GATE 2011 ECE - Control Systems - Complete Video Solutions

2011

1. The differential equation 100d²y/dt²-20dy/dt+y = x(t) describes a system with an input x(t) and an output y(t).The system which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

Answer:A

Solution :   https://www.youtube.com/watch?v=nGDKxd0P1DA

2. for the transfer function G(jω) = 5 + jω, the corresponding Nyquist plot for positive frequency has the form

Answer:A

Solution :   https://www.youtube.com/watch?v=F0oR9sCCy80

3. The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by

Answer:B

Solution :   https://www.youtube.com/watch?v=ARZuGJ_JqBo

4. The block diagram of a system with one input u and two outputs y₁ and y₂ is given below.

A state space model of the system in terms of the state vector ẋ and the vector ẏ = [y₁ y₂]^T is

Answer:B

Solution :  https://www.youtube.com/watch?v=CsciojvPQF8

5. If F(s) = L[f(t)] = 2(s+1)/(s²+4s+7), then the initial and final values of f(t) are respectively

a) 0,2

b) 2,0

c) 0,2/7

d) 2/7,0

Answer:B

Solution :   https://www.youtube.com/watch?v=Eq8IxIWokfo

Common Data Questions 6 & 7:

The input – output transfer function of a plant H(s) = 100/s(s+10)². The plant is placed in a unity negative feedback configuration as shown in figure below.

6. The signal flow graph that DOES NOT model the plant transfer function H(s) is

Answer:D

Solution :   https://www.youtube.com/watch?v=gSg5jPv06fQ

7. The gain margin of the system under closed loop unity negative feedback is

a) 0 dB

b) 20 dB

c) 26 dB

d) 46 dB

Answer:C

Solution :   https://www.youtube.com/watch?v=HreyReFPqag