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Recent questions and answers in Control Systems
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GATE Electrical 2013  Question: 40
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\dfrac{s+1}{5s^2+6s+2} \\$ $\dfrac{s+1}{s^2+6s+2} \\$ $\dfrac{s+1}{s^2+4s+2} \\$ $\dfrac{1}{5s^2+6s+2}$
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2
GATE Electrical 2013  Question: 28
The openloop 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 openloop system is $1$ $5$ $10$ $100$
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3
GATE Electrical 2013  Question: 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 $\dfrac{39.8}{s} \\$ $\dfrac{39.8}{s^2} \\$ $\dfrac{32}{s} \\$ $\dfrac{32}{s^2}$
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Control Systems
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4
GATE Electrical 2013  Question: 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.
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Control Systems
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5
GATE Electrical 2013  Question: 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 ... within $\mid s\mid=1$ All the roots of the characteristic equation must be located on the left side of $j\omega$ axis
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6
GATE Electrical 2013  Question: 3
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is? $u(t) \\$ $t\:u(t) \\$ $\dfrac{t^2}{2}u(t) \\$ $e^{t}u(t)$
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7
GATE Electrical 2013  Question: 2
The transfer function $\dfrac{V2(s)}{V1(s)}$ of the circuit shown below is $\dfrac{0.5s+1}{s+1} \\$ $\dfrac{3s+6}{s+2} \\$ $\dfrac{s+2}{s+1} \\$ $\dfrac{s+1}{s+2}$
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Control Systems
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8
GATE Electrical 2014 Set 3  Question: 44
The block diagram of a system is shown in the figure If the desired transfer function of the system is $\dfrac{C(s)}{R(s)}=\dfrac{s}{s^2+s+1}$ then $G(s)$ is $1$ $s$ $1/s$ $\dfrac{s}{s^3+s^2s2}$
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Feb 12, 2017
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Control Systems
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9
GATE Electrical 2014 Set 3  Question: 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 $0$ $1/2$ $2/3$ $1$
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statespacefunctions
steadystateerror
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10
GATE Electrical 2014 Set 3  Question: 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 $1.73$ $dB$
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Control Systems
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bodeplot
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11
GATE Electrical 2014 Set 3  Question: 18
A singleinput singleoutput 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 ... are in left half of the splane It is not possible to say whether or not the system is stable from the information given
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Control Systems
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12
GATE Electrical 2014 Set 3  Question: 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 $h_0=b_0b_1a_1$ , the inputoutput transfer function, $G(s)=\dfrac{C(s)}{U(s)}$ ... $G(s)=\dfrac{b_1s+b_0}{s^2+a_1s+a_0} \\$ $G(s)=\dfrac{a_0s+a1}{s^2+b_0s+b_1}$
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13
GATE Electrical 2014 Set 2  Question: 46
The second order dynamic system $\dfrac{dX}{dt}=PX+Qu$ $y=RX$ has the matrices $P$, $Q$ and $R$ as follows: $P=\begin{bmatrix} 1 & 1\\ 0& 3 \end{bmatrix}$ ... the following controllability and observability properties: Controllable and observable Not controllable but observable Controllable but not observable Not controllable and not observable
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dynamicsystem
controlability
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14
GATE Electrical 2014 Set 2  Question: 45
For the transfer function $G(s)=\dfrac{5(s+2)}{s(s+0.25)(s^2+4s+25)}$ The values of the constant gain term and the highest corner frequency of the Bode plot respectively are $3.2$ , $5.0$ $16.0$ , $4.0$ $3.2$ , $4.0$ $16.0$ , $5.0$
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Control Systems
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15
GATE Electrical 2014 Set 2  Question: 44
A system with the open loop transfer function $G(s)=\dfrac{K}{s(s+2)(s^2+2s+2)}$ 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 ______
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16
GATE Electrical 2014 Set 2  Question: 33
A discrete system is represented by the difference equation $\begin{bmatrix} X_1(k+1)\\ X_2(k+2) \end{bmatrix}=\begin{bmatrix} a & a1\\ a+1 & a \end{bmatrix}\begin{bmatrix} X_1(k)\\X_2(k) \end{bmatrix}$ It has initial conditions $X_1(0)$ = $1$ ... $a$ = $1$, are $1\pm j0$ $1\pm j0$ $\pm 1+j0$ $0\pm j1$
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17
GATE Electrical 2014 Set 2  Question: 17
The closed loop transfer function of a system is $T(s)=\dfrac{4}{s^2+0.4S+4}$ The steady state error due to unit step input is __________.
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18
GATE Electrical 2014 Set 2  Question: 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 $A \sin(3t+\alpha )$ , then the value of $A$ is $1/30$ $1/15$ $3/4$ $4/3$
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19
GATE Electrical 2014 Set 1  Question: 44
For the given system, it is desired that the system be stable. The minimum value of $\alpha$ for this condition is ____________. .
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20
GATE Electrical 2014 Set 1  Question: 51
In the figure shown, assume the opamp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function $\dfrac{V_o(\omega )}{V_i(\omega )}?$
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operationalamplifier
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21
GATE Electrical 2014 Set 1  Question: 18
The root locus of a unity feedback system is shown in the figure The closed loop transfer function of the system is $\dfrac{C(s)}{R(s)}=\dfrac{K}{(s+1)(s+2)} \\$ $\dfrac{C(s)}{R(s)}=\dfrac{K}{(s+1)(s+2)+K} \\$ $\dfrac{C(s)}{R(s)}=\dfrac{K}{(s+1)(s+2)K} \\$ $\dfrac{C(s)}{R(s)}=\dfrac{K}{(s+1)(s+2)+K}$
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bodeplot
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22
GATE Electrical 2015 Set 2  Question: 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
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realroots
imaginaryroots
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23
GATE Electrical 2015 Set 2  Question: 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 ________.
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Control Systems
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openloopsystem
independantsystem
numericalanswers
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0
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24
GATE Electrical 2015 Set 2  Question: 11
The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is $V_{i} = 2 \sin(2\pi \times 2000t)$. The amplitude of the output voltage $V_{o}$ (in Volt) is ________.
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pidcontroller
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25
GATE Electrical 2015 Set 1  Question: 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 ... a frequency less than $K$ It corresponds to a frequency $K$ Root locus of modified system never transits to unstable region
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unityfeedbacksystem
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26
GATE Electrical 2015 Set 1  Question: 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 $(−2 \pm j3)$.
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secondorderrealsystem
poles
zeroes
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27
GATE Electrical 2015 Set 1  Question: 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 ... input and $y_{2}$ is the only output. When $u_{2}$ is the only input and $y_{2}$ is the only output.
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28
GATE Electrical 2015 Set 1  Question: 39
The opamp shown in the figure has a finite gain $A = 1000$ and an infinite input resistance. A stepvoltage $V_{i} = 1 \: mV$ 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 $V_{o}$ is $1001$ $101$ $11$ $1$
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29
GATE Electrical 2015 Set 1  Question: 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? $\dfrac{1000(s+10)}{s+1000} \\$ $\dfrac{10(s+10)}{s(s+1000)} \\$ $\dfrac{s+1000}{10s(s+10)} \\$ $\dfrac{s+1000}{10(s+10)}$
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30
GATE Electrical 2015 Set 1  Question: 25
For the signalflow graph shown in the figure, which one of the following expressions is equal to the transfer function $\dfrac{Y(s)}{X_{2}(s)}\bigg \vert _{X_{1}(s)=0}$ ? $\dfrac{G_{1}}{1+G_{2}(1+G_{1})} \\$ $\dfrac{G_{2}}{1+G_{1}(1+G_{2})} \\$ $\dfrac{G_{1}}{1+G_{1}G_{2}} \\$ $\dfrac{G_{2}}{1+G_{1}G_{2}}$
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31
GATE Electrical 2015 Set 1  Question: 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 ... to the phase angle of the input voltage? $0 \\$ $\pi \\$ $\dfrac{\pi}{2} \\$ $\dfrac{\pi}{2}$
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32
GATE Electrical 2015 Set 1  Question: 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 $(b)$? $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{4}{5} \\$ $1$
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33
GATE Electrical 2016 Set 2  Question: 52
The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function $G(s)=\frac{Ks}{(s1)(s4)}$ is $1$ $2$ $5$ $9$
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unityfeedbacksystem
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34
GATE Electrical 2016 Set 2  Question: 50
A secondorder 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 $1.02$ ... $\frac{102}{s^{2}+10s+100}$ $\frac{100}{s^{2}+10s+100}$ $\frac{102}{s^{2}+5s+100}$
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35
GATE Electrical 2016 Set 2  Question: 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 $0 < T < \frac{4(K+1)}{K1}$ $0 < K < \frac{4(T+2)}{T2}$ $0 < K < \frac{T+2}{T2}$ $0 < T < \frac{8(k+1)}{K1}$
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36
GATE Electrical 2016 Set 1  Question: 32
Loop transfer function of a feedback system is $G(s)H(s)=\dfrac{s+3}{s^{2}(s3)}$. 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
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mapping
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37
GATE Electrical 2016 Set 1  Question: 31
Consider the following statespace representation of a linear timeinvariant 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 __________.
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38
GATE Electrical 2016 Set 1  Question: 30
Consider the following asymptotic Bode magnitude plot ($\omega$ is in rad/s). Which one of the following transfer functions is best represented by the above Bode magnitude plot? $\dfrac{2s}{(1+0.5s)(1+0.25s)^{2}} \\$ $\dfrac{4(1+0.5s)}{s(1+0.25s)} \\$ $\dfrac{2s}{(1+2s)(1+4s)} \\$ $\dfrac{4s}{(1+2s)(1+4s)^{2}}$
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logarithmicplot
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39
GATE Electrical 2016 Set 1  Question: 6
The transfer function of a system is $\dfrac{Y(s)}{R(s)}=\dfrac{s}{s+2}$. The steady state output $y(t)$ is $A \cos (2t + \phi)$ for the input $\cos (2t)$. The values of $A$ and $\phi$ respectively are $\dfrac{1}{\sqrt{2}}, 45^\circ$ $\dfrac{1}{\sqrt{2}}, +45^\circ$ $\sqrt{2}, 45^\circ$ $\sqrt{2}, +45^\circ$
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laplacetransform
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40
GATE Electrical 2016 Set 1  Question: 7
The phase crossover frequency of the transfer function $G(s)=\dfrac{100}{(s+1)^{3}}$ in rad/s is $\sqrt{3} \\$ $\dfrac{1}{\sqrt{3}} \\$ $3 \\$ $3\sqrt{3}$
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