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Recent questions tagged control-systems

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GATE Electrical 2026 | Question: 3
The Laplace transform of the step response of a system is given by\[Y(s)=\frac{100}{s(s+100)}\]The rise time is defined as the time taken for the response to go from $0.1...
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GATE Electrical 2026 | Question: 19
The asymptotic Bode magnitude plot of a system is shown.Which one of the following options best represents the transfer function of the system?$G(s)=\dfrac{1+\dfrac{s}{\o...
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GATE Electrical 2026 | Question: 42
A system is characterized by the following state equation and output equation ( $u$ : input, $\mathbf{X}$ : state vector, $y$ : output)\[\begin{array}{c}\dot{\mathbf{x}}=...
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GATE Electrical 2026 | Question: 43
A system is represented in state-space form as follows:( $u$ : input, $\mathbf{X}$ : state vector, $y$ : output)\[\begin{array}{c}\dot{\mathbf{x}}=\left[\begin{array}{cc}...
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GATE Electrical 2025 | Question: 12
Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of t...
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GATE Electrical 2025 | Question: 13
The Nyquist plot of a strictly stable $G(s)$ having the numerator polynomial as $(s-3)$ encircles the critical point $-1$ once in the anti-clockwise direction. Which one ...
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347
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GATE Electrical 2025 | Question: 19
The open-loop transfer function of the system shown in the figure, is$$ G(s)=\frac{K s(s+2)}{(s+5)(s+7)}$$For $K \geq 0$, which of the following real axis point(s) is/are...
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GATE Electrical 2025 | Question: 31
Let $G(s)=\frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, isstable for all $K>2$.unstable for all $K>2$.unstable for all $K>1$.stable for al...
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GATE Electrical 2025 | Question: 32
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system $\boldsymbol{S}$. The output is observed to be the contin...
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GATE Electrical 2025 | Question: 44
Consider ordinary differential equations given by$\begin{array}{l} \dot{x}_{1}(t)=2 x_{2}(t) \\ \dot{x}_{2}(t)=r(t) \end{array}$with initial conditions $x_{1}(0)=1$ and $...
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GATE Electrical 2025 | Question: 52
Consider the state-space model$\begin{array}{l}\dot{\boldsymbol{x}}(t)=A \boldsymbol{x}(t)+B r(t) \\y(t)=C \boldsymbol{x}(t)\end{array}$where $\boldsymbol{x}(t), r(t), y(...
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223
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GATE Electrical 2025 | Question: 55
A controller $D(s)$ of the form $\left(1+K_{D} s\right)$ is to be designed for the plant $G(s)=\frac{1000 \sqrt{2}}{s(s+10)^{2}}$ as shown in the figure. The value of $K_...
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GATE Electrical 2024 | Question: 10
​​​​For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is$\frac{G(s)}{1+2 G(s)}$$-\frac{G(s)}{1+2 G(s)}$$\frac{G(s)}{1-2 G(s)}$$-\frac{G...
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GATE Electrical 2024 | Question: 11
​​​​​Consider the standard second-order system of the form $\frac{\omega_{n}^{2}}{s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}}$ with the poles $p$ and $p^{*}$ having negati...
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GATE Electrical 2024 | Question: 12
​​​​Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a firstorder pol...
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GATE Electrical 2024 | Question: 35
Which of the following differential equations is/are nonlinear?$t x(t)+\frac{d x(t)}{d t}=t^{2} e^{t}, \quad x(0)=0$$\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(...
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GATE Electrical 2024 | Question: 47
Consider the closed-loop system shown in the figure with\[G(s)=\frac{K\left(s^{2}-2 s+2\right)}{\left(s^{2}+2 s+5\right)} .\]The root locus for the closed-loop system is ...
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970
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GATE Electrical 2024 | Question: 48
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20 \mathrm{~dB} /$ decade at least till...
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GATE Electrical 2024 | Question: 49
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of...
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GATE Electrical 2023 | Question: 2
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is$\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}...
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587
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GATE Electrical 2023 | Question: 3
In the Nyquist plot of the open-loop transfer function$$G(s)H(s) = \frac{3s+5}{s-1}$$corresponding to the feedback loop shown in the figure, the infinite semi-circular ar...
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GATE Electrical 2023 | Question: 4
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral...
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GATE Electrical 2023 | Question: 26
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$$\frac{e^{-2.514 s}}{s+1}$$1.04...
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GATE Electrical 2023 | Question: 28
Consider a lead compensator of the form $$K(s)=\frac{1+\frac{s}{a}}{1+\frac{s}{\beta a}}, \beta>1, a>0$$The frequency at which this compensator produces maximum phase lea...
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267
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GATE Electrical 2023 | Question: 36
Consider the state-space description of an $\text{LTI}$ system with matrices$\qquad A=\left[\begin{array}{cc}0 & 1 \\-1 & -2\end{array}\right], B=\left[\begin{array}{l}0 ...
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561
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GATE Electrical 2022 | Question: 1
The transfer function of a real system, $H(s)$, is given as:$H\left ( s \right ) = \dfrac{As + B}{S^{2} + Cs + D}$where $\text{A, B, C}$ and $D$ are positive constants. T...
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633
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GATE Electrical 2022 | Question: 7
The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is $-180^{\circ}$. Th...
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335
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GATE Electrical 2022 | Question: 9
The open loop transfer function of a unity gain negative feedback system is given by $G\left ( s \right ) = \dfrac{k}{s^{2}+4s-5}$. The range of $k$ for which the system ...
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GATE Electrical 2022 | Question: 27
An $\text{LTI}$ system is shown in the figure where $$G \left ( s \right ) = \dfrac{100}{s^{2}+0.1s+100}$$ The steady state output of the system, to the input $r(t)$, is ...
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GATE Electrical 2022 | Question: 28
The open loop transfer function of a unity gain negative feedback system is given as $$G \left ( s \right ) = \dfrac{1}{s\left ( s+1 \right )}$$The Nyquist contour in the...
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