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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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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: 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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228
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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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725
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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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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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592
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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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339
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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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552
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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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