GATE EE 2011 | Root Locus Techniques Question 6 | Control Systems

The open loop transfer function $$G(s)$$ of a unity feedback control system is given as, $$G\left( s \right) = {{k\left( {s + {2 \over 3}} \right)} \over {{s^2}\left( {s + 2} \right)}}.\,\,$$ From the root locus, it can be inferred that when $$k$$ tends to positive infinity

three roots with nearly equal real parts exist on the left half of the $$s$$-plane

one real root is found on the right half of the $$s$$-plane

the root loci cross the $$j\omega $$ axis for a finite value of $$k;k \ne 0$$

three real roots are found on the right half of the $$s$$-plane

GATE EE 2010

MCQ (Single Correct Answer)

-0.6

The characteristic equation of a closed-loop system is $$s\left( {s + 1} \right)\left( {s + 3} \right) + \,\,k\left( {s + 2} \right) = 0,\,\,k > 0.$$

Which of the following statements is true?

Its roots are always real

It cannot have a breakaway point in the range $$ - 1 < {\mathop{\rm Re}\nolimits} \left[ s \right] < 0$$

Two of its roots tend to infinity along the asymptotes $${\mathop{\rm Re}\nolimits} \left[ s \right] = - 1$$

It may have complex roots in the right half plane

GATE EE 2006

MCQ (Single Correct Answer)

-0.6

A closed loop system has the characteristic function $$\left( {{s^2} - 4} \right)\left( {s + 1} \right) + K\left( {s - 1} \right) = 0.$$
Its root locus plot against $$K$$ is