GATE : Control Systems National Champion Test for ESE & GATE EC Exams

Question 1

For the unity feedback system, the given system What will be the transfer function in the network shown below?

Question 2

An open loop system represented by the Transfer Function

is

Question 3

The system shown in the figure is

Question 4

The Bode plot of a Transfer Function G (5) is shown in the figure below.

The gain (20 log|G(s)|) is 32 dB and -8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G (s) is

Question 5

The gain margin of a unity feedback control system with the open loop transfer function G(s) =

is

Question 6

A system with transfer function

is excited by sin (ωt). The steady-state output of the system is zero at

Question 7

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function

?

Question 8

For a tachometer if θ(t) is rotor displacement is radians, e(t) is the output voltage and K_t is the tachometer constant in V/rad/sec, then the transfer function,

will be

Question 9

A control system is defined by the following mathematical relationship

The response of the system as t →

is

Question 10

The Transfer Function

of the circuit shown below is

Question 11

A unity feedback system has an open loop transfer function, $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-EE-ME-19-Mar\GATE-EE-2002_files\image116.png$ . The root locus plot is

Question 12

The transfer function of a second-order real system with a perfectly flat magnitude response of unity has a pole at (2 – j3). List all the poles and zeroes.

Question 13

Figure shows a feedback system where K > 0.

The range of K for which the system is stable will be given by

Question 14

The system

with A =

is

Question 15

Consider the following Nyquist plot of loop transfer function over ω = 0 to ω = ∞. Which of these plot’s represents a stable closed loop system.

Question 16

What will be the corner frequency, in Hz, for the system shown?

Question 17

The feedback system shown below oscillates at 2 rad/s when

Question 18

In the signal flow diagram given in the figure u₁ and u₂ are possible inputs possible inputs whereas y₁ and y₂ are possible outputs.
When would the SISO system derived from this diagram be controllable and observable?

Question 19

The following equation defines a separately excited dc motor in the form of a differential equation

The above equation may be organized in the state–space form as follows

Where the P matrix is given by

Question 20

The state variable description of a linear autonomous system is X = AX, where X is the two-dimensional state vector and A is the system matrix given by The roots of the characteristic equation are

Question 21

For the system

with u as unit impulse and with zero initial state, the output y, becomes

Question 22

The transfer functions of two compensators are given below:

Which one of the following statements is correct?

Question 23

The system

is to be compensated such that its gain-crossover frequency becomes same as its uncompensated phase-crossover frequency and provides a 45^o phase margin. To achieve this, one may use

Question 24

The transfer functions of two compensators are given below:

Which one of the following statements is correct?

Question 25

The Laplace transform of a function f(t) is F(s) =

As t →∞, f(t) approaches

Question 26

The block diagram of a closed loop control system is given by figure. The values of K and P such that the system has a damping ratio of 0.7 and an undamped natural frequency ω_n of 5 rad/sec, are respectively equal to

Question 27

Which is correct about control system block diagram?

Question 28

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

This transfer function has

Question 29

For the equation If X(0)=0, & X'(0)= 0 then the solution x(t) approaches the following values at t →∞

Question 30

The block diagram shown in figure gives a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is