Wednesday, April 29, 2015

GATE 2013 Control Systems - Complete Video Solutions


1. The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20log|G(s)|) is 32 dB and – 8 dB at 1 rad/sec and 10 rad/sec respectively. The phase is negative for all ω. Then G(s) is
a) 39.8/s
b) 39.8/s2
c) 32/s
d) 32/s2


2. Which one of the following is NOT TRUE for a continuous time causal and stable LTI system?
a) all the poles of the system must lie on the left side of the jω axis
b) zeros of the system can lie anywhere in the s-plane
c) all the poles must lie with in |s| = 1
d) all the roots of the characteristic equation must be located on the let side of the jω axis


3. A polynomial f(x) = a4x4+a3x3+a2x2+a1xa0 with all coefficients positive has
a) no real roots
b) no negative real root
c) odd number of real roots
d) at least one positive and one negative real root

Solution :

4. Assuming zero initial conditions, the response y(t) of the system given below for a unit step input, u(t) is __________________

a) u(t)
b) t.u(t)
c) (1/2)t2.u(t)
d) e-t.u(t)


5. The transfer function V2(s)/V1(s) of the circuit shown is


6. The open loop transfer function of a DC motor is given as ω(s)/Va(s) = 10/(1+10s). when connected in feedback as shown below.
The approximate value of Ka that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open loop system is
a) 1
b) 5
c) 10
d) 100


7. A system is described by the differential equation d2y/dt2+5dy/dt+6y(t) = x(t). Let x(t) be a rectangular pulse given as x(t) = 1 for 0<t<2 and zero otherwise. Assuming that y(0) = 0 and dy/dt = 0 at t=0, then the Laplace transform of y(t) is


8. The signal flow graph for a system is given below.
The transfer function Y(s)/U(s) for this system is


9. The state diagram of the system is shown below. A system is described by the state variable equations

a. State variable equations of the system shown in the above figure is


b. The state transition matrix eAt of the system shown in the figure above is

Solution (a & b) :

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