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

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

(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}

k, z, p, a, b

c

are positive constants. The value of

(a+b+c)

is ____________ (rounded off to the nearest integer).

Consider a closed-loop control system with unity negative feedback and

KG(s)

in the forward path. where the gain

K = 2.

The complete Nyquist plot of the transfer function

G(s)

is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume

G(s)

has no poles on the closed right-half of the complex …

The root-locus plot of a closed-loop system with unity negative feedback and transfer function

KG(s)

in the forward path is shown in the figure. Note that

K

0

\infty.

Select the transfer function

G(s)

that results in the root-locus plot of the closed-loop system as shown in the figure.

Consider an even polynomial

p(s)

p(s) = s^{4} + 5s^{2} + 4 + K,

K

is an unknown real parameter. The complete range of

K

p(s)

has all its roots on the imaginary axis is _____________.

Two linear time-invariant systems with transfer functions

G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}

have unit step responses

y_{1}(t)

y_{2}(t),

respectively. Which of the following statements is/are true?

The block diagram of a closed-loop control system is shown in the figure.

R(s), Y(s),

D(s)

are the Laplace transforms of the time-domain signals

r(t), y(t),

d(t),

respectively. Let the error signal be defined as

e(t) = r(t) – y(t).

Assuming the reference input

r(t) = 0

t,

the steady-state error

e (\infty),

The block diagram of a feedback control system is shown in the figure The transfer function

\dfrac{Y{\left ( s \right )}}{X {\left ( s \right )}}

of the system is

The complete Nyquist plot of the open-loop transfer function

G(s)H(s)

of a feedback control system in the figure. If

G(s)H(s)

has one zero in the right-half of the

s

-plane, the number of poles that the closed-loop system will have in the right-half of the

s

The electrical system shown in the figure converts input source current

i_{s}(t)

to output voltage

v_{o}(t)

i_{L}(t)

in the inductor and voltage

v_{c}(t)

across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e.,

i_{L}(0) =0

v_{c}(0)=0

. The system is

A unity feedback system that uses proportional-integral (

\text{PI}

) control is shown in the figure. The stability of the overall system is controlled by tuning the

\text{PI}

control parameters

K_{P}

K_{I}

. The maximum value of

K_{I}

that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable …

P, Q

R

are the decimal integers corresponding to the

4

-bit binary number

1100

considered in signed magnitude,

1

’s complement, and

2

’s complement representations, respectively. The

6

2

’s complement representation of

(P+Q+R)

The state diagram of a sequence detector is shown below. State

S_{0}

is the initial state of the sequence detector. If the output is

1

The characteristic equation of a system is

s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.

In the root locus plot for the given system, as

K

0

\infty

, the break-away or break-in points(s) lie within

The components in the circuit given below are ideal. If

R=2\:k \Omega

C=1

\mu F

-3

dB cut-off frequency of the circuit in Hz is

It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form

x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\dfrac{j\pi n}{2}\right),

c_{1}

c_{2}

are arbitrary real numbers. The desired three-tap filter is given by

h[0]=1,\quad h[1]=a,\quad h[2]=b

The state transition diagram for the circuit shown is

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability od feedback controllers. Identify which of the following statements is FALSE:

The open loop transfer function

G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}

p

is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is

6

for unit ramp input, the parameter

p

Consider a stable system with transfer function,

G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}

b_1, \dots ,b_p

a_1, \dots ,a_q

are real valued constants.The slope of the Bode log magnitude curve of

G(s)

-60 \text{dB/decade}

ω\to \infty

.A possible pair of values for

p

A linear time invariant (LTI) system with the transfer function

G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}

is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for

0< K < \infty

intersects the imaginary axis for

K=1.5

. The closed loop system is stable for