Shivaji University , Kolhapur

Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

Multiple Choice Questions

1) Three blocks with gains of 5,8 and 4 are connected in series. The total
gain of the arrangement is
a. 17 b. 160
c. 44 d. 37
2) Static error co-efficients are used as a measure of the effectiveness of
closed loop systems for specified ________ input signal.
a. acceleration b. Velocity
c. Position d. All of the above
3) If the unit step response of a network is (1-e-at ) then its unit impulse
response will be
a. ae-at b. 1
ae- a

c. 1 -at d. (1-a)e-at
e
a
4) A unity feedback system has an open loop transfer function. The value of k
that yields a damping ratio of 0.5 for the closed loop system is
k
G(s)=
s(s+3)
a. 1 b. 3
c. 5 d. 9
5) The loop gain GH of a closed loop system is given by the following
expression
k
G(s)=
s(s+2)(s+4)
The value of K for which the system just becomes unstable is
a. 6 b. 8
c. 48 d. 96
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

6) The gain margin of a system is 0dB. It represents

a. Stable system b. Unstable system
c. Conditional stable system d. Marginally stable system
7) In state space model matrix A is called
a. System matrix b. Input matrix
c. State matrix d. Transmission matrix
8) The nature of the transient system depends on
a. Only on system poles b. Only on inputs applied
c. Both on system poles and d. None of these
applied inputs
9) The unit impulse response of a system given as 𝑐(𝑡) = -4 e-t + 6 e-2 t The
step response of the same system for t≥0 equal to
a. 3e-2 t +4 e- t +1 b. -3e-2 t +4 e- t +1

c. -3e-2 t +4 e- t -1 d. 3e-2 t -4 e- t +1

10) If the characteristic equation of a closed - loop system is s2 +2s+2=0 ,

then the system is
a. overdamped b. critically damped
c. underdamped d. undamped
11) The feedback system shown below oscillates at 2 rad/s 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
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

12) A system has position error constant kp=3. The steady state error for input
of 8u(t) is
a. 2.67 b. 2
c. ∞ d. 0
13) Three blocks with gains of 4,6 and 8 are connected in parallel. The total
gain of the arrangement is
a. 18 b. 32
c. 196 d. 52
14) If the gain K of the system increases the steady state error of the system
a. Decreases b. Increases
c. May increase or decrease d. Remains unchanged
15) Consider a unity feedback control system whose forward path transfer
function
10
G(s)= 2
s
The steady state error, for a step input is
a. 1.0 b. ∞
c. 0.0 d. Does not exist
16) The nature of the transient system depends on
a. Only on system poles b. Only on inputs applied
c. Both on system poles and applied d. None of these
inputs
17) If the characteristic equation of a closed - loop system is s2 +2s+2=0, then
the system is
a. overdamped b. critically damped
c. underdamped d. undamped
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

18) A system has position error constant kp=3. The steady state error for input
of 8u(t) is
a. 2.67 b. 2
c. ∞ d. 0
19) For a first order instrument a 5% settling time is equal to
a. three time the time constant b. two time the time constant
c. time constant d. time required for the output
signal to reaches 5% of the
final value
20) For the polynomial 𝑝(s)= s5 +s4 +2s3 +2s2 +3s+15 the number of roots
which lie in the right half of the s -plane is
a. 4 b. 3
c. 2 d. 1
21) Consider a system with transfer function.
s+6
G(s)= 2
ks +s+6
Its damping ratio will be 0.5 when the value of k is
a. 0.33 b. 3
c. 0.16 d. 6
22) The effect of adding poles and zero can be calculated quickly by
a. Nicholas Chart b. Nyquist Plot
c. Bode Plot d. Root Locus
23) The transfer function of the system depends on
a. Nature of input b. Nature of output
c. System parameter alone d. initial condition
24) Electrical resistance is analogous to
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

a. Intertia b. Dampers
c. Spring d. Fluid capacity
25) Steady state error is always zero in response to the displacement input for
The steady state error, for a step input is
a. Type 0 system b. Type 1 system
c. Type 2 system d. Type (N > 1) system for N=
0, 1, 2….N
26) The number of roots in the left half of the s-plane of the given equation s3
+ 3s2 + 4s + 1 = 0 is:
a. 1 b. 2
c. 3 d. 0
27) PID controller
a. Decreases steady state error and b. Rise time decreases
improves stability
c. Transient response becomes d. Increases steady state error
poorer
28) Loop gain is in signal flow graph is equal to:
a. Product of all branch gains in a b. Product of all branch gains
loop while traversing the forward
path
c. Summation of all branch gains in a d. Sum of all branch gains while
loop traversing the forward path
29) Routh Hurwitz criterion cannot be applied when the characteristic equation
of the system containing coefficient’s which is/are
a. Exponential function of s b. Sinusoidal function of s
c. Complex d. Exponential and sinusoidal
function of s and complex
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

30) Which of the test signals are best utilized by the stability analysis.
a. Impulse b. Step
c. Ramp d. Parabolic
31) State space analysis is applicable for non-linear systems and for multiple
input and output systems.
a. True b. False
c. Can’t say d. None of these
32) For a stable closed loop system, the gain at phase crossover frequency
should always be:
a. < 20 dB b. < 6 dB
c. > 6 dB d. > 0 dB
33) The system in originally critically damped if the gain is doubled the system
will be
a. Remains same b. Overdamped
c. Under damped d. Undamped
34) The steady state error for a unit step input is ________.
a. 1/kp b. 1/(1-kp)
c. 1/2kp d. 1/(1+kp)
35) The damping ratio and peak overshoot are measures of:
a. Relative stability b. Speed of response
c. Steady state error d. Absolute stability
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

UNIT-I Introduction
1) Compare Open Loop and Closed Loop Systems
2) Write a mathematical model for Mass, Spring and Damper.
3) Explain various block diagram reduction rules.
4) State Mason’s Gain Formula. Explain various terms in signal flow graph
5) Define Mason’s gain formula and using it explain the procedure for solving
signal flow Graph.
6) Draw signal flow graph and determine overall transfer function using Mason’s
Gain formula.

7) Determine overall transfer function using Mason’s gain formula.

 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

8) Find overall transfer function for the given signal flow graph.

R(S) C(S)

9) Determine overall transfer function using block diagram reduction rules.

10) Determine overall transfer function using block diagram reduction rules.
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

UNIT-II Time Response Analysis

1) Derive relation between impulse response and step response of first order
system.
2) Derive the expression for time response of first order system for step input.
3) Derive the expressions for tr, tp, ts, %Mp .
4) For certain feedback system transfer function is given by,
C(s) 25
= 2
R(s) s +6s+ 25
Determine tr, tp, ts, %Mp.
5) The open loop transfer function of a unity feedback system is
10
G(s)=
s(s+4)
Determine the rise time, peak time, peak overshoot and settling time
6) Define i) position error constant ii) velocity error constant iii) acceleration error
constant. Derive the steady state error constant and steady state errors for type ‘0’
and type ‘1’ .
7) The open loop transfer function of a unity feedback control system is given by,
20
G(s)=
s(s+2)(s+5)
Find the steady-state error when it is subjected to the input, r(t)=5+3t+2t2 .
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

8) For unity feedback system

60
𝐺(𝑠) =
𝑠(𝑠 + 5)

Determine
i) Type of system.
ii) Steady state error constant.
iii) Steady state error if input is r(t) = 8t
9) For unity feedback system
𝐾
𝐺(𝑠) =
𝑠(𝑠 + 10)
Find gain K with damping ratio of 0.5 and then determine tr, tp, ts, %Mp.
10) The control system having unity feedback has
20
𝐺(𝑠) =
𝑠(1 + 4𝑠)(𝑠 + 1)
Determine
i)Type of system

ii) Static error coefficient if input is r(𝑡) = 2 + 4𝑡 + .

UNIT-III Stability Analysis In S-Domain

1) State and explain Routh criterion for system stability.

2) State and explain Routh criterion special cases.

3) Determine system stability by applying Routh’s test
𝑠 + 2𝑠 + 8𝑠 + 15𝑠 + 20𝑠 + 16𝑠 + 16 = 0
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

Determine system stability of the system represented by characteristic equation

using Routh’s criterion.
𝑠 + 4𝑠 + 8𝑠 + 8𝑠 + 7𝑠 + 4 = 0
4) The characteristic equations for certain feedback control systems are given by
𝑠 + 4𝑠 + 13𝑠 + 36𝑠 + 𝐾 = 0
Determine the range of values of K for the system to be stable, value of K for
marginal stability and the frequency of sustained oscillation.
5) Determine the range of K such that unity feedback system with an open loop
transfer function
K
G(s)=
s(s2 +s+1)(s+4)
is stable.
6) For unity feedback system
K
G(s)=
(𝑠 + 1) (s+4)
i)Find range of K for stability.
ii) Find frequency of oscillations when system is marginally stable.
7) Using Routh-Hurwitz criterion determine stability of closed loop system and
determine number of roots in the right half of s-plane and on jω axis.
i) 𝑠 + 2𝑠 + 10𝑠 + 20𝑠 + 5 = 0
ii) 𝑠 + 9𝑠 + 4𝑠 − 36𝑠 − 32 = 0
8) Explain root locus construction rules.
9) Draw root locus for
𝑘
𝐺(𝑠) ⋅ 𝐻(𝑠) =
𝑠(𝑠 + 2)(𝑠 + 4)
And determine stability.
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

10) Explain the effects of adding poles and zeros to G(s) H(s) on the root locus.

UNIT-IV Frequency Response Analysis

1) State and explain stability using bode plots.
2) Explain the procedure for constructing the bode plot function.
3) State and explain various frequency domain specifications.
4) Describe Nyquist stability criterion.
5) Sketch bode plot for and determine phase and gain crossover frequencies.
20(s+20)
G(s)=
(s+1)(s+2)(s+10)
6) Sketch bode plot for and determine phase and gain crossover frequencies.
10
G(s)=
s (1+0.5s)(1+0.1s)
7) Draw Nyquist plot and comment on stability of system
1
𝐺(𝑠) ⋅ 𝐻(𝑠) =
𝑠(𝑠 + 1)
8) Define polar plot. Sketch polar plot for unity feedback system with open loop
transfer function
1
𝐺(𝑠) ⋅ 𝐻(𝑠) =
(𝑠 + 4)(𝑠 + 2)
9) Sketch Bode plot and determine gain crossover and phase crossover
Frequencies
100(𝑠 + 3)
G(s)=
𝑠. (𝑠 + 1)(𝑠 + 5)
10) Draw Nyquist plot for the system and comment on stability.
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

1
𝐺(𝑠) ⋅ 𝐻(𝑠) =
(𝑠 + 1)(𝑠 + 2)
UNIT-V Compensators
1) What is the need of compensation? Explain lead compensator in detail.
2) Explain lag compensator in detail.
3) Explain lag-lead compensator in detail.
4) Explain the design procedure for a lead compensator.
5) Explain the design procedure for a lag compensator.
6) Explain PID controller in detail.
7) Derive the expression for transfer function of Lead Compensator.
8) Derive the expression for transfer function of Lag Compensator.
9) Compare Lag compensation vs lead compensation.
10) Explain limitations of lag compensator and lead compensator.

UNIT-VI State Space Analysis

1) Explain terms state, state variable, state vector and state space.
2) Derive state model for linear system.
3) Obtain state model for circuit shown below.
 Shivaji University , Kolhapur
Question Bank For Mar 2022 ( Summer ) Examination

Subject Code :PCC-ETC-403 (79183) Subject Name : Control System Engineering

4) Obtain the state model of system in controllable canonical form having transfer
function.
Y(s) s3 +5s2 +8s+12
=
U(S) s3 +7s2 +12s+6
5) Obtain state model for RLC network shown below. The current through R2 is
output required

6) Explain state variable representation of control system.

7) Derive transfer function from state model of continuous time system
8) Obtain state model in Jordan's canonical form of system having transfer function.
Y(s) 2s2 +6s+5
=
U(S) s3 +4s2 +5s+2
9) Obtain the state model in Jordan’s canonical form of system having
transfer function
10) Obtain state model for series RLC circuit.

Vi(t) Vo(t)
i(t)