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The open-loop transfer function of a dc motor is given as $\frac{\omega \left(s\right)}{V_a\left(a\right)}=\frac{10}{1+10s}$. When connected in feedback as shown below, the approximate value of $K_a$ that will reduce the time constant of the closed loop system, by one hundred times as compared to that of the open-loop system is

If $s^3+3s^2+4s+A=0$ , then all the roots of this equation are in the left half plane provided that

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

The block diagram of a system with one input $u$ and two output $y_1$ and $y_2$ is given below.

A state space model ofthe above system in terms ofthe state vector $x$ and the output vector $y={\left[\begin{array}{cc}{y}_1& y_2\end{array}\right]}^T$ is

The input-output transfer function of a plant $H\left(s\right)=\frac{100}{s(s+10{)}^2}$, The plant is placed in a unity negative feedback configuration as shown in the figure below.





The signal flow graph that DOES NOT model the plant transfer function $H\left(s\right)$ is

The Bode magnitude plot of

$H\left(j\omega \right)=\frac{{10}^4(1+j\omega )}{(10+j\omega )(100+j\omega {)}^2}is$

Consider a casual second-order system will be transfer function

$G\left(s\right)=\frac{1}{1+2s+s^2}$

with a unit-step $R\left(s\right)=\frac{1}{s}$ as an input. Let $C\left(s\right)$ be the corresponding output. The time taken by the system output $c\left(t\right)$ to reach $94\%$ of its steady-state value $\underset{t\to \infty }{lim}c\left(t\right)$, rounded off to two decimal places, is

The unit step response of a system with the transfer function $G\left(s\right)=\frac{1-2s}{1+s}$ is given by which one of the following waveforms?

A control system with damping ratio $\xi =\sqrt{3}$ is represented by the block diagram which employs proportional plus error rate control. The value of error rate constant K when unit step is given as input to system will be

Consider the system shown below:



This system is stable for

A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

The signal flow graph of a system is shown in the figure. The transfer function $\frac{C\left(s\right)}{R\left(s\right)}$ of the system is

A second order system has closed loop poles located as $s=-3\pm j4.$The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places) is

1. 0.78

A system with transfer function:

$G\left(s\right)=\frac{(s^2+9)(s+2)}{(9s+1)(s+3)(s+4)}$

is excited $sin\left(\omega t\right)$. The steady-state output of the system is zero at

Transfer function of a first order system is given by$G\left(s\right)=\frac{1}{Ts+1}$



Impulse response of the system is

The closed loop frequency response $\left|G\right(j\omega \left)\right|$ versus frequency of a second order prototype system is shown in figure below.





The corresponding unit step response of the system is

1. 1.047

In the signal flow graph of figure the gain C/R will be

The system with the open loop transfer function $G\left(s\right)H\left(s\right)=\frac{1}{s(s^2+s+1)}$ has a gain margin of

The open loop transfer function of an unity feedback open loop system is $\frac{2s^2+6s+5}{(s+1{)}^2(s+2)}$. The characteristic equation of the closed loop system is

1. 30

Let the state- space representation of an LTI system be $\dot{X}\left(t\right)=AX\left(t\right)+Bu\left(t\right),y\left(t\right)=CX\left(t\right)+Du\left(t\right)$ where $A,B,C$ are matrices, $D$ is a scalar, $u\left(t\right)$ is the input to the system, and $y\left(t\right)$ is its output. Let $B=[001{]}^T$ and $d=0$. Which one of the following option for $A$ and $C$ will ensure that the transfer function ofthis LTI system is

$H\left(s\right)=\frac{1}{s^3+3s^2+2s+1}$

Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of three systems?

The open loop transfer function of a unity feedback system is given by $G\left(s\right)=\frac{3e^{-2s}}{s(s+2)}$

The gain and phase crossover frequencies in rad/sec are, respectively

The C/R for the signal flow graph in figure is:

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system, are given as $G\left(s\right)=\frac{K(s+2)}{s^2+2s+2}andH\left(s\right)=1$, respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is

1. -3.41

Consider a standard negative feedback configuration with

$G\left(s\right)=\frac{1}{(s+1)(s+2)}andH\left(s\right)=\frac{s+\alpha }{s}.$ For the closed loop system to have poles on the imaginary axis, the value of $\alpha$ should be equal to (up to one decimal place)

1. 9

The transfer function of a phase-lead compensator is given by

$G_e\left(s\right)=\frac{1+3Ts}{1+Ts}whereT>0.$

The maximum phase-shift provided by such a compensator is

Which of the following can be the pole -zero configuration of a phase-lag controller (lag compensator) ?

The steady state error of a stable 'type 0' unity feedback system for a unit step function is

Consider a control system having open-loop transfer function of

$G\left(s\right)H\left(s\right)=\frac{1}{s^2(s-a)(s-b)(s-c)}$

If a,b,c are positive, then the polar plot of the system will be

A system with the transfer function $\frac{Y\left(s\right)}{X\left(s\right)}=\frac{s}{s+p}$ has an output $y\left(t\right)=\cos (2t-\frac{\pi }{3})$ for the input signal $x\left(t\right)=p\cos (2t-\frac{\pi }{2}).$ Then, the system parameter ${}^{\prime }{p}^{\prime }$ is

For the given circuit, which one of the following is the correct state equation?

The polar diagram of a conditionally stable system for open loop gain $K=1$ is shown in the figure. Theopen loop transfer function of the system is known to be stable. The closed loop system is stable for

A control system is represented by following state space representation

$\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}-5& 1\\ 0& -4\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right]u\left(t\right)$



$y=\left[\begin{array}{cc}1& 4\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$

If two such systems are connected in parallel then overall transfer function of the combined system is

For the system

$\dot{X}=\left[\begin{array}{cc}2& 0\\ 0& 4\end{array}\right]X+\left[\begin{array}{c}1\\ 1\end{array}\right]u;y=\left[\begin{array}{cc}4& 0\end{array}\right]X,$

with $u$ as unit impulse and with zero initial state, the output $y$ becomes

The approximate phase response of $\frac{{100}^2{e}^{-0.01s}}{s^2+0.2s+{100}^2}is$

Consider a system with the transfer function $G\left(s\right)=\frac{s+6}{K{s}^2+s+6}$. Its damping ratio will be $0.5$ when the value of $K$ is

Figure shows the polar plot of a system. The transfer function of the system is

The asymptotic log-magnitude curve for open loop transfer function is sketched below,





Open loop transfer function is

For a second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

The open-loop transfer function of a plant is given as $G\left(s\right)=\frac{1}{s^2-1}.$ If the plant is operated in a unity feedback configuration,then the lead compensator that can stabilize this control system is

The condition for stability of a closed-loop system with a characteristic $s^3+b{s}^2+cs+1=0$, with positive coefficients is

The transfer function for the state variable representation $X=AX+BU,Y=CX+DU$, is given by

The differential equation $100\frac{d^{2}y}{d{t}^2}-20\frac{dy}{dt}+y=x\left(t\right)$ describes a system with an input $x\left(t\right)$ and an output $y\left(t\right)$.The system, which is initially relaxed is excited by a unit step input. The output $y\left(t\right)$ can be represented by the waveform

Given the matrix:

$A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -6& -11& -6\end{array}\right]$



Its eigen values are ______.

The figure below shows the bode magnitude and phase plots of a stable transfer function

$G\left(s\right)=\frac{n_0}{s^3+d_2{s}^2+d_{1}s+d_0}$



Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop in stable for $k<k_0$. The maximum value of $k_0$ is

1. 0.1

The number of open right half plane poles of $G\left(s\right)=\frac{10}{s^5+2s^4+3s^3+6s^2+5s+3}$ is

Which of the following is the transfer function of a system having the Nyquist plot shown in figure below?

The transfer function of s system is $G\left(s\right)=\frac{100}{(s+1)(s+100)}.$ For a unit -step input to the system the approximate settling time for $2\%$ criterion is