci for the system.

Questions Asked from Root Locus Techniques (Marks 5)

Number in Brackets after Paper Indicates No. of Questions

GATE EE Subjects

Electric Circuits

Electromagnetic Fields

Signals and Systems

Electrical Machines

Engineering Mathematics

General Aptitude

Power System Analysis

Electrical and Electronics Measurement

Analog Electronics

Control Systems

Power Electronics