Register

Recent questions and answers in Control Systems

0 0 votes
1 1 answer
263
263 views
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 $0.1...
User Avatar
0 0 votes
0 0 answers
88
88 views
GATE Electrical 2026 | Question: 19
The asymptotic Bode magnitude plot of a system is shown.Which one of the following options best represents the transfer function of the system?$G(s)=\dfrac{1+\dfrac{s}{\o...
User Avatar
0 0 votes
0 0 answers
71
71 views
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}}=...
User Avatar
0 0 votes
0 0 answers
65
65 views
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}...
User Avatar
1 1 vote
1 1 answer
347
347 views
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...
User Avatar
0 0 votes
0 0 answers
539
539 views
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...
User Avatar
1 1 vote
0 0 answers
634
634 views
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 ...
User Avatar
0 0 votes
0 0 answers
187
187 views
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...
User Avatar
0 0 votes
0 0 answers
181
181 views
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(...
User Avatar
0 0 votes
0 0 answers
223
223 views
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_...
User Avatar
0 0 votes
0 0 answers
1.3k
1.3k views
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...
User Avatar
0 0 votes
0 0 answers
951
951 views
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...
User Avatar
0 0 votes
0 0 answers
1.6k
1.6k views
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...
User Avatar
0 0 votes
0 0 answers
720
720 views
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 ...
User Avatar
0 0 votes
0 0 answers
968
968 views
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...
User Avatar
0 0 votes
0 0 answers
636
636 views
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...
User Avatar
0 0 votes
0 0 answers
809
809 views
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}...
User Avatar
0 0 votes
0 0 answers
584
584 views
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...
User Avatar
0 0 votes
0 0 answers
324
324 views
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...
User Avatar
0 0 votes
0 0 answers
549
549 views
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...
User Avatar
0 0 votes
0 0 answers
265
265 views
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 ...
User Avatar
0 0 votes
0 0 answers
632
632 views
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...
User Avatar
0 0 votes
0 0 answers
334
334 views
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 ...
User Avatar
0 0 votes
0 0 answers
351
351 views
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 ...
User Avatar
0 0 votes
0 0 answers
781
781 views
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...
User Avatar
0 0 votes
0 0 answers
371
371 views
GATE Electrical 2022 | Question: 29
The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $\zeta$ and $\omega_{n}$, respectively. The values of $\ze...
User Avatar
0 0 votes
0 0 answers
329
329 views
GATE Electrical 2021 | Question: 11
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is$\frac{G}{1+GH}$$\frac{GH}{1+GH}$$\frac{1}{1+GH}$$\frac{1}{1+...
User Avatar
0 0 votes
0 0 answers
401
401 views
GATE Electrical 2021 | Question: 20
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$...
User Avatar
0 0 votes
0 0 answers
333
333 views
GATE Electrical 2021 | Question: 46
Consider a closed-loop system as shown. $G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )}$ is the plant transfer function and $G_{c}(S)=1$ is the compensato...
User Avatar
0 0 votes
0 0 answers
343
343 views
GATE Electrical 2021 | Question: 47
In the given figure, plant $G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )}$ and compensator $G_{C}\left ( s \r...
User Avatar
Help get things started by asking a question.