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SELVAM COLLEGE OF TECHNOLOGY,NAMAKKAL DEPT OF EEE
SUB: CONTROL SYSTEMS. UNIT I
TWO MARKS 1. Define System. A system is a combination or an
arrangement of different physical components which act together as
an entire unit to achieve certain objective. 2. Define Control
system. To control means to regulate, to direct or to command.
Hence a control system is an arrangement of different physical
elements connected in such a manner so as to regulate, direct or
command itself or some other system. 3. Define Plant. The portion
of a system which is to be controlled or regulated is called the
plant or the process. 4. Define Controller. The element of the
system itself or external to the system which controls the plant or
the process is called controller. 5. Define Input. It is an applied
signal or an excitation signal applied to a control system from an
external energy source in order to produce a specified output. 6.
Define Output. It is the particular signal of interest or the
actual response obtained from a control system when input is
applied to it. 7. Define disturbance. Disturbance is a signal which
tends to adversely affect the value of the output of a system. 8.
Define internal disturbance. If such a disturbance is generated
within the system itself, it is an internal disturbance. 9. Define
external disturbance. The disturbance generated outside the system
acting as an input to the system in addition to its normal input,
affecting the output adversely is an external disturbance. 10.
Write any four major classification of control system. 1. Open loop
and closed loop control system. 2. Time varying and time-invariant
system. 3. Linear and nonlinear system. 4. Lumped parameter and
distributed parameter control system.
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11. What is mean by Principle of superposition? Principle of
superposition means the response to several inputs can be obtained
by considering one input at a system and the algebraically adding
the individual results. 12. What is mean by Deterministic control
system? A control system is said to be deterministic when its
response to input as well as behaviour to external disturbance is
predictable and repeatable. 13. Write short notes about SISO and
MIMO. A system having only one input and one output is called
single input and single output system. Some systems may have
multiple input and multiple outputs, these are called multiple
input and multiple output systems. 14. Define Open loop system. A
system in which output is dependent on input but controlling action
is totally independent of the output or changes in input of the
system, is called an open loop system. 15. Define closed loop
system. A system in which controlling action or input is somehow
dependent on the output or changes in output is called closed loop
system. 16. Write any four advantages of open loop system. 1. Such
systems are simple in construction. 2. Very much convenient when
output is difficult to measure. 3. Such systems are easy when
maintenance point is view. 4. Such systems are economical. 17.
Write any four disadvantages of open loop system. 1. Such systems
are inaccurate and unreliable because accuracy of such system is
totally dependent on the accurate precalibration of the controller.
2. Such systems give inaccurate results if there are variations in
the external environment. 3. Similarly they cannot sense internal
disturbances in the system, after the controller stage. 4. To
maintain the quality and accuracy, recalibration of the controller
is necessary, time to time. 18. Give any four real time application
of open loop system. 1. Sprinkler used to water a lawn. 2. Stepper
motor positioning system. 3. Automatic toaster system. 4. Traffic
light controller. 19. Give any four real time application of closed
loop system. 1. Human being. 2. Home heating system. 3. Ship
stabilization system. 4. Voltage stabilizer.
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20. Define feedback. Feedback is a property of the system by
which it permits the output to be compared with the reference input
to generate the error signal based on which appropriate controlling
action can be decided. 21. What are called feedback systems?
Systems in which the effect of the disturbance must show up in the
error before the controller can take proper corrective action are
called feedback systems. 22. Define Laplace Transform. The Laplace
transform is defined as below, Let f (t) be a real function of a
real variable t defined for t>0, then
F(s) =L [f (t)] =
0
).( dtetf st
Where F (s) is called Laplace transform of f (t). And the
variable s which appears in F(s) is frequency dependent complex
variable. It is given by, js += Where =real part of complex
variable s. = Imaginary part of complex variable s. 23. Define
Linearity of Laplace transform. The transform of a finite sum of
time functions is the sum of the Laplace transforms of the
individual functions. So if F1(s), F2(s), , Fn(s) are the laplace
transforms of the time functions f1 (t), f2(t),, fn(t) respectively
then, L{f1(t)+f2(t)+..+fn(t)}=F1(s)+F2(s)+Fn(s). 24. Define scaling
Theorem. If K is a constant then the Laplace transform of k(t) is
given as K times the Laplace transform of f(t). L [K f (t)] =K F(s)
where K is constant. 25. Define Real translation or shifting
theorem. This theorem is useful to obtain the Laplace transform of
the shifted or delayed function of time. If F(s) is the Laplace
transform of f (t) then the Laplace transform of the function
delayed by time T is L {f (t-T)} =e-Ts F(s). 26. Define Initial
value theorem. The Laplace transform is very useful to find the
initial value of the time function f (t). Thus if F(s) is the
Laplace transform of f (t) then, )()()0(
0ssFLimtfLimf
st
+ ==+
.
The only restriction is that f (t) must be continuous or at the
most, a step discontinuity at t=0.
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27. Define Final value theorem. The Laplace transform is very
useful to find the final value of the time function f (t). Thus if
F(s) is the Laplace transform of f (t) then, )()(
0ssFLimtfLim
st =
.
The only restriction is that the roots of the denominator
polynomial of F(s) i.e. poles of F(s) have negative or zero real
parts. 28. What is called Transfer function? The effect of system
parameters, role of system parameters in the performance of system
can be expressed as ratio of output to input. Mathematically such a
function explaining the effect of such parameters on input to
produce output is called transfer function. 29. Define Transfer
function. Mathematically it is defined as th ratio of laplace
transform of output (response) of the system to the laplace
transform of input (excitation or driving function), under the
assumption that all initial conditions are zero. 30. Define impulse
function. The impulse function is defined as, F (t) = A for t=0 = 0
for t=0 31. Define poles of a transfer function. The values of s,
which make the T.F. infinite after substitution in the denominator
of a T.F. are called Poles of that T.F. 32. Define characteristic
equation of a transfer function. The equation obtained by equating
denominator of a transfer function to zero, whose roots are the
poles of that transfer function is called characteristic equation
of that system. F(s) = b0sn+b1sn-1+b2sn-2+ + bn = 0 is called the
characteristic equation. 33. Define Zero of a transfer function.
The value of s which make the T.F. zero after substituting in the
numerator are called zeros of the T.F. 34. Define order of a
transfer function. The highest power of s present in the
characteristic equation i.e. in the denominator polynomial of a
closed loop transfer function of a system is called order of a
system. 35. What is the basic concept of block diagram
representation? If a given system is complicated, it is very
difficult to analyse it as a whole. With the help of transfer
function approach, we can find transfer function of each and every
element of the complicated system. And by showing connection
between the elements, complete system can be splitted into
different blocks and can be analyzed conveniently. This is the
basic concept of block diagram representation.
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36. Define Pole Zero plot. Plot obtained by locating all poles
and zeros of a T.F. in s-plane is called pole-zero plot of a
system. 37. What is called functional block? To draw the block
diagram of a practical system, each element of practical system is
represented by a block. The block is called functional block. 38.
What is called branches? The connection between the blocks is shown
by lines called branches of the block diagram. An arrow is
associated with each and every branch which indicates the direction
of flow of signal along the branch. 39. What are the basic elements
of block diagram? 1. Blocks, 2. Transfer functions of elements
shown inside the blocks, 3. Summing points, 4. Take off points, 5.
Arrows. 40. What are the advantages of block diagram? 1. Very
simple to construct the block diagram for complicated systems. 2.
The function of individual element can be visualized from block
diagram. 41. What are the disadvantages of Block diagram? 1. Block
diagram does not include any information about the physical
construction of the system. 2. Source of energy is generally not
shown in the block diagram. So number of different block diagrams
can be drawn depending upon the point of view of analysis. So block
diagram for given system is not unique. 42. What is simple or
canonical form of closed loop system? A block diagram in which,
forward path contains only one block, one summing point and one
take off point represents simple or canonical form of a closed loop
system. 43. What is called signal flow graph representation? The
graphical representation of the variables of a set of linear
algebraic equations representing the system is called signal flow
graph representation. 44. Write about branches? All the dependent
and independent variables are represented by the nodes. The
relationships between various nodes are represented by joining the
nodes as per the equations. The lines joining the nodes are called
branches. 45. What are called nodes of a graph? As variables are
important elements of the set of equations for the system, these
are represented first in signal flow graph by small circles called
nodes of signal flow graph. Each node represents a separate
variable of the system. 46. Define forward path. A path from the
input to output node is defined as forward path.
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47. Define Source node source node and chain node. The node
having only outgoing branches is known as source or input node. The
node having an only incoming branch is known as sink node or output
node.A node having incoming and outgoing branches is known as chain
node. 48. Define feedback loop. A path which originates from a
particular node and terminating at the same node, traveling through
at least one other node, with out tracing any node twice is called
feedback loop. 49. Define self loop. A feedback loop consisting of
only one node is called self loop. A self loop cannot appear while
defining a forward path or feedback loop as node containing it gets
traced twice which is not allowed. 50. Define path gain and loop
gain. The product of branch gains while going through a forward
path is known as path gain. This can be also called as forward path
gain. The product of all the gains of the branches forming a loop
is called loop gain. 51. Define dummy node. If there exists
incoming and outgoing branches both at first and last node
representing input and output variables then as per definition
these cannot be called as source node or sink node. In such a case
a separate input and output nodes can be created by adding branches
with gain 1. Such nodes are called dummy nodes. 52. Define
non-touching loops. If there is no node common in between the two
or more loops, such loops are said to be non- touching loops. 53.
State masons formula. The formula can be stated as
= KK
TFOverallT . .
Where k= no. of forward paths 54. What are the two methods of
obtaining electrical analogous network? 1. Force-voltage analogy
(Direct) 2. Force-current analogy (indirect) 55. Write short notes
about servomotors. The servo system is one in which the output is
some mechanical variable like position, velocity or acceleration.
Such systems are generally automatic control systems which work on
the error signals. The error signals are amplified to drive motors
used in such systems. These motors used in servo systems are called
servomotors.
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SELVAM COLLEGE OF TECHNOLOGY,NAMAKKAL DEPT OF EEE
SUB:CONTROL SYSTEMS. UNIT II
TWO MARKS 1. Define Zero. The zero of a function, F(s) is the
value at which the function, F(s) becomes zero, Where F(s) is a
function of complex variable s. 2. What is the order of a system?
The order of the system is given by the order of the differential
equation governing the system. It is also given by the maximum
power of s in the denominator polynomial of transfer function. The
maximum power of s is also gives the number of poles of the system
and so the order of the system is also given by number of poles of
the transfer function. 3. What is called time constant form? Those
elements are constant of system K and poles of G(s)H(s) at origin
of G(s)H(s) is expressed in a particular form called time constant
form. 4. Write any four disadvantages of static error co-efficient
method. 1. Method cannot give error if inputs are other than the
three standard test inputs. 2. Most of the times, method gives
mathematical answer of the error as 0 or infinite and hence does
not provide precise value of the error. 3. Method does not provide
variation of error with respect to time, which will be otherwise
very useful from design point of view. 4. The method is applicable
only for stable systems 5. Define time response. The response given
by the system which is function of the time, to the applied
excitation is called time response of a control system. 6. Define
transient response. The output variation during the time, it takes
to achieve its final value is called as transient response. The
time required to achieve the final value is called transient
period. 7. Define steady state response. It is that part of the
time response which remains after complete transient response
vanishes from the system output. 8. What is called steady state
error? The difference between the desired output and the actual
output of the system is called steady state error which is denoted
as ess. This error indicates the accuracy and plays an important
role in designing the system. 9. Define step input. It is the
sudden application of the signal as shown. Mathematically it can be
described as, r(t) = A for t>=0 = 0 for t
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10. Define ramp input. It consist of rate of change in input
i.e. gradual application of input as shown. Magnitude of ramp input
is nothing but the slope. Mathematically, r (t) = At for t>=0 =
0 for t=0 = 0 for t < 0 12. Define Impulse input. It is the
input applied instantaneously (for short duration of time) of very
high amplitude as shown.
It is the pulse whose magnitude is infinite while its width
tends to zero i.e. t 0, applied momentarily. Mathematically, r(t) =
A, for t=0 = 0, for t=0 13. Define damping ratio. The damping ratio
is defined as the ratio of actual damping to critical damping. 14.
Give the expression for damping ratio of mechanical and electrical
system. The damping ratio of second order mechanical translational
system, =B/2 MK. The damping ratio of second order mechanical
rotational system, =B/2 JK. The damping ratio of second order
electrical system, =R/2 L/C. 15. How the system is classified
depending on the value of damping? Depending on the value of
damping, the system can be classified into the following four cases
Case 1: Undamped system, =0
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Case 2: Underdamped system, 0< 1. 16.What is the importance
of test signals? The test signals can be easily generated in test
laboratories and the characteristics of test signals resembles, the
characteristics of actual input signals. The test signals are used
to predetermine the performance of the system. 17. 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. 18. What is weighting function? The impulse
response of system is called weighting function. It gives inverse
laplace transform of system transfer function. 19. Define Pole. The
pole of a function, F(s) is the value at which the function, F(s)
becomes infinite, Where F(s) is a function of complex variable S.
20. How the system is classified depending on the value of damping.
Depending on the value of damping, the system cen be classified
into the following four cases Case 1: Undamped system Case 2: Under
damped system Case 3: critically damped system Case 4: over damped
system 21. What will be the nature of response of a second order
system with different types of damping? For Undamped system the
response is oscillatory. For Under damped system the response is
damped oscillatory. For Critically damped system the response is
exponentially rising. For over damped system the response is
exponentially rising but the rise time will be very large. 22.
Sketch the response of a second order under damped system. 23. What
is damped frequency of oscillation? In under damped system the
response is damped oscillatory. The frequency of damped Oscillation
is given by
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24. List the time domain specifications. The time domain
specifications are
1. Delay time 2. Rise time 3. Peak time 4. Maximum peak
overshoot 5. Settling time.
25. Define delay time. It is the time taken for response to
reach 50% of the final value, for the very first time. 26. Define
rise time. It is the time taken for response to raise from 0 to
100% for the very first time. For under damped system, the rise
time is calculated from 0 to 100%. But for over damped system, it
is the time taken by the response to raise from 10% to 90%. For
critically damped system, it is the time taken for response to
raise from 5% to 95%. 27. Define Peak time. It is the time taken
for the response to reach the peak value for the very first time
(or) It is the time taken for the response to reach peak overshoot,
Mp. 28. Define Peak overshoot. It is defined as the ratio of the
maximum peak value measured from final value to final value. Let
final value= c( ), Maximum value=c(tp) Peak over shoot, Mp= 29.
Define Settling time. It is defined as the time taken by the
response to reach and stay with in a specified error and the error
is usually specified as % of final value. The usual tolerable error
is 2% or 5% of the final value. 30. What is type number of a
system? What is its significance? The type number is given by
number of poles of loop transfer function at the origin. The type
number of the system decides the steady state error. 31.
Distinguish between type and order of a system. 1. Type number is
specified for loop transfer function but order can be specified for
any transfer function. (open loop or closed loop transfer
function). 2. The type number is given by number of poles of loop
transfer function lying at origin of s-plane but the order is given
by the number of poles of transfer function. 32. For the system
with following transfer function, determine type and order of the
system. Ans: 1. Type-1, Order-4 2. Type-2, Order-4 3. Type-0,
Order-2 4. Type-3, Order-5
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33. What are static error constants? The Kp,Kv and Ka are called
static error constants. These constants are associated with steady
state error in a particular type of system and for a standard
input. 34. Define positional error constant. The positional error
constant Kp = Lt G(s)H(s). The steady state error in type-0 system
when the input is unit step is given by 1/(1+Kp). 35. Define
Velocity error constant. The Velocity error constant Kv=Lt sG(s)
H(s). The steady state error in type-1 system for unit ramp input
is given by 1/Kv. 36. Define acceleration error constant. The
acceleration error constant Ka=Lt s2G(s) H(s). The steady state
error in type-2 system for unit parabolic input is given by 1/Ka.
37. What are generalized error coefficients? They are the
coefficients of generalized error series. The generalized error
series is given by.The Coefficients C0,C1,C2 are called generalized
error coefficient or dynamic error coefficients. The nth
coefficient, Cn=Lt dnF(s)/dsn, Where F(s)=1/(1+G(s)H(s)). 38. Give
the relation ship between generalized and static error
coefficients. The following expressions shows the relation between
generalized and static error coefficient C0=1/(1+Kp),
C1=1/Kv,C2=1/Ka. 39. Mention two advantages of generalized error
constants over static error constants. 1. Generalized error series
gives error signal as a function of time. 2. Using generalized
error constants the steady state error can be determined for any
type of the input but static error constants are used to determine
steady state error when the input is anyone of the standard input.
40. What is the effect on system performance, when a proportional
controller is introduced in a system? The proportional controller
improves the steady state tracking accuracy, disturbance signal
rejection and relative stability of the system. It also increases
the loop gain of the system which results in reducing the
sensitivity of the system to parameter variations. 41. What is the
disadvantage in proportional controller? The disadvantage in
proportional controller is that it produces a constant steady state
error. 42. 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.
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43. What is the effect of PD controller on the system
performance? The effect of PD controller is to increase the damping
ratio of the system and so the peak overshoot is reduced. 44. Why
derivative controller is not used in control systems? The
derivative controller produces a control action based on rate of
change of error signal and it does not produce corrective measures
for any constant error. Hence derivative controller is not used in
control systems.
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SELVAM COLLEGE OF TECHNOLOGY,NAMAKKAL DEPT OF EEE
SUB:CONTROL SYSTEMS. UNIT III
TWO MARKS 1. What is frequency response? The frequency response
is steady-state output of the system, when the input is a
sinusoidal signal. 2. What are the advantages of frequency response
analysis? 1. The absolute and relative stability of the closed loop
system can be estimated from the knowledge of the open loop
frequency response. 2. The practical testing of system can be
easily carried with available sinusoidal signal generators and
precise measurement equipments. 3. What are the frequency domain
specifications? 1. Resonant peak 2. Resonant frequency 3. Band
width 4. Cut-off rate 5. Gain margin 6. Phase Margin 4. Define
resonant peak? The maximum value of the magnitude of closed loop
transfer function is called resonant peak. 5. What is resonant
frequency? The frequency at which resonant peak occurs is called
resonant frequency. The resonant peak is the maximum value of the
magnitude of closed loop transfer function. 6. Define bandwidth?
The bandwidth is the range of frequencies for which the system gain
is more than -3db. 7. What is cut-off rate? The slope of the
log-magnitude curve near the cut-off frequency is called cut-off
rate. 8. Define Gain Margin? The gain margin, kg is defined as the
reciprocal of the magnitude of open loop transfer function, at
phase cross over frequency, Gain Margin, Kg=1/ |G(jw)| and when
expressed in decibels it is 20 log kg. 9. Define phase Margin? The
phase margin, is that amount of additional phase lag at the gain
cross-over frequency, required to bring the system to the verge of
instability. It is given by, 180+ , where is the phase of g(jw) at
the gain cross over frequency. Phase Margin, = 180+
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10. What is phase and gain cross over frequency? The gain cross
over frequency is the frequency at which the magnitude of the open
loop transfer function is unity. The phase cross over frequency is
the frequency at which the phase of the open loop transfer function
is 180. 11. Write the expression for resonant peak and resonant
frequency. Resonant peak, Mr = Resonant frequency, 12. Write short
note on the correlation between the time and frequency response?
There exists a correlation between time and frequency response of
first or second order systems. The frequency domain specification
can be expressed in terms of the time domain parameter and .For a
peak overshoot in time domain specification there is a
corresponding resonant peak in frequency domain. For higher order
systems there is no explicit correlation between time and frequency
response. 13. What is bode plot? The bode plot is a frequency
response plot of the transfer function of a system. It consists of
two plots-magnitude plot and phase plot. The magnitude plot is a
graph between magnitude of a system transfer function in db and the
frequency . The phase plot is a graph between the phase or
arguments of a system transfer function in degrees and the
frequency . Usually, both the plots are plotted on a common x-axis
in which the frequencies are expressed in logarithmic scale. 14.
What is approximate bode plot? In approximate bode plot, the
magnitude plot of first and second order factors are approximated
by two straight lines, Which are asymptotes to exact plot. One
straight line is at odb, for the frequency range 0 to and other
straight line is drawn with a slope of +20n db/dec for the
frequency range . Here is the corner frequency. 15. Define corner
frequency? The magnitude plot can be approximated by asymptotic
straight lines. The frequencies corresponding to the meeting point
of asymptotes are called corner frequency. The slope of the
magnitude plot changes at every corner frequencies. 16. What are
the advantages of bode plot? 1. The magnitudes are expressed in db
and so a simple procedure is available to add magnitude of each
term one by one. 2. The frequency domain specification can be
easily determined. 17. What is the value of error the approximate
magnitude plot of a first order factor at the corner frequency? The
error in the approximate magnitude plot of a first order factor at
the corner frequency is +3mdb, where m is multiplicity factor.
Positive error for numerator factor and negative error for
denominator factor.
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18. What is the value of error in the approximate magnitude plot
of a quadratic factor with at the corner frequency? The error is
+6db, for the quadratic factor with =1. Positive error for
numerator factor and negative error for denominator factor. 19.
What is polar plot? The polar plot of a sinusoidal transfer
function g(j ) is a polar plot of the magnitude of G(j ) versus the
phase angle/argument of G(j ) on polar or rectangular co-ordinates
as is varied from zero to infinity. 20. What is minimum phase
system? The minimum phase systems are systems with minimum phase
transfer functions. In minimum phase transfer functions, all poles
and zeros will lie on the left half of s-plane. 21. What are
All-Pass systems? The all pass systems are systems with all pass
transfer functions. In all pass transfer functions, the magnitude
is unity at all frequencies and the transfer function will have
anti-symmetric pole zero-pattern. 22. What is non-minimum phase
transfer function? A transfer function which has one or more zeros
in the right half s-plane is known as non-minimum phase transfer
function. 23. What is Nichols plot? The Nichols plot is a frequency
response plot of the open loop transfer function of a system. It is
a graph between magnitude of G(j ) in db and the phase of g(j ) in
degree, plotted on a ordinary graph sheet. 24. What are M and N
circles? The magnitude, m of closed loop transfer function with
unity feedback will be in the form of circle on complex plane for
each constant value of M. The family of these circles is called M
circles. Let N=tan where is the phase of closed loop transfer with
unity feedback. For each constant value of N, a circle can be drawn
in the complex plane. The family of these circles are called N
circles. 25. How closed loop frequency response is determined from
open loop frequency using M and n circles? The G(j ) locus or the
polar plot of open loop system is sketched on the standard M and n
circles chart. The meeting point of M circle with G(j ) locus gives
the magnitude of closed loop system. The locus with N-circle gives
the value of phase of closed loop system. 26. What is Nicholas
Chart? The Nicholas chart consists of m and n contours superimposed
on ordinary graph. Along each M contour the magnitude of closed
loop system, M will be constant. Along each N contour, the phase of
closed loop system will be constant. The ordinary graph consists of
magnitude in db, marked on the y-axis and the phase in degrees
marked on x axis. The Nicholas chart is used to find the closed
loop frequency response from the open loop frequency response.
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27. How the closed loop frequency response is determined from
the open loop frequency response using Nicholas chart? The G(j )
locus or the Nicholas plot is sketched on the standard Nicholas
chart. The meeting point of M-contour with G(j ) locus gives the
magnitude of closed loop system and the meeting point with N circle
gives the argument/phase of the closed loop system. 28. What are
the advantages of Nicholas chart? 1. The gain of the system can be
adjusted to satisfy the given specification. 2. The frequency
domain specification can be easily determined. 29. In minimum phase
system, how the start and end of polar plot are identified? 30.
Draw the polar plot of G(s)=1(1+sT).
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SELVAM COLLEGE OF TECHNOLOGY, NAMAKKAL-03 DEPARTMENT OF EEE
CLASS/SEM: III ECE/V SEM CONTROL SYSTEMS
UNIT-IV TWO MARKS
1. Define BIBO stability. A linear relaxed system is said to
have BIBO stability if every bounded (finite) input results in a
bounded (finite) output. 2. What is impulse response? The impulse
response of a system is the inverse Laplace transform of the system
transfer function. 3. What is the requirement for BIBO
stability?
The requirement for BIBO stability is that, where )(m is the
impulse response of the
system.