EE 58 CONTROLENGINEERING QUESTION BANK
QUESTION BANK
EE 58 CONTROLENGINEERING
Prepared by
BENSINGH P B
Lecturer in EEE
TREC
1. What is frequency
response?
A frequency responses the steady state
response of a system when the input to the system is a sinusoidal signal.
2. List out the different frequency domain specifications?
The frequency domain specification
are
i)Resonant peak. ii)Resonant frequency.
3. Define –resonant
Peak (mr)?
The maximum
value of the magnitude of closed loop
transfer function is called resonant peak.
4. Define –Resonant
frequency(mf)?
The
frequency at which resonant peak occurs
is called resonant frequency.
5. What is bandwidth?
The
bandwidth is the range of frequencies for which the system gain Is more than 3
dbB.The bandwidth is a measure of the ability
of a feedback system to reproduce the input signal ,noise rejection
characteristics and rise time.
6. Define Cut-off
rate?
The slope
of the log-magnitude curve near the cut-off is called cut-off rate. The cut-off
rate indicates the ability to distinguish the signal from noise.
7. Define –Gain
Margin?
The gain margin,kg is defined as the reciprocal
of the magnitude of the open loop transfer function at phase cross over
frequency.
Gain margin kg = 1 / | G(jw pc) |.
8. Define Phase cross
over?
The
frequency at which, the phase of open loop transfer functions is called phase
cross over frequency w pc.
9. What is phase
margin?
The phase
margin ,g
is the amount of phase lag at the gain cross over frequency required to bring
system to the verge of instability.
11. Define Gain cross
over?
The gain
cross over frequency w gc
is the frequency at which the magnitude of the open loop transfer function is
unity..
12. What is Bode
plot?
The Bode
plot is the frequency response plot of the transfer function of a system. A
Bode plot consists of two graphs. One is the plot of magnitude of sinusoidal transfer function
versus log w.The
other is a plot of the phase angle of a sinusoidal function versus log w.
13. What are the main
advantages of Bode plot?
The main
advantages are:
Multiplication of magnitude can be in to addition.
A simple method for sketching an approximate log curve is
available.
It is based on asymptotic approximation. Such approximation
is sufficient if rough information on the frequency response characteristic is
needed.
The phase angle curves can be easily drawn if a template for
the phase angle curve of 1+ jw is available.
14. Define Corner
frequency?
The
frequency at which the two asymptotic meet in a magnitude plot is called
corner frequency.
15. Define Phase lag
and phase lead?
A negative phase angle is called
phase lag.
A
positive phase angle is called phase
lead.
16. What are M
circles?
The magnitude
of closed loop transfer function with unit feed back can be shown to be in the
for every value if M.These circles are called M circles.
17. What is Nichols
chart?
The chart
consisting if M & N loci in the log magnitude versus phase
diagram is called Nichols chart.
18. What are two
contours of Nichols chart?
Nichols
chart of M and N contours, superimposed on ordinary graph. The M contours are
the magnitude of closed loop system in decibels and the N contours are the
phase angle locus of closed loop system.
19. How is the Resonant Peak
The resonant peak is given by the
value of m.contour
which is tangent to G(jw ) locus.
The resonant frequency is given by
the frequency of G(jw
) at the tangency point.
The bandwidth is given by frequency
corresponding to the intersection point of
G(jw
) and –3dB M-contour.
20.What are the
advantages of Nichols chart?
The advantages are:
It is used to find the closed loop frequency response from open loop frequency response.
Frequency domain specifications can be determined from
Nichols chart.
The gain of the system can be adjusted to satisfy the given
specification.
21. What are the two
types of compensation
i. Cascade
or series compensation
ii.
Feedback compensation or parallel compensation
22. What are the
three types of compensators
i. Lag compensator
ii. Lead
compensator
iii.
Lag-Lead compensator
23. What are the uses
of lead compensator
speeds up the transient response
Increases the margin of stability
of a system
Increases the system error constant
to a limited extent.
24. What is the use
of lag compensator
*Improve the steady state behavior
of a system, while nearly preserving its transient response.
25. When is lag lead compensator
is required
The lag lead compensator is
required when both the transient and steady state response of a system has to be improved
26. What is a
compensator
A device inserted into the system
for the purpose of satisfying the specifications is called as a compensator.
26. What is nyquist
contour
The contour that encloses entire
right half of S plane is called nyquist
contour.
27. State Nyquist
stability criterion.
If the Nyquist plot of the open
loop transfer function G(s) corresponding to the nyquist control in the S-plane
encircles the critical point –1+j0 in
the counter clockwise direction as many times as the number of right half
S-plane poles of G(s),the closed loop system is stable.
28. Define Relative
stability
Relative stability is the degree of
closeness of the system,it an indication of strength or degree of stability.
29. What are the two
segments of Nyquist contour.
i. An finite line segment C1 along
the imaginary axis.
ii. An arc C2 of infinite radius.
30. What are root
loci.
The path taken by the roots of the
open loop transfer function when the loop gain is varied from 0 to α are called
root loci.
31. What is a
dominant pole.
The dominant pole is a air of
complex conjugate pair which decides the transient response of the system.
32. What are the main
significances of root locus.
i. The main root locus technique is
used for stability analysis.
ii. Using root locus technique the
range of values of K, for as table system can be determined
33. What are the
effect of adding a zero to a system.
Adding a zero to a system increases
peak overshoot appreciably.
34. What are N
circles.
If the phase of closed loop
transfer function with unity feedback is α, then tan α will be in the form of
circles for every value of α. These circles are called N circles.
35. What is control
system?
A system consists of a number of components
connected together to perform a specific function . In a system when the output quantity is controlled by varying
the input quantity then the system is
called control system.
36. What are the two
major types of control system?
The two major types of control system are open
loop and closed loop
37. Define open loop
control system.
The
control system in which the output quantity has no effect upon the input
quantity are called open loop control system. This means that the output is not
feedback to the input for correction.
38. Define closed
loop control system.
The control system in which the output
has an effect upon the input quantity so as to maintain the desired output
value are called closed loop control system.
39. What are the
components of feedback control system?
The components of feedback control
system are plant , feedback path elements, error detector and controller.
40. Define transfer
function.
The T.F of a system is defined as
the ratio of the laplace transform of output to laplace
transform of input with zero initial conditions.
41. What are the basic
elements used for modeling mechanical translational system.
Mass, spring and dashpot
42. What are the
basic elements used for modeling mechanical rotational system?
Moment of inertia J,fdashpo with rotational
frictional coefficient B and torsional spring with stiffness K
43. Name two types of
electrical analogous for mechanical system.
The two types of analogies for the
mechanical system are
Force voltage and force current analogy
44.What is block
diagram?
A block diagram of a system is a pictorial
representation of the functions performed by each component of the system and
shows the flow of signals.The basic elements of block diagram arew block,
branch point and summing point.
45. What is the basis
for framing the rules of block diagram reduction technique?
The rules for block diagram reduction
technique are framed such that any modification made on the diagram does not
alter the input output relation.
46. What is a signal
flow graph?
A signal flow graph is a diagram
that represents a set of simultaneous algebraic equations .By taking L.T the
time domain differential equations governing a control system can be
transferred to a set of algebraic equations in s-domain.
47. What is
transmittance?
The transmittance is the gain acquired
bythe signal when it travels from one node to another node in signal flow
graph.
48. What is sink and
source?
Source is the input node in the signal fow
graph and it has only outgoing branches. Sink is a output node in the signal
flow graph and it has only incoming branches.
49. Define
nontouching loop.
The loops are said to be non touching
if they do not have common nodes.
50. Write Masons Gain
formula.
Masons Gain formula states that the
overall gain of the systm is
T = 1/ ΔΣk Pk
Δk
k-o.of forward paqths in the signal flow graph.
Pk- Forward path gain of kth forward path
Δ = 1-[sum of
individual loop gains ] +[sum of gain products of allpossible combinations of
two non touching loops]-[sum of gain products of allpossible combinations of
three non touching loops]+…
Δk - Δ for that part of the graph which is not
touching kth forward path.
51. Write the
analogous electrical elements in force voltage analogy for the elements of
mechanical translational system.
Force-voltage e
Velocity v-current i
Displacement x-charge q
Frictional coeff B-Resistance R
Mass M- Inductance L
Stiffness K-Inverse of capacitance
1/C
52. Write the
analogous electrical elements in force current analogy for the elements of
mechanical translational system.
Force-current i
Velocity v-voltage v
Displacement x-fluxφ
Frictional coeff B-conductance 1/R
Mass M- capacitance C
Stiffness K-Inverse of inductance
1/L
53. Write the force
balance equation of an ideal mass element .
F = M d2x /dt2
54. Write the force
balance equation of ideal dashpot element .
F = B dx /dt
55. Write the force
balance equation of ideal spring element .
F = Kx
56. Distinguish
between open loop and closed loop system
Open loop
|
Closed loop
|
1.Innaccurate
2.Simple and economical
3.The changes in output due to external disturbance are
not corrected
4.They are generally stable
|
Accurate
Complex and costlier
The changes in output due to external disturbances are
corrected automatically
Great efforts are needed to design a stable system
|
57. What is
servomechanism?
The servomechanism is a feedback control
system in which th output is mechanical position (or time derivatives of
position velocity and acceleration,)
58. Why is negative
feedback invariably preferred in closed loop system?
The negative feedback results in better
stability in steady state and rejects
any disturbance signals.
59. What is transient
response
The transient response is the
response of the system when the system changes from one state to another.
60. What is steady
state response.
The steady state response is the
response of the system when it approaches infinity.
61. What is an order
of a system.
The order of asystem is the order
of the differential equation governing the system.The order of the system can
be obtained from the transfer function of the given system.
62. Define Damping
ratio.
Damping ratio is defined as the
ratio of actual damping to critical damping.
63. List the time
domain specifications.
The time domain specifications are
i.Delay time
ii.Rise time
iii.Peak time
iv.Peak overshoot
64. Define Delay
time.
The time taken for response to reach
50% of final value for the very first time is delay time.
65. Define Rise time.
The time taken for response to
raise from 0% to 100% for the very first time is rise time.
66. Define peak time.
The time taken for the
response to reach the peak value for the
first time is peak time.
67. Define peak
overshoot.
Peak overshoot is defined as the
ratio of maximum peak value measured from the Maxmium value to final value
68. Define Settling
time.
Settling time is defined as the
time taken by the response to reach and stay within specified error
69. What is the need
for a controller?
The controller is
provided to modify the error signal for better control action
70. What are the different
types of controllers.
Proportional controller
PI controller
PD controller
PID controller
71. What is
proportional controller?
It is device that produces a control signal
which is proportional to the input error signal.
72. What is PI
controller?
It is
device that produces a control signal
consisting of two terms –one proportional to error signal and the other
proportional to the integral of error signal.
72. What is PD
controller
PD controller is a proportional plus derivative controller which produces an
output signal consisting of two time -one proportional to error singal and
other proportional to the derivative of the signal.
73 What is the
significance of integral controller and derivative controller in aPID
controller.
The proportional controller
stabilizes the gain but produces a steady state error. The integral control
reduces or eliminates the steady state error.
74. Why derivative
controller is not used in control systems.
The derivative controller produces
a control action based on the rate of change of error signal and it does not
produce corrective measures for any constant error.
75. Define Steady
state error.
The steady state error is defined
as the value of error as time tends to infinity.
76. What is the
drawback of static coefficients.
The main draw back of static
coefficient is that it does not show the variation of error with time and input
should be standard input.
77. What is step
signal.
The step signal is a signal whose
value changes from zero to A at t= 0 and remains constant at A for t>0.
78. What is ramp
signal
The ramp signal is a signal whose
value increases linearly with time from an initial value of zero at t=0.the
ramp signal resembles a constant velocity.
79. What is a parabolic
signal.
The parabolic signal is a signal
whose value varies as a square of time from an initial value of zero at
t=0.This parabolic signal represents constant acceleration input to the signal.
80. What are the
three constants associated with a steady state error.
Positional
error constant
Velocity
error constant
Acceleration
error constant
81. What are the main
advantages of generalized error co-efficients.
Steady state is function of time.
Steady state can be determined from
any type of input
82. What are the
effects of adding a zero to a system.
Adding a
zero to a system results in pronounced early peak to system response thereby
the peak overshoot increases appreciably.
83. State-Magnitude
criterion.
The
magnitude criterion states that s=sa will be a point on root locus if for that
value of s , | D(s) | = |G(s)H(s) | =1
The Angle
criterion states that s=sa will be a point on root locus for that value of s, ,
∟D(s) = ∟G(s)H(s) =odd multiple of 180°
85. What is a
dominant pole?
The
dominant pole is a pair of complex conjucate pair which decides the transient
response of the system.
86. What is stepper
motor?
A
stepper motor is a device which transforms electrical pulses into equal
increments of rotary shaft motion called steps.
87. What is
servomotor?
The
motors used in automatic control systems or in servomechanism are called
servomotors. They are used to convert electrical signal into angular motion.
88. Name the test
signals used in control system
The commonly
used test input signals in control system are impulse step ramp acceleration
and sinusoidal signals.
89. Define BIBO
stability.
A
linear relaxed system is said to have
BIBIO stability if every bounded input
results in a bounded output.
90. What is the
necessary condition for stability.
The
necessary condition for stability is that all the coefficients of the
characteristic polynomial be positive.
91. What is the
necessary and sufficient condition for stability.
The
necessary and sufficient condition for stability is that all of the elements in the first column of
the routh array should be positive.
92. What is
quadrantal symmetry?
The symmetry
of roots with respect to both real and imaginary axis called quadrantal
symmetry.
93. What is limitedly
stable system?
For a bounded
input signal if the output has constant amplitude oscilllations Then the system
may be stable or unstable under some limited constraints such a system is
called limitedly stable system.
94. What is synchro?
A
synchro is a device used to convert an angular motion to an electrical signal
or viceversa.
95. What is steady
state error?
The steady state error is the value of
error signal e(t) when t tends to infinity.
96. What are static
error constants.
The Kp Kv and
Ka are called static error constants.
97. What is the
disadvantage in proportional controller?
The disadvantage
in proportional controller is that it produces a constant steady state error.
98. What is the
effect of PD controller on system performance?
The effect
of PD controller is to increase the damping ratio of the system and so the peak
overshoot is reduced.
99. Why derivative
controller is not used in control system?
The
derivative controller produces a control action based on rare of change of error signal and it does not produce
corrective measures for any constant error. Hence derivative controller is not used in control
system
100. What is the
effect of PI controller on the system performance?
The PI
controller increases the order of the system by one, which results in reducing
the steady state error .But the system becomes less stable than the original system.
101.Define
Resolution of a DAC converter.
It is the smallest change in
voltage which may be produced at the output of the converter.
102.What is monotonic DAC
It
is one that produces an increase in output for each successive digital input.
103.Define Settling time.
It
is defined as the time taken for the converter output to stabilize within ½ LSB
of the correct value.
104. Define Sampler.
A sampler is a
device which converts an analog signal into a train of amplitude-modulated
pulses.
105. What is a hold device.
A
hold device maintains the value of pulse for a prescribed time duration.
106. Define Acquisition time.
The time elapsing
between the triggering edge of the sample pulse and settling state of the
output voltage.
107.Define Aperture time
The time delay
between the hold pulse and actual opening of the switch.
108. Define Droop rate.
It indicates the
gradient of output voltage during the hold state.
109.List some of the properties of Z transform
1.Linearity
2.Shifting
3.Initial
Value theorem
4.Final
value theorem
110.Define Controllability
A
system is said to be completely state controllable if it is possible to
transfer the system state from any initial state X(to) to any other desired state
X(t) in specified finite time by a controlvector U(t).
111.Define observability.
A
system is said to be completely state observable if every state X(t) can be
completely identified by measuremnts of output y(t) over a finite time
interval.
112.Give the Z transform of a unit pulse function
Z(δ(k))
= 1
113. Give the Z transform of a unit step function
Z(u(k))
= z / z-1
114. Give the Z transform of CoswkT
Z(CoswkT) = z
(z-coswT)/ z2-2zcoswT +1
115.List the Linearity property
Z(
af(k) + bg(k)) = aF(z) + bG(z)
116. List the Shifting property
Z(f(k+1))
= z[F(z) –f(0)]
117. Give the Z transform of a unit ramp function
Z[g(k)]
= z/ (z-1)2
118. Give the Z transform of Knf(k)
Z[Knf(k)]
= [-z d/dz]n F(z)
119. List the Scale change property
Z[akf(k)]
= F(z/a)
120.What is state observer
A
device ( or a computer program ) that estimates or observes the state variables
is state observer.
121.List the different methods of discretization
1.Impulse
Invariant transformation
2.
Impulse Invariant transformation and artificial holds
3.Mapping
of differentials
4.Bilinear
transformation
5.
Bilinear transformation and frequency prewarping
6.Matched
Z transform
122.List the properties which characterize the compensation filter.
1.No
. of poles and zeros
2.bandwith
3.DC
gain
4.Phase
margin
123.List the properties of
Impulse Invariant transformation
1)
D(z) has the same impulse response as D(s)
2)
If D(s) is stable so is D(z)
3)
D(z) does not preserve the frequency response of D(s)
124.What is the procedure to be followed to avoid aliasing problem.
Low
pass filter H(s) can be cascaded with D(s) resulting in new modified
filter.This filter
is called a guard filter.
125. What are the drawbacks of guard filter.
1.It
introduces a time lag which causes degradation in performance.
2.Modified
discrete filter is more complicated.
126. List the properties of
Impulse Invariant transformation
1)
If D(z) is not properly tabulated it requires partial fraction expansion
2)
If D(s) is stable so is D(z)
3)
D(z) does not preserve the frequency response of D(s)
127. What is the main disadvantage of forward differences method.
It
generates unstable filters.
128. What is the other name for bilinear transformation
It
is also called Tutsin transformation and Trapezoid integration method.
129. What is bilinear transformation
S
= 2( 1 – z-1)/ T(1 + z-1)
130. List the properties of bilinear transformation
1)
It is easy to apply.
2)
If D(s) is stable so is D(z)
3)
D(z) does not preserve the frequency response of D(s)
UNIT – 1
1.Determine the transfer function X1(S) / F(S) and X2(S) / F(S) of the mechanical system
shown in figure.
2. Write the
governing differential equations of the mechanical system shown in figure.
3. Write the governing differential equations of the
mechanical system shown in figure.
4. Obtain the closed loop transfer function C(S) / R(S) of
the system whose block
diagram is shown
in figure. Use Block diagram reduction
technique and verify the
transfer
function with signal flow graph
technique.
6.Derive the transfer function of Armature controlled d.c. motor .
7. Explain the rules
for block diagram reduction.
8. Derive the transfer function of Field control d.c. motor with
necessary block diagram.
9. Write
the differential equations governing the Mechanical system shown in fig. and
determine the transfer function.
10. Determine the transfer function Y2(S)/F(S) of
the system shown in fig.
UNIT – II
1.Derive the expressions and draw the response of
first order system for unit step
input.
2. Derive the expressions for Rise time, Peak
time, Peak overshoot.
3. A potential control system with velocity
feedback is shown in fig. What is the
response of the system for unit step input?
4. Measurements conducted on a Servomechanism
show the system response to be c(t)=1+0.2 ê 60t-1.2 ê –10 t. when subjected to
a unit step. Obtain an expression for closed loop transfer function.
5. A positional control system with velocity
feedback is shown in fig. What is the response c(t) to the unit step input.
Given that ς =0.5.and also calculate rise time, peak time, Maximum overshoot
and settling time.
6. A unity feedback control system has an open
loop transfer function G(S) = 10/S(S+2). Find the rise time, percentage over
shoot, peak time and settling Time.
7. A closed loop servo is represented by the
differential equation, where c is the displacement of the output shaft, r is
the displacement of the input shaft and e= r-c. Determine undamped natural
frequency, damping ratio and percentage maximum overshoot for unit step input.
8. For a unity feedback control system the open
loop transfer function G(S) = 10(S+2)/ S2 (S+1).
Find (a) Position, velocity and acceleration
error constants. (b) The steady state error when the input is R(S) where R(S)
=3/S –2/S2 +1/3S3 (16)
9. The open loop transfer function of a servo
system with unity feed back system is G(S) = 10/ S(0.1S+1).Evaluate the static
error constants of the system. Obtain the steady state error of the system when
subjected to an input given by the polynomial r(t) = a0 +a1t +a2 /2 t2 .
10.Draw the response of second order system for
critically damped case and when
input is unit step.
UNIT – III
1. What are the specifications in time domain used to
specify indirectly time domain
specifications?
2. What are M circles and N circles?
3. Define phase margin.
4. Define gain margin.
5. Define gain cross over frequency.
6. Define phase cross over frequency.
7. What is Nichol’s chart?
8. How is phase margin determined from a bode plot?
9. How is closed loop response obtained from the Nichol’s
chart?
10. What are the advantages of Nichols chart?
11. How is the Resonant
Peak
from Nichols
chart?
12. Define Corner frequency?
13. What is Bode plot?
14. What are advantages of Bode plot?
15. What is frequency response?
16. List out the different frequency domain specifications?
17. Define –resonant Peak?
18. Define –Resonant frequency.
19. What is bandwidth?
20. Define Cut-off rate?
21. What is polar plot?
22. How do you find the stability of the system by using
polar plot/
23. Define all pass system.
24. What is minimum phase system?
25. How do you find the stability of the system by using
gain margin and phase margin?
UNIT – IV
1. State Nyquist stability criterion.
2. Define BIBO stability.
3. Mention the limitations of Routh – Hurwitz criterion.
4. Write the condition for unstable system.
5. What is marginally stable system?
6. Explain how stability is determined from Routh – Hurwitz
table?
7. Explain relative stability of the system?
8. State the advantages of Nyquist plot.
9. What are break away points?
10. What are all pass systems?
UNIT – V
- Describe the various components in a digital control system with
necessary block diagram?
2. Explain
any two applications of digital controllers
. . Explain
About Digital PID Contriller
Explain
About Digital PI Contriller
5. Explain
About Digital PD Contriller
7. Explain
About PLC
8. Explain
About hold device.
9. Explain
About Sampler.
- What is
the principal concern with parameter variations
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