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.

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SubjectTopicYearType

A unity negative feedback system has the open-loop transfer function

G(s) = \frac{K}{s(s+1)(s+3)}

. The value of the gain

K (>0)

at which the root locus crosses the imaginary axis is ________

For the signal flow graph shown in the figure, the value of

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

Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued. The value of

f_{H}\: – f_{L}\:( \text{in}\: Hz)

is ___________.

For the system shown in the figure,

s=-2.75

lies on the root locus if

K

200\: m

long transmission line having parameters shown in the figure is terminated into a load ܴ

R_{L}

. The line is connected to a

400\: V

source having source resistance

R_{S}

through a switch, which is closed at

t = 0.

The transient response of the circuit at the input of the line

(z = 0)

is also drawn in the figure. The value of …

Consider two real valued signals,

x(t)

band-limited to

[-500\:Hz,500\:Hz]

y(t)

band-limited to

[-1\:kHz,1\:kHz].

z(t) = x(t)\cdot y(t),

the Nyquist sampling frequency (in

kHz

Consider the feedback system shown in the figure. The Nyquist plot of

G(s)

is also shown. Which one of the following conclusions is correct?

The phase margin in degrees of

G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}

calculated using the asymptotic Bode plot is ______.

The natural frequency of an undamped second-order system is

40

rad/s. If the system is damped with a damping ratio

0.3

, the damped natural frequency in

rad/s

is ___________.

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are

1

1

1 \Omega

, respectively, the operating angular frequency (in rad/s) is _________.

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is _________.

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a

4

th order all-pole system?

For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

The Bode plot of a transfer function

G(s)

is shown in the figure below. The gain

(20\log \mid G(s)\mid)

32\:dB

-8\:dB

1\:rad/s

10\:rad/s

respectively. The phase is negative for all

\omega.

G(s)

Assuming zero initial condition, the response

y(t)

of the system given below to a unit step input

u(t)

The signal flow graph for a system is given below. The transfer function

\dfrac{Y(s)}{U(s)}

for this system is

The state diagram of a system is shown below. A system is described by the state-variable equations

\dot{X}= AX+Bu;\:\: y = CX+Du

The state transition matrix

e^{At}

of the system shown in the figure above is

The open-loop transfer function of a unity-gain feedback control system is given by

\text{G}(s)=\frac{\text{K}}{(s+1)(s+2)}

The gain margin of the system in

\text{dB}

In the system shown below,

x(t)=(\sin t) u(t)

. In steady-steady-state, the response

y(t)

Consider the function

f(t)

having Laplace transform

\text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0

The final value of

f(t)