stability

Let $G(s) = \frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, is

The Nyquist plot of a strictly stable G(s) having the numerator polynomial as (s – 3) encircles the critical point –1 once in the anti-clockwise direction. Which one of the followi...

Let $G(s) = \frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, is

In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at F very close to circuit breaker 1. The circuit breakers...

In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s + 5}{s - 1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of t...

Which of the following statement(s) is/are true?

Which of the following statement(s) is/are true?

The open loop transfer function of a unity gain negative feedback system is given by $$G(s) = {k \over {{s^2} + 4s - 5}}$$. The range of k for which the system is stable, is

The characteristic equation of a linear time-invariant (LTI) system is given by $\Delta(s) = s^4 + 3s^3 + 3s^2 + s + k = 0$. The system is BIBO stable if

A closed loop system has the characteristic equation given by s³ + Ks² + (K+2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30° is ______. (Give the answer up to two decimal places.)

The number of roots of the polynomial, $s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200$, in the open left half of the complex plane is

The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin δ, where δ is the rotor angle. Th...

A closed loop system has the characteristic equation given by $${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, which one of the following conditi...

The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the complex $$s$$-plane is

Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which have real parts strictly less than $$-1$$ is _____________.

Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$ Take the Nyquist contour in the clockwise dir...

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $$𝑥$$ and...

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$𝐻(𝑠).$$ It is given that $$\left| {G\left( s \right)H\left(...

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

An open loop system represented by the transfer function $$G\left( s \right) = {{\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$ is

The system $$\mathop X\limits^ \bullet = AX + BU$$ with $$A = \left[ {\matrix{ { - 1} & 2 \cr 0 & 2 \cr } } \right],$$ $$B = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$ is

A cascade of 3 Linear Time Invariant systems is casual and unstable. From this, we conclude that

The first two rows of Routh's tabulation of a third order equation are as follows $$$\left. {\matrix{ {{s^3}} \cr {{s^2}} \cr } } \right|\matrix{ 2 & 2 \cr 4 & 4 \cr } $$$ this mea...

A system with input $$x(t)$$ and output $$y(t)$$ is defined by the input $$-$$ output relation: $$y\left( t \right) = \int\limits_{ - \infty }^{ - 2t} {x\left( \tau \right)} d\tau...

The algebraic equation $$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$ $$F\left( s \right) = 0$$ has

A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,

For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be

A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {1 - s} \right)} \over {\left( {1 + s} \right)}}$$

The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,j0)$$ in the $$G(s) H(s)$$ plane. The phase margin of the sy...

For the system $$X = \left[ {\matrix{ 2 & 3 \cr 0 & 5 \cr } } \right]X + \left[ {\matrix{ 1 \cr 0 \cr } } \right]u,$$ Which of the following statement is true?

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

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\,...

A unity feedback system has an open-loop transfer function of $$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \right)}^2}}}$$ (a) Determine the magnitude of $$G\left( {j\o...

Open-loop transfer function of a unity - feedback system is $$$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau _D}}} = {{{e^{ - s{\tau _D}}}} \over {s\left( {s + 1} \right)...

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 r...

Out of the considerations (i) to (iv) listed below, (i) No distance limitation related to steady state stability (ii) No reactive power requirement from the system at the two termi...

The number of roots on the equation $$2{s^4} + {s^3} + 3{s^2} + 5s + 7 = 0$$ that lie in the right half of $$S$$ plane is:

The system represented by the transfer function $$G\left( s \right) = {{{s^2} + 10s + 24} \over {{s^4} + 6{s^3} - 39{s^2} + 19s + 84}}$$ has . . . pole $$(s)$$ in the right-half $$...

HVDC transmission is preferred to EHV __ AC because

The number of positive real roots of the equation $${s^3} - 2s + 2 = 0$$ is __________.

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...