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

Consider two transfer functions

\mathrm{G}_1(s)=\frac{1}{s^2+a s+b} \text{ and } \mathrm{G}_2(s)=\frac{s}{s^2+a s+b}

3\text{-dB}

bandwidths of their frequency responses are, respectively

A negative resistance

R_{\text{neg }}

is connected to a passive network

N

having driving point impedance

Z_{1}

(s) as shown below. For

Z_{2}(s)

to be positive real,

The unit-step response of a system starting from rest is given by

\qquad C(t)=1-e^{-2 t} \text{ for } t \geq 0

The transfer function of the system is

The Nyquist plot of

\mathrm{G}(j \omega) \mathrm{H}(j \omega)

for a closed loop control system, passes through

(-1, j 0)

\mathrm{GH}

plane. The gain margin of the system in

\mathrm{dB}

The positive values of

\text{“K”}

a

” so that the system shown in the figure below oscillates at a frequency of

2 \mathrm{rad} / \mathrm{sec}

respectively are

The unit impulse response of a system is

h(t)=e^{-t}, t \geq 0

For this system, the steady-state value of the output for unit step input is equal to

The transfer function of a phase-lead compensator is given by

G_{c}(s)=\frac{1+3 T s}{1+T s} \text{ where } T>0

The maximum phase-shift provided by such a compensator is

A linear system is described by the following state equation

X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc} 0 & 1 \\ -1 & 0\end{array}\right]

The state-transition matrix of the system is

Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is

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

a

' so that the system has a phase-margin equal to

\frac{\pi}{4}

is approximately equal to

Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is

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

With the value of '

a

' set for a phase-margin of

\frac{\pi}{4}

, the value of unit-impulse response of the open-loop system at

t=1

second is equal to

A linear system is equivalently represented by two sets of state equations.

\dot{X}=\mathrm{AX}+\mathrm{BU} \text{ and } \dot{W}=\mathrm{CW}+\mathrm{DU} \text{. }

The eigenvalues of the representations are also computed as

\{\lambda\}

\{\mu\}

. Which one of the following statements is true?

Despite the presence of negative feedback, control systems still have problems of instability because the

The polar diagram of a conditionally stable system for open loop gain

\text{K}=1

is shown in the figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

In the derivation of expression for peak percent overshoot,

M_{p}=\exp \left(\frac{-\pi \zeta}{\sqrt{1-\zeta^{2}}}\right) \times 100 \%

, which one of the following conditions is NOT required?

A ramp input applied to an unity feedback system results in

5 \%

steady state error. The type number and zero frequency gain of the system are respectively

A double integrator plant,

\mathrm{G}(s)=\frac{\mathrm{K}}{s^{2}}, \mathrm{H}(\mathrm{s})=1

is to be compensated to achieve the damping ratio

\zeta=0.5

, and an undamped natural frequency,

\omega_{n}=5 \; \mathrm{rad/s}

. Which one of the following compensator

G_{e}(s)

will be suitable?

Statement for Linked Answer Questions 82a and 82b: The dopen loop transfer function of a unity feedback system is given by

\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}

The gain and phase crossover frequencies in

\mathrm{rad} / \mathrm{sec}

are, respectively

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

, the point of intersection of the asymptotes of the root loci with the real axis is

Consider the Bode magnitude plot shown in the given figure. The transfer function

\mathrm{H}(s)

The transfer function

H(s)=\frac{V_{0}(s)}{V_{i}(s)}

of an R-L-C circuit is given by

H(s)=\frac{10^{6}}{s^{2}+20 s+10^{6}}

The Quality factor (Q-factor) of this circuit is