### 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

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

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

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 and the vector = [y1 y2]T

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

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

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