control qns

8/13/2019 Control Qns

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1.What is frequency response?

A frequency response is 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 pea. ii)Resonant frequency.

!."efine #resonant $ea %&r)?

The ma'imum (alue of the magnitude of closed loop transfer function is

called

resonant pea.

."efine #Resonant frequency%&f)?

The frequency at which resonant pea occurs is called resonant

frequency.

*.What is +andwidth?

The +andwidth is the range of frequencies for which the system gain ,s

more than

! d+-.The +andwidth is a measure of the a+ility of a feed+ac system to

reproduce the

input signal noise re/ection characteristics and rise time.

0."efine utoff rate?

The slope of the logmagnitude cur(e near the cutoff is called cutoff

rate. The

cutoff rate indicates the a+ility to distinguish the signal from noise.

3."efine #4ain 5argin?

The gain marging is defined as the reciprocal of the magnitude of the


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open loop

transfer function at phase cross o(er frequency.

4ain margin g 6 1 7 8 4%/w pc) 8.

9."efine $hase cross o(er?

The frequency at which the phase of open loop transfer functions is

called phase

cross o(er frequency w pc.

:.What is phase margin?

The phase margin g is the amount of phase lag at the gain cross o(er

frequency

required to +ring system to the (erge of insta+ility.

11."efine 4ain cross o(er?

The gain cross o(er frequency w gc is the frequency at which the

magnitude of

the open loop transfer function is unity..

12.What is -ode plot?

The -ode plot is the frequency response plot of the transfer function of a

system.

A -ode plot consists of two graphs. ;ne is the plot of magnitude of

sinusoidal transfer

function (ersus log w.The other is a plot of the phase angle of a sinusoidal

function

(ersus log w.

1!.What are the main ad(antages of -ode plot?

The main ad(antages are/B in the

counter

clocwise direction as many times as the num+er of right half =plane

poles of

4%s)the closed loop system is sta+le.

29."efine Relati(e sta+ility


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Relati(e sta+ility is the degree of closeness of the systemit an indication of

strength or degree of sta+ility.

2:.What are the two segments of yquist contour?

i. An finite line segment 1 along the imaginary a'is.

ii. An arc 2 of infinite radius.

!B.What are root loci?

The path taen +y the roots of the open loop transfer function when the

loop gain

is (aried from B to E are called root loci.

!1.What is a dominant pole?

The dominant pole is a air of comple' con/ugate pair which decides the

transient

response of the system.

!2.What are the main significances of root locus?

i. The main root locus technique is used for sta+ility analysis.

ii. Fsing root locus technique the range of (alues of G for as ta+le system

can +e

determined

!!.What are the effect of adding a Hero to a system?

Adding a Hero to a system increases pea o(ershoot apprecia+ly.

!.What are circles?

,f the phase of closed loop transfer function with unity feed+ac is E then

tan E

will +e in the form of circles for e(ery (alue of E. These circles are called

circles.

!*.What is control system?


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A system consists of a num+er of components connected together to

perform a specific

function . ,n a system when the output quantity is controlled +y (arying

the input

quantity then the system is called control system.

!0.What are the two ma/or types of control system?

the two ma/or types of control system are open loop and closed loop

!3."efine 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

feed+ac to the input

for correction.

!9."efine 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 (alue are called closed loop control system.

!:.What are the components of feed+ac control system?

the components of feed+ac control system are plant feed+ac path

elements error

detector and controller.

B."efine transfer function.

The T.C of a system is defined as the ratio of the laplace transform of

output to laplace

transform of input with Hero initial conditions.

1.What are the +asic elements used for modeling mechanical


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translational system.

5ass spring and dashpot

2.What are the +asic elements used for modeling mechanical rotational

system?

5oment of inertia Ifdashpo with rotational frictional coefficient - and

torsional spring

with stiffness G

!.ame two types of electrical analogous for mechanical system.

The two types of analogies for the mechanical system are

Corce (oltage and force current analogy

.What is +loc diagram?

A +loc diagram of a system is a pictorial representation of the functions

performed +y

each component of the system and shows the flow of signals. The +asic

elements of +loc

diagram are +locs +ranch point and summing point.

*.What is the +asis for framing the rules of +loc diagram reduction

technique?

The rules for +loc diagram reduction technique are framed such that any

modification made on the diagram does not alter the input output

relation.

0.What is a signal flow graph?

A signal flow graph is a diagram that represents a set of simultaneous

alge+raic equations

.-y taing L.T the time domain differential equations go(erning a control

system can +e


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transferred to a set of alge+raic equations in sdomain.

3. What is transmittance?

The transmittance is the gain acquired +y the signal when it tra(els from

one node to

another node in signal flow graph.

9.What is sin and source?

=ource is the input node in the signal flow graph and it has only outgoing

+ranches.

=in is a output node in the signal flow graph and it has only incoming

+ranches.

:."efine non touching loop.

The loops are said to +e non touching if they do not ha(e common

nodes.

*B.Write 5asons 4ain formula.

5asons 4ain formula states that the o(erall gain of the system is

T 6 17 EE $ E

o.of forward paths in the signal flow graph.

$ Corward path gain of th forward path

E 6 1Jsum of indi(idual loop gains K >Jsum of gain products of all possi+le

com+inations of two non touching loopsKJsum of gain products of all

possi+le

com+inations of three non touching loopsK>

E E for that part of the graph which is not touching th forward path.

*1.Write the analogous electrical elements in force (oltage analogy for

the elements

of mechanical translational system.


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Corce(oltage e

Melocity (current i

"isplacement 'charge q

Crictional coeff -Resistance R

5ass 5 ,nductance L

=tiffness G,n(erse of capacitance 17

*2.Write the analogous electrical elements in force current analogy for the

elements

of mechanical translational system.

Corcecurrent i

Melocity ((oltage (

"isplacement 'flu'E

Crictional coeff -conductance 17R

5ass 5 capacitance

=tiffness G,n(erse of inductance 17L

*!.Write the force +alance equation of an ideal mass element .

C 6 5 d2' 7dt2

*. Write the force +alance equation of ideal dashpot element .

C 6 - d' 7dt

**. Write the force +alance equation of ideal spring element .

C 6 G'

*0."istinguish +etween open loop and closed loop system

;pen loop losed loop

1.,nnaccurate

2.=imple and economical

!.The changes in output due to e'ternal


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distur+ance are not corrected

Accurate

omple' and costlier

The changes in output due to e'ternal

distur+ances are corrected automatically

.They are generally sta+le

4reat efforts are needed to design a sta+le

system

*3.What is ser(omechanism?

The ser(omechanism is a feed+ac control system in which th output is

mechanical

position %or time deri(ati(es of position (elocity and acceleration)

*9.Why is negati(e feed+ac in(aria+ly preferred in closed loop system?

The negati(e feed+ac results in +etter sta+ility in steady state and re/ects

any

distur+ance signals.

*:.What is transient response?

The transient response is the response of the system when the system

changes from one

state to another.

0B.What is steady state response?

The steady state response is the response of the system when it

approaches infinity.

01.What is an order of a system?

The order of asystem is the order of the differential equation go(erning the

system.The


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order of the system can +e o+tained from the transfer function of the

gi(en system.

02."efine "amping ratio.

"amping ratio is defined as the ratio of actual damping to critical

damping.

0!.List the time domain specifications.

The time domain specifications are

i."elay time

ii.Rise time

iii.$ea time

i(.$ea o(ershoot

0."efine "elay time.

The time taen for response to reach *BN of final (alue for the (ery first

time is delay

time.

0*."efine Rise time.

The time taen for response to raise from BN to 1BBN for the (ery first time is

rise time.

00."efine pea time.

The time taen for the response to reach the pea (alue for the first time is

pea time.

03."efine pea o(ershoot.

$ea o(ershoot is defined as the ratio of ma'imum pea (alue measured

from the

5a'mium (alue to final (alue

09."efine =ettling time.


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=ettling time is defined as the time taen +y the response to reach and

stay within

specified error

0:.What is the need for a controller?

The controller is pro(ided to modify the error signal for +etter control

action

3B.What are the different types of controllers?

$roportional controller

$, controller

$" controller

$," controller

31.What is proportional controller?

,t is de(ice that produces a control signal which is proportional to the

input error

signal.

32.What is $, controller?

,t is de(ice that produces a control signal consisting of two terms #one

proportional to error signal and the other proportional to the integral of

error signal.

32. What is $" controller?

$" controller is a proportional plus deri(ati(e controller which produces

an output signal consisting of two time one proportional to error signal

and other proportional to the deri(ati(e of the signal.

3! What is the significance of integral controller and deri(ati(e

controller in a$," controller?

The proportional controller sta+iliHes the gain +ut produces a steady state


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error.

The integral control reduces or eliminates the steady state error.

3.Why deri(ati(e controller is not used in control systems?

The deri(ati(e controller produces a control action +ased on the rate of

change of

error signal and it does not produce correcti(e measures for any constant

error.

3*."efine =teady state error.

The steady state error is defined as the (alue of error as time tends to

infinity.

30.What is the draw+ac of static coefficients?

The main draw +ac of static coefficient is that it does not show the

(ariation of

error with time and input should +e standard input.

33. What is step signal?

The step signal is a signal whose (alue changes from Hero to A at t6 B and

remains constant at A for tOB.

39. What is ramp signal?

The ramp signal is a signal whose (alue increases linearly with time from

an

initial (alue of Hero at t6B.the ramp signal resem+les a constant (elocity.

3:.What is a para+olic signal?

The para+olic signal is a signal whose (alue (aries as a square of time

from an

initial (alue of Hero at t6B.This para+olic signal represents constant

acceleration


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input to the signal.

9B.What are the three constants associated with a steady state error?

$ositional error constant

Melocity error constant

Acceleration error constant

91.What are the main ad(antages of generaliHed error coefficients?

i) =teady state is function of time.

ii) =teady state can +e determined from any type of input

92. What are the effects of adding a Hero to a system?

Adding a Hero to a system results in pronounced early pea to system

response there+y the pea o(ershoot increases apprecia+ly.

9!. =tate5agnitude criterion.

The magnitude criterion states that s6sa will +e a point on root locus if for

that (alue of s 8 "%s) 8 6 84%s)%s) 8 61

9.=tate # Angle criterion.

The Angle criterion states that s6sa will +e a point on root locus for that

(alue of s E"%s) 6 E4%s)%s) 6odd multiple of 19BP

9*. What is a dominant pole?

The dominant pole is a pair of comple' con/ugate pair which decides the

transient response of the system.

90.What is stepper motor?

A stepper motor is a de(ice which transforms electrical pulses into equal

increments of rotary shaft motion called steps.

93.What is ser(omotor?

The motors used in automatic control systems or in ser(omechanism are

called


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ser(omotors. They are used to con(ert electrical signal into angular

motion.

99.ame the test signals used in control system

the commonly used test input signals in control system are impulse step

ramp

acceleration and sinusoidal signals.

9:."efine -,-; sta+ility.

A linear rela'ed system is said to ha(e -,-,; sta+ility if e(ery +ounded

input

results in a +ounded output.

:B.What is the necessary condition for sta+ility.

The necessary condition for sta+ility is that all the coefficients of the

characteristic polynomial +e positi(e.

:1.What is the necessary and sufficient condition for sta+ility.

The necessary and sufficient condition for sta+ility is that all of the

elements in

the first column of the routh array should +e positi(e.

:2.What is quadrantal symmetry?

The symmetry of roots with respect to +oth real and imaginary a'is called

quadrantal symmetry.

:!.What is limitedly sta+le system?

Cor a +ounded input signal if the output has constant amplitude

oscilllations Then

the system may +e sta+le or unsta+le under some limited constraints such

a system is

called limitedly sta+le system.


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:.What is synchros?

A synchros is a de(ice used to con(ert an angular motion to an electrical

signal or

(ice(ersa.

:*.What is steady state error?

The steady state error is the (alue of error signal e%t) when t tends to

infinity.

:0.What are static error constants.

The Gp G( and Ga are called static error constants.

:3.What is the disad(antage in proportional controller?

The disad(antage in proportional controller is that it produces a constant

steady state

error.

:9.What is the effect of $" controller on system performance?

The effect of $" controller is to increase the damping ratio of the system

and so the

pea o(ershoot is reduced.

::.Why deri(ati(e controller is not used in control system?

The deri(ati(e controller produces a control action +ased on rare of

change of error

signal and it does not produce correcti(e measures for any constant error.

ence

deri(ati(e controller is not used in control system

1BB.What is the effect of $, controller on the system performance?

The $, controller increases the order of the system +y one which results in

reducing


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the steady state error .-ut the system +ecomes less sta+le than the original

system.

=i'teen 5ars Questions

1. Cor a gi(en mechanical or electrical or electromechanical system

deri(e the transfer

function.

Cree +ody diagram

"ifferential equation

Transfer function

2."etermination of the o(erall transfer function using -loc diagram

reduction technique.

Reduction of +loc diagram

"etermination of Transfer function

!. "etermination of the o(erall transfer function from the gi(en signal flow

graph using 5asonSs gain formula.

Reduction of signal flow graph

Apply masons gain formula

.Write the procedure for constructing the +loc diagram of a gi(en

mechanical or electrical or electromechanical system.

Write the differential equation

"e(elop +loc diagram

*.Cind the electrical analogical (aria+les of a mechanical rotational

system.

Write the differential equation

"raw the equi(alent electrical networ

0."eri(e the e'pressions of the time domain specifications for a second


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order system with unit step input.

Time response of second order system

Rise time

$ea time

$ea o(ershoot

=ettling time

3.Cind the time response of a first order system for (arious standard inputs.

Apply the input

=ol(e using partial differential equation

Apply in(erse Laplace transform

!. Cind the time response of a second order system for unit step input.

Apply the input

=ol(e using partial differential equation

Apply in(erse Laplace transform

9.$ro+lems using static error coefficients or generaliHed error coefficients.

Cind the error coefficient

Apply in formula

:.'plain the woring of =ynchro transmitter and recei(er.

"iagram

Woring principle

1B.Write the rules for constructing the root locus.

Locate poles @ Ueros

Cind centroid @ asymptotes

Cind -rea away or -rea in points

Cind crossing point in imaginary a'is

11.$ro+lems using root locus technique.


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Locate poles @ Ueros

Cind centroid @ asymptotes

Cind -rea away or -rea in points

Cind crossing point in imaginary a'is

12.=ta+ility analysis using RouthSs criterion.

onstruct routh arry

hec the first column for sta+ility

1!."eri(e the e'pression for the frequency domain specifications of a

second

order system.

4ain 5argin

$hase margin

4ain cross o(er frequency

$hase crosso(er frequency

1.4i(en the open loop transfer function 4%s)%s)617s%s>1)%2s>1) of a unity

feed+ac system. Cind the gain margin and phase margin using polar

plot.

Ans< gain margin 61.2d+

phase margin 612o

Cind croner frequency

alculate gain @ phase for (arious Malues of w

=etch the plot

1*.Write the step +y step procedure for plotting the magnitude plot and

phase

plot of a open loop system represented +y the transfer function 4%s).

Cind croner frequency


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alculate gain @ phase for (arious Malues of w

=etch the plot

10.;+tain the resonant pea resonant frequency +and widthgain

margin

phase margin of the system represented +y the open loop transfer

function

4%/E)61B7 /E%1>B.1 /E)%1>B.B* /E).

=ol(e +y using icholas chart.

resonant pea 6* d+

resonant frequency 69 rad7sec

+and width612 rad7sec

gain margin69.* d+

phase margin6!Bo

13.4i(en the open loop transfer function a system with unity feed

+ac4%s)%s)6G7s%s>2)%s>1B)."etermine the range of G for which closed

loop system is sta+le.

yquist sta+ility criterion.

BVGV2B.

19.Write the procedure for designing the lead compensator.

Cind the (alue of G

Cind the phase margin of uncompensated system

Cind the new phase margin

Cind new gain cross o(er frequency

alculate - @ T

Cind 4c%=)

Cind 4o%s)


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Merify $hase margin

1:.Write the procedure for designing the lag compensator.

Cind the (alue of G


Cind the new phase margin @ gain cross o(er frequency

alculate E @ T

Cind 4c%=)

Cind 4o%s)

Merify $hase margin

2B.Write the procedure for designing the laglead compensator.

Cind the (alue of G


Cind the new phase margin

Cind new gain cross o(er frequency

alculate - E T1 @ T2

Cind 4c%=)

Cind 4o%s)

Merify $hase margin

21."esign $ro+lems

22.Write how will you select a suita+le compensator for the gi(en system.

Ref +oo Ad(anced ontrol Theory +y agoor Gani Fnit ,

control qns

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