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 system with the open loop transfer function

\mathrm{G}(\mathrm{s}) \mathrm{H}(s)=\frac{1}{s\left(s^{2}+s+1\right)}

has a gain margin of

The characteristic polynomial of a system is

q(s)=2 s^{5}+s^{4}+4 s^{3}+2 s^{2}+2 s+1

. The system is

The transfer function of a system is

\mathrm{G}(s)=\frac{100}{(s+1)(s+100)}

. For a unit-step input to the system the approximate settling time for

2 \%

criterion is

The system shown in the figure is remains stable when

The Nyquist plot for the open-loop transfer function

G(s)

of a unity negative feedback system is shown in the figure, if

G(s)

has no pole in the right-half of

s

-plane, the number of roots of the system characteristic equation in the right-half of

s

-plane is

The root-locus diagram for a closed-loop feedback system is shown in the figure is. The system is overdamped.

If the characteristic equation of a closed-loop system is

s^{2}+2 s+2=0

, then the system is

The transfer function of a system is given by

H(s)=\frac{1}{s^{2}(s-2)}

. The impulse response of the system is

The feeback control system in the figure is stable.

The open-loop

\text{DC}

gain of a unity negative feedback system with closed-loop transfer function

\frac{s+4}{s^{2}+7 s+13}

An electrical system and its signal-flow graph representations are shown in the figure respectively. The values of

G_{2}

and

H

, respectively, are

A system with an input

x(t)

and output

y(t)

is described by the relation.

y(t)=t x(t)

. This system is

An amplifier with resistive negative feedback has two left half plane poles in its open-loop transfer function. The amplifier

Given that

\mathcal{L}[f(t)]=\frac{s+2}{s^2+1}, \mathcal{L}[f(t)]=\frac{s^2+1}{(s+3)(s+2)},

h(t)=\int_0^1 f(\tau) g(t-\tau) d \tau, \mathcal{L}[h(t)]

A system described by the transfer function

\mathrm{H}(s)=\frac{1}{s^{3}+\alpha s^{2}+k s+3}

is stable. The constraints on

\alpha

and

k

are

A system has a phase response given by

\phi(\omega)

, where

w

is the angular frequency. The phase delay and group delay at

\omega=\omega_{0}

are respectively given by

The phase margin (in degrees) of a system having the loop transfer function

\mathrm{G}(s) \mathrm{H}(s)=\frac{2 \sqrt{3}}{s(s+1)} \text{ is }

The system moded described by the state equations is

\begin{array}{l} \mathrm{X}=\left[\begin{array}{cc} 0 & 1 \\ 2 & -3 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 1 \end{array}\right] u \\ \mathrm{Y}=\left[\begin{array}{ll} 1 & 1 \end{array}\right] x \end{array}

The gain margin (in

d \mathrm{B}

) of a system a having the loop transfer function

\mathrm{G}(s) \mathrm{H}(s)=\frac{\sqrt{2}}{s(s+1)} \text{ is }

For a second-order system with the closed-loop transfer function

T(s)=\frac{9}{s^{2}+4 s+9}

the settling time for

2

- percent band, in seconds, is