Wednesday, September 16, 2015

Black Diagram Reduction, Signal Flow Graph, Mason's Gain formula, Final value theorem - Topicwise Questions in Control Systems (1987 -2015)

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) ∞


Answer: C
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


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



2004

1. Consider the signal flow graph shown in figure. The gain X5/X1 is

Answer: C
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


Answer: A
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

Answer: A
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) ∞
Answer: C
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
Answer: D
Solution : https://www.youtube.com/watch?v=cvCDerivzj0


2010
1. Given f(t) = L–1[(3s + 1) / (s3 + 4s2 + (k-3)s)]. If Limt -> ∞ f(t) = 1, then the value of k is
a) 1
b) 2
c) 3
d) 4
Answer: D
Solution : https://www.youtube.com/watch?v=q65ZfJH4Ww0

2011
1. 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 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

Answer: D
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

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


2012
1. The unilateral Laplace transform of f(t) is 1/(s2+s+1). The unilateral transform of t.f(t) is

Answer: D
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 = t2 – 1/2
c) x = t2/2
d) x = t/2
Answer: D
Solution : https://www.youtube.com/watch?v=G2uWH7-U30w

2013
1. 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
Answer: B
Solution : https://www.youtube.com/watch?v=Z6o8dcPFVgI


2014
1. For the system shown,
when the X1(s) = 0, the transfer function Y(s)/X2(s) is


Answer: D
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


Answer: A
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


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


4. The input -3e2tu(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 _____________


Answer: ZERO
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


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


2. By performing cascading and/or summing/differencing operations using transfer function blocks G1(s) and G2(s), one CANNOT realize a transfer function of the form


Answer: B
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 _____________


Answer: 0.4
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 – e0.2t
c) 50 – 49e-0.2t
d) 50 – 49e0.2t


Answer: C
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, Ra = 1 ohm, La = 0.1 H, J = 5 kg-m2, 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
Answer: 0.5
Solution : https://www.youtube.com/watch?v=mbkr17M1Cng


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