GATE EC Control Systems questions

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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 Nyquist plot of the transfer function

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

does not encircle the point

(-1+j0)

K=10

but does encircle the point

(-1+j0)

K=100

. Then the closed loop system (having unity gain feedback) is

For the system shown in the figure,

Y(s)/X(s)

Which of the following statements is incorrect?

Consider an LTI system with magnitude response

\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid > 20 \end{cases}

and phase response

\arg \{ H(f) \}= – 2f.

If the input to the system is …

The transfer function of a causal LTI system is

H(s)=1/s

. If the input to the system is

x(t)=[\sin(t)/\pi t] u(t)

u(t)

is a unit step function, the system output

y(t)

t\to \infty

is ____________

A unity feedback control system is characterized by the open-loop transfer function

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

</em>k

for which the system oscillates at

2

rad/s is ___________

A second-order LTI system is described by the following state equations,

\begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{array}

x_1(t)

x_2(t)

are the two state variables and

r(t)

denotes the input. The output

c(t)=x_1(t)

. The system is

A unity feedback control system is characterized by the open-loop transfer function

G(s)=\frac{10K(s+2)}{s^3+3s^2+10}

The Nyquist path and the corresponding Nyquist plot of

G(s)

are shown in the figures below. If

0 < K < 1

, then the number of poles of the closed-loop transfer function that lie in the right-half of the

s

Consider the plot

f(x)

x

as shown below. Suppose

F(x)= \int_{-5}^{x} f(y) dy

. Which one of the following is a graph of

F(x)

Match the inferences

X

Y

Z

, about a system,to the corresponding properties of the elements of first column in Rouths' Table of the system characteristic equation. …

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

z

-parameter matrix for the two-port network shown is

\begin{bmatrix} 2j\omega &j\omega \\ j\omega & 3+2j\omega \end{bmatrix},

where the entries are in

\Omega

Z_{b}\left ( j\omega \right )=R_{b}+j\omega .

Then the value of

R_{b}

\Omega

) equals ________

The number and direction of encirclements around the point

-1+j0

in the complex plane by the Nyquist plot of

G(s)=\frac{1-s}{4+2s}

The asymptotic Bode phase plot of

G\left ( s \right )=\frac{k}{\left ( s+0.1 \right )\left ( s+10 \right )\left ( s+p_{1} \right )},

k

p_{1}

both positive, is shown below. The value of

p_{1}

Consider the signal

x(t) = \cos(6\pi t) + \sin (8\pi t)

t

is in seconds. The Nyquist sampling rate (in samples/second) for the signal

y(t) = x(2t + 5)

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

G

of the system is

For the unity feedback control system shown in the figure, the open-loop transfer function

G(s)

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

The steady state error

e_{ss}

due to a unit step input is

An analog baseband signal, bandlimited to

100\ Hz

, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities

p_1 = p_4 = 0.125

p_2 = p_3

. The information rate (bits/sec) of the message source is _______

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as

\begin{array}{|c|cc} \hline s^3 & 1 &(2K+3) \\ s^2 & 2K & 4 \end{array}

K

for which the system is stable is

Negative feedback in a closed-loop control system

\textbf{ DOES NOT}