Highest voted questions in Control Systems

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1

GATE2013-40
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\dfrac{s+1}{5s^2+6s+2}$ $\dfrac{s+1}{s^2+6s+2}$ $\dfrac{s+1}{s^2+4s+2}$ $\dfrac{1}{5s^2+6s+2}$

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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2

GATE2013-28
The open-loop transfer function of a dc motor is given as $\dfrac{\omega (s)}{V_a(s)}=\dfrac{10}{1+10s}$.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 $1$ $5$ $10$ $100$

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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3

GATE2013-13
In the feedback network shown below,if the feedback factor $k$ is increased, then the input impedance increases and output impedance decreases. input impedance increases and output impedance also increases. input impedance decreases and output impedance also decreases. input impedance decreases and output impedance increases.

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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4

GATE2013-15
The Bode plot of a transfer function $G(s)$ is shown in the figure below. The gain $\big(20 \log\mid G(s) \mid \big)$ is $32 dB$ and $-8 dB$ at $1$ rad/s and $10$ rad/s respectively. The phase is negative for all $\omega$. Then $G(s)$ is $\frac{39.8}{s} \\$ $\frac{39.8}{s^2} \\$ $\frac{32}{s} \\$ $\frac{32}{s^2}$

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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5

GATE2013-2
The transfer function $\dfrac{V2(s)}{V1(s)}$ of the circuit shown below is $\dfrac{0.5s+1}{s+1}$ $\dfrac{3s+6}{s+2}$ $\dfrac{s+2}{s+1}$ $\dfrac{s+1}{s+2}$

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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6

GATE2013-3
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is? $u(t)$ $t\:u(t)$ $\dfrac{t^2}{2}u(t)$ $e^{-t}u(t)$

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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7

GATE2013-5
Which of the following statement is NOT TRUE for a continuous time causal and stable $LTI$ system? All the poles of the system must lie on the left side of $j\omega$ axis Zeros of the system can lie anywhere in the $s$ – plane All the poles must lie within $\mid s\mid=1$ All the roots of the characteristic equation must be located on the left side of $j\omega$ axis

asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)

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8

GATE2014-3-46
The magnitude Bode plot of a network is shown in the figure The maximum phase angle $\phi _m$ and the corresponding gain $G_m$ respectively, are $-30^{\circ}$ and $1.73$ $dB$ $-30^{\circ}$ and $477$ $dB$ $+30^{\circ}$ and $4.77$ $dB$ $+30^{\circ}$ and $1.73$ $dB$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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9

GATE2014-3-44
The block diagram of a system is shown in the figure If the desired transfer function of the system is $\frac{C(s)}{R(s)}=\frac{s}{s^2+s+1}$ then $G(s)$ is $1$ $s$ $1/s$ $\frac{-s}{s^3+s^2-s-2}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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10

GATE2014-3-45
Consider the system described by following state space equations $\begin{vmatrix} \dot{x_1}\\ \dot{x_2} \end{vmatrix}=\begin{vmatrix} 0 &1 \\ -1 & -1 \end{vmatrix}\begin{vmatrix} x_1\\x_2 \end{vmatrix}+\begin{vmatrix} 0\\1 \end{vmatrix}u$ ... $u$ is unit step input, then the steady state error of the system is $0$ $1/2$ $2/3$ $1$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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11

GATE2014-3-17
The signal flow graph of a system is shown below. $U(s)$ is the input and $C(s)$ is the output. Assuming, $h_1=b_1$ and $h_0=b_0-b_1a_1$ , the input-output transfer function, $G(s)=\frac{C(s)}{U(s)}$ of the system is given by $G(s)=\frac{b_0s+b_1}{s^2+a_0s+a_1} \\ $ $G(s)=\frac{a_1s+a_0}{s^2+b_1s+b_0} \\ $ $G(s)=\frac{b_1s+b_0}{s^2+a_1s+a_0} \\$ $G(s)=\frac{a_0s+a1}{s^2+b_0s+b_1}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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12

GATE2014-3-18
A single-input single-output feedback system has forward transfer function $G(s)$ and feedback transfer function $H(s)$. It is given that $|G(s)H(s)|< 1$ . Which of the following is true about the stability of the system? The system is always stable The ... are in left half of the s-plane It is not possible to say whether or not the system is stable from the information given

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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13

GATE2014-2-44
A system with the open loop transfer function $G(s)=\frac{K}{s(s+2)(s^2+2s+2)}$ is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of $K$ is ______

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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14

GATE2014-2-45
For the transfer function $G(s)=\frac{5(s+2)}{s(s+0.25)(s^2+4s+25)}$ The values of the constant gain term and the highest corner frequency of the Bode plot respectively are $3.2$ , $5.0$ $16.0$ , $4.0$ $3.2$ , $4.0$ $16.0$ , $5.0$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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15

GATE2014-2-46
The second order dynamic system $\frac{dX}{dt}=PX+Qu$ $y=RX$ has the matrices $P$, $Q$ and $R$ as follows: $P=\begin{bmatrix} -1 & 1\\ 0& -3 \end{bmatrix}$ ... system has the following controllability and observability properties: Controllable and observable Not controllable but observable Controllable but not observable Not controllable and not observable

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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16

GATE2014-2-33
A discrete system is represented by the difference equation $\begin{bmatrix} X_1(k+1)\\ X_2(k+2) \end{bmatrix}=\begin{bmatrix} a & a-1\\ a+1 & a \end{bmatrix}\begin{bmatrix} X_1(k)\\X_2(k) \end{bmatrix}$ It has initial conditions $X_1(0)$ = $1$; $X_2(0)$ = $0$. The pole locations of the system for $a$ = $1$, are $1\pm j0$ $-1\pm j0$ $\pm 1+j0$ $0\pm j1$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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17

GATE2014-2-17
The closed loop transfer function of a system is $T(s)=\frac{4}{s^2+0.4S+4}$ The steady state error due to unit step input is __________.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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18

GATE2014-2-9
Consider an LTI system with transfer function $H(s)=\frac{1}{s(s+4)}$ If the input to the system is $cos(3t)$ and the steady state output is $Asin(3t+\alpha )$ , then the value of $A$ is $1/30$ $1/15$ $3/4$ $4/3$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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19

GATE2014-1-44
For the given system, it is desired that the system be stable. The minimum value of $\alpha$ for this condition is ____________. .

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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20

GATE2014-1-51
In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function $\dfrac{V_o(\omega )}{V_i(\omega )}?$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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21

GATE2014-1-18
The root locus of a unity feedback system is shown in the figure The closed loop transfer function of the system is $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)}$ $\frac{C(s)}{R(s)}=\frac{-K}{(s+1)(s+2)+K}$ $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)-K}$ $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)+K}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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22

GATE2015-2-24
An open loop control system results in a response of $e^{-2t}(\sin 5t+\cos 5t)$ for a unit impulse input. The $DC$ gain of the control system is ________.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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23

GATE2015-2-25
Nyquist plots of two functions $G_{1}(s)$ and $G_{2}(s)$ are shown in figure. Nyquist plot of the product of $G_{1}(s)$ and $G_{2}(s)$ is

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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24

GATE2015-2-11
The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is $V_{i} = 2 \sin(2\pi × 2000t)$. The amplitude of the output voltage $V_{0}$ (in Volt) is ________.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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25

GATE2015-1-55
The open loop poles of a third order unity feedback system are at $0, −1, −2$. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be $K$. Now suppose we introduce a zero in the open loop ... corresponds to a frequency less than $K$ It corresponds to a frequency $K$ Root locus of modified system never transits to unstable region

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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26

GATE2015-1-52
In the signal flow diagram given in the figure, $u_{1}$ and $u_{2}$ are possible inputs whereas $y_{1}$ and $y_{2}$ are possible outputs. When would the SISO system derived from this diagram be controllable and observable? When $u_{1}$ is the only input and $y_{1}$ is ... is the only input and $y_{2}$ is the only output. When $u_{2}$ is the only input and $y_{2}$ is the only output.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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27

GATE2015-1-53
The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2 − j3)$. List all the poles and zeroes. Poles at $(2 \pm j3)$, no zeroes. Poles at $(\pm 2 − j3)$, one zero at origin. Poles at $(2 − j3)$, $(−2 + j3)$, zeroes at $(−2 − j3)$, $(2 + j3)$. Poles at $(2 \pm j3)$, zeroes at $(−2 \pm j3)$.

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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28

GATE2015-1-39
The op-amp shown in the figure has a finite gain $A = 1000$ and an infinite input resistance. A step-voltage $V_{i} = 1 mV$ is applied at the input at time $t = 0$ as shown. Assuming that the operational amplifier is not saturated, the time constant (in millisecond) of the output voltage $V_{0}$ is $1001$ $101$ $11$ $1$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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29

GATE2015-1-24
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? $\frac{1000(s+10)}{s+1000}$ $\frac{10(s+10)}{s(s+1000)}$ $\frac{s+1000}{10s(s+10)}$ $\frac{s+1000}{10(s+10)}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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30

GATE2015-1-25
For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function $\frac{Y(s)}{X_{2}(s)}\mid _{X_{1}(s)=0}$ ? $\frac{G_{1}}{1+G_{2}(1+G_{1})}$ $\frac{G_{2}}{1+G_{1}(1+G_{2})}$ $\frac{G_{1}}{1+G_{1}G_{2}}$ $\frac{G_{2}}{1+G_{1}G_{2}}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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31

GATE2015-1-10
The impulse response $g(t)$ of a system, $G$, is as shown in Figure $(a)$. What is the maximum value attained by the impulse response of two cascaded blocks of $G$ as shown in Figure $(b)$? $\frac{2}{3}$ $\frac{3}{4}$ $\frac{4}{5}$ $1$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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32

GATE2015-1-13
Consider the circuit shown in the figure. In this circuit $R=1 k\Omega$, and $C=1 \mu F$. The input voltage is sinusoidal with a frequency of $50$ Hz, represented as a phasor with magnitude $V_{i}$ and phase angle $0$ radian as shown in the figure. The output voltage is ... $0$ $\pi$ $\frac{\pi}{2}$ $-\frac{\pi}{2}$

asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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33

GATE2016-2-52
The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function $G(s)=\frac{Ks}{(s-1)(s-4)}$ is $1$ $2$ $5$ $9$

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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34

GATE2016-2-50
A second-order real system has the following properties: a) the damping ratio $\zeta=0.5$ and undamped natural frequency $\omega _{n}=10$ rad/s b) the steady state value of the output, to a unit step input, is $1.02$. The transfer function of the system is $\frac{1.02}{s^{2}+5s+100}$ $\frac{102}{s^{2}+10s+100}$ $\frac{100}{s^{2}+10s+100}$ $\frac{102}{s^{2}+5s+100}$

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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35

GATE2016-2-39
The open loop transfer function of a unity feedback control system is given by $G(s)=\frac{k(s+1)}{s(1+Ts)(1+2S)'}, K > 0, T > 0.$ The closed loop system will be stable if $0 < T < \frac{4(K+1)}{K-1}$ $0 < K < \frac{4(T+2)}{T-2}$ $0 < K < \frac{T+2}{T-2}$ $0 < T < \frac{8(k+1)}{K-1}$

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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36

GATE2016-1-30
Consider the following asymptotic Bode magnitude plot (ω is in rad/s). Which one of the following transfer functions is best represented by the above Bode magnitude plot? $\frac{2s}{(1+0.5s)(1+0.25s)^{2}}$ $\frac{4(1+0.5s)}{s(1+0.25s)}$ $\frac{2s}{(1+2s)(1+4s)}$ $\frac{4s}{(1+2s)(1+4s)^{2}}$

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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37

GATE2016-1-31
Consider the following state-space representation of a linear time-invariant system. $x(t)=\begin{pmatrix} 1&0 \\ 0&2 \end{pmatrix} x(t), y(t)= c^{T} x(t), c =\begin{pmatrix} 1& \\ 1& \end{pmatrix} \text {and} x(0)= \begin{pmatrix} 1& \\ 1& \end{pmatrix}$ The value of y(t) for $t =\log_{e} 2$ is __________.

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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38

GATE2016-1-32
Loop transfer function of a feedback system is $G(s)H(s)=\frac{s+3}{s^{2}(s-3)}$. Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $G(s) H (s)$ encircles $-1 + j0$ Once in clockwise direction Twice in clockwise direction Once in anticlockwise direction Twice in anticlockwise direction

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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39

GATE2016-1-6
The transfer function of a system is $\frac{Y(s)}{R(s)}=\frac{s}{s+2}$. The steady state output $y(t)$ is $A \cos (2t + \phi)$ for the input $\cos (2t)$. The values of A and $\phi$ respectively are $\frac{1}{\sqrt{2}}$, -45° $\frac{1}{\sqrt{2}}$, +45° $\sqrt{2}$, -45° $\sqrt{2}$, +45°

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)

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40

GATE2016-1-7
The phase cross-over frequency of the transfer function $G(s)=\frac{100}{(s+1)^{3}}$ in rad/s is $\sqrt{3}$ $\frac{1}{\sqrt{3}}$ $3$ $3\sqrt{3}$

asked Jan 30, 2017 in Control Systems by makhdoom ghaya (9.3k points)