Root Locus Techniques · Control Systems · GATE EE

The root locus of unity feedback system is shown in figure

The closed loop transfer function of the system is

Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is

Which of the following figure(s) represent valid root loci in the $$s$$ - plane for positive $$K?$$ Assume that the system has transfer function with real coefficient.

A unity feedback system has an open-loop transfer function of the form $$KG\left( s \right) = {{K\left( {s + a} \right)} \over {{s^2}\left( {s + b} \right)}};\,\,\,\,b > a$$ Which of the loci shown in Fig. can be valid root-loci for the system?

Consider the closed-loop system shown in the figure with $$G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}.$$ The root locus for the closed-loop system is to be drawn for $0 \leq K < \infty$. The angle of departure (between $0^{o}$ and $360^{o})$ of the root locus branch drawn from the pole $(−1 + j2)$, in degrees, is _________________ (rounded off to the nearest integer).

The root locus of the feedback control system having the characteristic equation $${s^2} + 6Ks + 2s + 5 = 0$$ where $$K>0,$$ enters into the real axis at

An open loop transfer function $$G(s)$$ of system is $$G\left( s \right) = {k \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

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

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?

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

A unity feedback system has an open loop transfer function, $$G\left( s \right) = {K \over {{s^2}}}.$$ The root locus plot is

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

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

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 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.