### GATE 2012 Control Systems - Complete Video Solutions

2012

1. The unilateral Laplace transform of f(t) is 1/(s2+s+1). The unilateral transform of t.f(t) is

2. With initial condition x(1) = 0.5, the solution of the differential equation, t.(dx/dt)+x = t is
a) x = t – 1/2
b) x = t2 – 1/2
c) x = t2/2
d) x = t/2

3. A system with transfer function is excited by sin(ωt).
The steady state output of the system is zero at

4. The feedback system shown below oscillates at 2 rad/sec, when

a) K = 2 and a = 0.75
b) K = 3 and a = 0.75
c) K = 4 and a = 0.5
d) K = 2 and a = 0.5

5. The state variable description of an LTI system is by

where y is the output and u is the input. The system is controllable for
a) a1 0, a2 = 0, a3 = 0
b) a1 = 0, a2 0, a3 0
c) a1 = 0, a2 0, a3 = 0
d) a1 0, a2 0, a3 = 0

The transfer function of a compensator is given as Gc(s)= (s+a)/(s+b).

6. Gc(s) is a lead compensator if
a) a = 1, b =2
b) a = 3, b =2
c) a = –3, b = –1
d) a = 3, b =1

7. The phase of the above lead compensator is maximum at