GATE EC Control Systems questions

Practise Control Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify the feedback structure before forming the transfer function. Check the characteristic equation and stability conditions before calculating steady-state behaviour.

20 on this page

SubjectTopicYearType

A causal system having the transfer function

\mathrm{H}(s)=\frac{1}{s+2}

is excited with

10 u(t)

. The time at which the output reaches

99 \%

of its steady state value is

A system has poles at

0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}

and

80 \mathrm{~Hz}

; zeros at

5 \mathrm{~Hz}, 100 \mathrm{~Hz}

and

200 \mathrm{~Hz}

. The approximate phase of the system response at

20 \mathrm{~Hz}

Consider the signal flow graph shown in the figure below. The gain

\frac{x_{5}}{x_{1}}

The open-loop transfer function of a unity feedback system is

G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}

The range of

\mathrm{K}

for which the system is stable is

For the polynomial

P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15

, the number of roots which lie in the right half of the s-plane is

The state variable equations of a system are:

\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}

The system is

Given

A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]

, the state transition matrix

e^{A t}

is given by

The Laplace transform of

i(t)

is given by

I(s)=\frac{2}{s(1+s)}

t \rightarrow \infty

, the value of

i(t)

lends to

The figure shows the Nyquist plot of the open-loop transfer function

\mathrm{G}(\mathrm{s}) \mathrm{H}(s)

of a system. If

\mathrm{G}(s) \mathrm{H}(\mathrm{s})

has one right-hand pole, the closed-loop system is

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

The signal flow graph of a system is shown in the figure. The transfer function

\frac{C(s)}{R(s)}

of the system is

The root locus of the system

\mathrm{G}(\mathrm{s}) \mathrm{H}(s)

=\frac{\mathrm{K}}{s(s+2)(s+3)}

has the break-away point located at

The approximate Bode magnitude plot of a minimum-phase system is shown in the figure. The transfer function of the system is

A second-order system has the transfer function

\frac{C(s)}{R(s)}=\frac{4}{s^{2}+4 s+4}

. With

r(t)

as the unit-step function, the response

c(t)

of the system is represented by

The gain margin and the phase margin of a feedback system with

\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{\mathrm{s}}{(\mathrm{s}+100)^{3}}

are

The zero-input response of a system given by the state-space equation

\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}\right]

and …

The transfer function

\mathrm{Y}(s) / \mathrm{U}(\mathrm{s})

of a system described by the state equations

x(t)=-2 x(t)+2 u(t)

and

y(t)=0.5 x(t)

The phase margin of a system with the open-loop transfer function

\mathrm{G}(s) \mathrm{H}(s)=\frac{(1-s)}{(1+s)(2+s)}

Which of the following points is NOT on the root locus of a system with the open-loop transfer function

\mathrm{G}(s) \mathrm{H}(s)=\frac{k}{s(s+1)(s+3)}

Consider a system with the transfer function

G(s)=\frac{s+6}{k s^2+s+6}

. Its damping ratio will be

0.5

when the value of

k