**2003**

1. The Laplace transform of i(t) is given by I(s) = 2 / [s(1 + s)]. As t → ∞, the value of i(t) tends to

a) 0

b) 1

c) 2

d) ∞

**Solution :**https://www.youtube.com/watch?v=DK3hqukI4co

**2**. The signal flow graph of a system is shown in figure.

The transfer function C(s)/R(s) of the system is

**Solution :**https://www.youtube.com/watch?v=UiYZch03Bsg

**2004**

1. Consider the signal flow graph shown in figure. The gain X

_{5}/X

_{1}is

**Solution :**https://www.youtube.com/watch?v=e6XPNiFMSGo

**2005**

1. Despite the percentage of negative feedback, control systems still have problems of Instability because the

a) components used have non-linearity

b) dynamic equations of the sub-systems are not know exactly

c) mathematical analysis involves approximations

d) system has large negative phase angle at high frequencies

**Solution :**https://www.youtube.com/watch?v=1FtNWWBjrSU

**2006**

1. In the system shown below, x(t) = (sint).u(t).

In steady state, the response y(t) will be

**Solution :**https://www.youtube.com/watch?v=QR9858_QPOg

2. The unit impulse response of a system is h(t) = e

^{–t}, t ≥ 0. For this system, the steady state value of the output for unit step input is equal to

a) –1

b) 0

c) 1

d) ∞

**Solution :**https://www.youtube.com/watch?v=8jfSroqXbV8

**2007**

1. If the Laplace Transform of a signal y(t) is Y(s) = 1

**/**[s(s – 1)], then its final value is:

a) – 1

b) 0

c) 1

d) unbounded

**Solution :**https://www.youtube.com/watch?v=cvCDerivzj0

**2010**

1. Given f(t) = L

^{–1}[(3s + 1) / (s

^{3}+ 4s

^{2}+ (k-3)s)]. If Lim

_{t -> ∞}f(t) = 1, then the value of k is

a) 1

b) 2

c) 3

d) 4

**Solution :**https://www.youtube.com/watch?v=q65ZfJH4Ww0

**2011**

1. If F(s) = L[f(t)] = 2(s+1)/(s

^{2}+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

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

**Common Data Questions 2 & 3:**

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.

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

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

3. 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

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

**2012**

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

^{2}+s+1). The unilateral transform of t.f(t) is

**Solution :**https://www.youtube.com/watch?v=91xwp0WF7Lw

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 = t

^{2}– 1/2

c) x = t

^{2}/2

d) x = t/2

**Solution :**https://www.youtube.com/watch?v=G2uWH7-U30w

**2013**

1. A system is described by the differential equation d

^{2}y/dt

^{2}+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

**Solution :**https://www.youtube.com/watch?v=Z6o8dcPFVgI

**2014**

1. For the system shown,

when the X

_{1}(s) = 0, the transfer function Y(s)/X

_{2}(s) is

**Solution :**https://www.youtube.com/watch?v=yx84ZRbjoZI

2. Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

a) always controllable

b) always observable

c) always stable

d) always unstable

**Solution :**https://www.youtube.com/watch?v=kx74sDKotOs

3. Consider the following block diagram in the figure.

The transfer function C(s)/R(s) is

**Solution :**https://www.youtube.com/watch?v=RRsPFl0GQVQ

4. The input -3e

^{2t}u(t), where u(t) is the unit step function, is applied to a system with transfer function (S-2)/(S+3). If the initial value of the output is -2, then the value of the output at steady state is _____________

**Solution :**https://www.youtube.com/watch?v=CnHCoihbAb0

**2015**

1. For the signal flow graph shown in the figure, the value of C(s)/R(s) is

**Solution :**https://www.youtube.com/watch?v=rqTM5Z91Ihc

2. By performing cascading and/or summing/differencing operations using transfer function blocks G

_{1}(s) and G

_{2}(s), one CANNOT realize a transfer function of the form

**Solution :**https://www.youtube.com/watch?v=4HChAlhqy2E

3. The transfer function of a mass-spring-damper system is given by

the frequency response data for the system are given in the following table.

The unit step response of the system approaches a steady state value of _____________

**Solution :**https://www.youtube.com/watch?v=dk2BLg2jp9U

4. Consider the differential equation dx/dt = 10 – 0.2x with initial condition x(0) = 1. The response x(t) for t > 0 is

a) 2 – e

^{-0.2t}

b) 2 – e

^{0.2t}

c) 50 – 49e

^{-0.2t}

d) 50 – 49e

^{0.2t}

**Solution :**https://www.youtube.com/watch?v=AXJqGP3EzsE

5. The position control of a DC servo-motor is given in the figure. The values of the parameters are KT = 1 N-mA, R

_{a}= 1 ohm, L

_{a}= 0.1 H, J = 5 kg-m

^{2}, B = 1 N-m/(rad/sec) and Kb = 1 volt/(rad/sec).

_{d}is _______.

The steady state position response(in radians) due to unit impulse disturbance torque T

**Solution :**https://www.youtube.com/watch?v=mbkr17M1Cng