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GATE2020EC: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{k(s+11)}{s(s+2)(s+8)}.$ The value of $\text{K}$, for which the system is marginally stable, is ___________.
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GATE2020EC: 49
A system with transfer function $G\left ( s \right )=\frac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5\cos3t.$ The steady state output of the system is $\frac{1}{\sqrt{10}}\cos\left ( 3t1.892 \right ).$ The value of $\text{a}$ is _______.
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3
GATE2020EC: 53
The transfer function of a stable discretetime $\text{LTI}$ system is $H\left ( z \right )=\frac{K\left ( z\alpha \right )}{z+0.5},$ where $\text{K}$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\left  \alpha \right > 1$ , for which the magnitude response of the system is constant over all frequencies, is ___________.
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gate2020ec
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4
GATE2019 EC: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \dfrac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
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Feb 12, 2019
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gate2019ec
networksolutionmethods
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5
GATE2019 EC: 31
Consider a causal secondorder system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unitstep $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steadystate value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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Feb 12, 2019
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gate2019ec
networksolutionmethods
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6
GATE2019 EC: 32
The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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gate2019ec
networksolutionmethods
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7
GATE2016330
A signal $2 \cos(\frac{2\pi}{3}t)\cos(\pi t)$ is the input to an LTI system with the transfer function $H(s)=e^s+e^{s}.$ If $C_k$ denotes the $k^{th}$ coefficient in the exponential Fourier series of the output signal, then $C_3$ is equal to $0$ $1$ $2$ $3$
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Mar 28, 2018
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gate2016ec3
continuoustimesignals
signalsandsystem
ltisystems
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8
GATE2016348
The forwardpath transfer function and the feedbackpath transfer function of a single loop negative feedback control system are given as $G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$ 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 _________
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gate2016ec3
numericalanswers
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9
GATE2016232
A continuoustime filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discretetime filter with transfer function $G\left ( z\right )= \frac{2z^{2}0.5032 \: z}{z^{2}0.5032 \: z+k}$ so ... filter, sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete timefilter. The value of $k$ is _________
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gate2016ec2
numericalanswers
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10
GATE2016145
The openloop transfer function of a unityfeedback control system is $G(s)= \frac{K}{s^2+5s+5}$. The value of $K$ at the breakaway point of the feedback contol system’s rootlocus plot is _________
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Mar 28, 2018
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gate2016ec1
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11
GATE2016146
The openloop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closedloop system to a unit step input to be $10 \%$, the value of $K$ is _________
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gate2016ec1
numericalanswers
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12
GATE2016147
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s 2$. The number of zeroes in the right half of the $s$plane is _________
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gate2016ec1
numericalanswers
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13
GATE2015321
The transfer function of a firstorder controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$
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gate2015ec3
networksolutionmethods
networks
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14
GATE2015219
By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the form $G_{1}(s)G_{2}(s) \\$ $\dfrac{G_{1}(s)}{G_{2}(s)} \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} + G_{2}(s)\right) \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)}  G_{2}(s)\right)$
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gate2015ec2
networksolutionmethods
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15
GATE2015221
A unity negative feedback system has an openloop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.
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gate2015ec2
numericalanswers
networksolutionmethods
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16
GATE2015247
The output of a standard secondorder system for a unit step input is given as $y(t) = 1\dfrac{2}{\sqrt{3}}e^{t}\cos \left(\sqrt{3t}\dfrac{\pi}{6}\right)$. The transfer function of the system is $\dfrac{2}{(s+2)(s+\sqrt{3})}$ $\dfrac{1}{s^{2}+2s+1}$ $\dfrac{3}{s^{2}+2s+3}$ $\dfrac{3}{s^{2}+2s+4}$
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gate2015ec2
networksolutionmethods
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17
GATE2015248
The transfer function of a massspringdamper system is given by $G(S) = \dfrac{1}{Ms^{2}+Bs+K}$ ... The unit step response of the system approaches a steady state value of ________.
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Mar 28, 2018
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gate2015ec2
numericalanswers
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18
GATE2015144
For the discretetime system shown in the figure, the poles of the system transfer function are located at $2,3 \\$ $\frac{1}{2},3 \\$ $\frac{1}{2}, \frac{1}{3} \\$ $2, \frac{1}{3}$
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gate2015ec1
networksolutionmethods
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19
GATE2015146
The openloop transfer function of a plant in a unity feedback configuration is given as $G(s) = \frac{K(s+4)}{(s+8)(s^29)}$. The value of the gain $K(>0)$ for which $1+j2$ lies on the root locus is _________.
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Mar 28, 2018
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gate2015ec1
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20
GATE2015147
A lead compensator network includes a parallel combination of $R$ and $C$ in the feedforward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}$, the value of $RC$ is ___________.
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gate2015ec1
numericalanswers
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21
GATE2015148
A plant transfer function is given as $G(s)= \bigg( K_p+ \frac{K_1}{s} \bigg) \frac{1}{s(s+2)}$. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is $K_p>\frac{K_1}{2}>0 \\$ $2K_1>K_p>0 \\$ $2K_1<K_p \\$ $2K_1>K_p$
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gate2015ec1
networksolutionmethods
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22
GATE2014447
Consider a transfer function $G_p(s) = \frac{ps^2+3ps2}{s^2+(3+p)s+(2p)}$ with $p$ a positive real parameter. The maximum value of $p$ until which $G_p$ remains stable is ___________.
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Mar 26, 2018
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gate2014ec4
numericalanswers
networksolutionmethods
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0
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23
GATE2014448
The characteristic equation of a unity negative feedback system is $1+KG(s)=0$. The open loop transfer function $G(s)$ has one pole at $0$ and two poles at $1$. The root locus of the system for varying $K$ is shown in the figure. The constant damping ratio line, ... locus at point A. The distance from the origin to point A is given as $0.5$. The value of $K$ at point A is ________.
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Mar 26, 2018
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gate2014ec4
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24
GATE2014318
For an allpass system $H(z)= \frac{(z^{1}b)}{(1az^{1})}$, where $\mid H(e^{j\omega }) \mid= 1,$ for all $\omega$. If $\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,$then $b$ equals $a$ $a^{*}$ $1/a^{*}$ $1/a$
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Mar 26, 2018
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gate2014ec3
networks
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25
GATE2014320
Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is $\frac{G_{1}G_{2}}{1+G_{1}G_{2}}$ $G_{1}G_{2}+G_{1}+1$ $G_{1}G_{2}+G_{2}+1$ $\frac{G_{1}}{1+G_{1}G_{2}}$
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Mar 26, 2018
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gate2014ec3
networksolutionmethods
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26
GATE2014344
Let $h(t)$ denote the impulse response of a causal system with transfer function $\frac{1}{s+1}.$ Consider the following three statements. $S1$: The system is stable. $S2$: $\frac{h(t+1)}{h(t)}$ is independent of $t$ for $t > 0$. $S3$: A noncausal system with the ... only $S1$ and $S2$ are true only $S2$ and $S3$ are true only $S1$ and $S3$ are true $S1$, $S2$ and $S3$ are true
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gate2014ec3
networksolutionmethods
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27
GATE2014221
For the following system, when $X_{1} (s) = 0$, the transfer function $\frac{Y(s)}{X_{2}(s)}$ is $\frac{s+1}{s^{2}}\\ $ $\frac{1}{s+1} \\$ $\frac{s+2}{s(s+1)} \\$ $\frac{s+1}{s(s+2)}$
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gate2014ec2
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28
GATE201254
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1,b=2$ $a=3,b=2$ $a=3,b=1$ $a=3,b=1$
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Mar 25, 2018
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gate2012ec
networksolutionmethods
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29
GATE201255
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $\frac{1}{\sqrt{3}}$ rad/s
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gate2012ec
networksolutionmethods
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30
GATE201220
A system with transfer function $G(s)=\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$ is excited by $\sin(\omega t)$. The steadystate output of the system is zero at $\omega=1\:rad/s$ $\omega=2\:rad/s$ $\omega=3\:rad/s$ $\omega=4\:rad/s$
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gate2012ec
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31
GATE201841
For a unity feedback control system with the forward path transfer function $G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}$The peak resonant magnitude $M_{r}$ of the closedloop frequency response is $2$. The corresponding value of the gain $\text{K}$ (correct to two decimal places) is _________.
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Feb 19, 2018
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gate2018ec
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1
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32
GATE201842
The figure below shows the Bode magnitude and phase plots of a stable transfer function $G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.$ Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop is stable for $k < k_{0}.$ The maximum value of $k_{0}$ is _________.
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33
GATE2017 EC2: 48
A unity feedback control system is characterized by the openloop transfer function $G(s)=\frac{10K(s+2)}{s^3+3s^2+10}$ The Nyquist path and the corresponding Nyquist plot of $G(s)$ are shown in the figures below. If $0 < K < 1$, then the number of poles of the closedloop transfer function that lie in the righthalf of the $s$plane is $0$ $1$ $2$ $3$
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34
GATE2017 EC2: 34
The transfer function of a causal LTI system is $H(s)=1/s$. If the input to the system is $x(t)=[\sin(t)/\pi t] u(t)$, where $u(t)$ is a unit step function, the system output $y(t)$ as $t\to \infty$ is ____________
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gate2017ec2
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35
GATE2017 EC1: 47
A linear time invariant (LTI) system with the transfer function $G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}3s+2)}$ is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for $0< K < \infty$ intersects the ... $K=1.5$. The closed loop system is stable for $K>1.5$ $1<K<1.5$ $0<K<1$ no positive value of $K$
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gate2017ec1
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