Hot questions in Control Systems / GO Electrical

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21

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 $h_0=b_0-b_1a_1$ , the input-output transfer function, $G(s)=\dfrac{C(s)}{U(s)}$ ... $G(s)=\dfrac{b_1s+b_0}{s^2+a_1s+a_0} \\$ $G(s)=\dfrac{a_0s+a1}{s^2+b_0s+b_1}$

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 functi...

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GATE Electrical 2014 Set 2 | Question: 33
A discrete system is represented by the difference equation $\begin{bmatrix} X_1(k+1)\\ X_2(k+2) \end{bmatrix}=\begin{bmatrix} a & a-1\\ a+1 & a \end{bmatrix}\begin{bmatrix} X_1(k)\\X_2(k) \end{bmatrix}$ It has initial conditions $X_1(0)$ = $1$ ... $a$ = $1$, are $1\pm j0$ $-1\pm j0$ $\pm 1+j0$ $0\pm j1$

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{bmatri...

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23

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

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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24

GATE Electrical 2013 | Question: 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 $1$ $5$ $10$ $100$

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 ...

piyag476

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piyag476 asked Feb 11, 2017

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25

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 $(b)$? $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{4}{5} \\$ $1$

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 sho...

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26

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 ________.

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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27

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 $1$ $s$ $1/s$ $\dfrac{-s}{s^3+s^2-s-2}$

The block diagram of a system is shown in the figureIf 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$$\d...

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28

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 $0$ $1/2$ $2/3$ $1$

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{v...

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29

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

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 $j\omega$ axisZ...

piyag476

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30

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

The second order dynamic system$\dfrac{dX}{dt}=PX+Qu$$y=RX$has the matrices $P$, $Q$ and $R$ as follows:$P=\begin{bmatrix} -1 & 1\\ 0& -3 \end{bmatrix}$ $Q=\begin{bmatri...

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31

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.

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 deriv...

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32

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 ________.

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 $V_{o}$ (i...

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33

GATE Electrical 2016 Set 2 | Question: 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 $1.02$ ... $\frac{102}{s^{2}+10s+100}$ $\frac{100}{s^{2}+10s+100}$ $\frac{102}{s^{2}+5s+100}$

A second-order real system has the following properties:a) the damping ratio $\zeta=0.5$ and undamped natural frequency $\omega _{n}=10$ rad/sb) the steady state value of...

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makhdoom ghaya asked Jan 29, 2017

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34

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? $\dfrac{2s}{(1+0.5s)(1+0.25s)^{2}} \\$ $\dfrac{4(1+0.5s)}{s(1+0.25s)} \\$ $\dfrac{2s}{(1+2s)(1+4s)} \\$ $\dfrac{4s}{(1+2s)(1+4s)^{2}}$

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...

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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 $0 < T < \frac{4(K+1)}{K-1}$ $0 < K < \frac{4(T+2)}{T-2}$ $0 < K < \frac{T+2}{T-2}$ $0 < T < \frac{8(k+1)}{K-1}$

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 ...

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36

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 $G(s)=\frac{Ks}{(s-1)(s-4)}$ is $1$ $2$ $5$ $9$

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$

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37

GATE Electrical 2016 Set 1 | Question: 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 __________.

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...

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38

GATE Electrical 2016 Set 1 | Question: 32
Loop transfer function of a feedback system is $G(s)H(s)=\dfrac{s+3}{s^{2}(s-3)}$. 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

Loop transfer function of a feedback system is $G(s)H(s)=\dfrac{s+3}{s^{2}(s-3)}$. Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $G(s) H ...

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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 $\dfrac{1}{\sqrt{2}}, -45^\circ$ $\dfrac{1}{\sqrt{2}}, +45^\circ$ $\sqrt{2}, -45^\circ$ $\sqrt{2}, +45^\circ$

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 ...

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40

GATE Electrical 2016 Set 1 | Question: 7
The phase cross-over frequency of the transfer function $G(s)=\dfrac{100}{(s+1)^{3}}$ in rad/s is $\sqrt{3} \\$ $\dfrac{1}{\sqrt{3}} \\$ $3 \\$ $3\sqrt{3}$

The phase cross-over 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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makhdoom ghaya asked Jan 29, 2017