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Components-3e-S 06/04/07

Chapter 6

HARDWARE COMPONENTS FOR AUTOMATION AND INDUSTRIAL

CONTROL

REVIEW QUESTIONS

6.1 What is a sensor?

Answer: As defined in the text, a sensor is a dei!e that !onerts a ph"si!a# stim$#$s or aria%#e of interest&s$!h as temperat$re, for!e, press$re, or disp#a!ement' into a more !onenient form &$s$a##" an e#e!tri!a#($antit" s$!h as o#ta)e' for the p$rpose of meas$rin) the stim$#$s.

6.* What is the differen!e %et+een an ana#o) sensor and a dis!rete sensor?

Answer: An ana#o) meas$rin) dei!e prod$!es a !ontin$o$s ana#o) si)na# s$!h as e#e!tri!a# o#ta)e, +hosea#$e aries in an ana#o)o$s manner +ith the aria%#e %ein) meas$red. A dis!rete meas$rin) dei!e

prod$!es an o$tp$t that !an hae on#" !ertain a#$es. is!rete sensor dei!es diide into t+o !ate)ories: &1'%inar", in +hi!h the meas$rin) dei!e prod$!es an on/off si)na#, and &*' di)ita#, in +hi!h the meas$rin)dei!e prod$!es either a set of para##e# stat$s %its or a series of p$#ses that !an %e !o$nted.

6.3 What is the differen!e %et+een an a!tie sensor and a passie sensor?

Answer: An a!tie sensor is one that responds to a stim$#$s +itho$t the need for an" externa# po+er. Apassie sensor is one that re($ires an externa# so$r!e of po+er in order to operate.

6.4 What is the transfer f$n!tion of a sensor?

Answer: A transfer f$n!tion is the re#ationship %et+een the a#$e of the ph"si!a# stim$#$s and the a#$e ofthe si)na# prod$!ed %" the sensor in response to the stim$#$s. t is the inp$t/o$tp$t re#ationship of thesensor.

6. What is an a!t$ator?

Answer: An a!t$ator is a hard+are dei!e that !onerts a !ontro##er !ommand si)na# into a !han)e in aph"si!a# parameter. An a!t$ator is a transd$!er, %e!a$se it !han)es one t"pe of ph"si!a# ($antit", s$!h ase#e!tri! !$rrent, into another t"pe of ph"si!a# ($antit", s$!h as rotationa# speed of an e#e!tri! motor.

6.6 ear#" a## a!t$ators !an %e !#assified into one of three !ate)ories, a!!ordin) to t"pe of drie po+er. amethe three !ate)ories.

Answer: he three !ate)ories are &1' e#e!tri!a#, &*' h"dra$#i!, and &3' pne$mati!.

6.7 ame the t+o main !omponents of an e#e!tri! motor.

Answer: he t+o !omponents are the stator, +hi!h is the stationar" !omponent, and the rotor, +hi!h rotatesinside the stator.

6. n a C motor, +hat is a !omm$tator?

Answer: !a##ed A !omm$tator is a rotar" s+it!hin) dei!e that rotates +ith the rotor and pi!2s $p !$rrentfrom a set of !ar%on %r$shes that are !omponents of the stator assem%#". ts f$n!tion is to !ontin$a##" !han)ethe re#atie po#arit" %et+een the rotor and the stator, so that the ma)neti! fie#d prod$!es a tor($e to!ontin$o$s#" t$rn the rotor.

6. What are the t+o important disadanta)es of C e#e!tri! motors that ma2e the AC motor re#atie#"attra!tie?

Answer: A!!ordin) to the text, the t+o important disadanta)es of C motors are &1' the !omm$tator and%r$shes $sed to !ond$!t !$rrent %et+een the stator assem%#" and the rotor res$#t in maintenan!e pro%#ems,and &*' the most !ommon e#e!tri!a# po+er so$r!e in ind$str" is a#ternatin) !$rrent, not dire!t !$rrent. norder to $se AC po+er to drie a C motor, a re!tifier m$st %e added to !onert the a#ternatin) !$rrent todire!t !$rrent.

6.10 o+ is the operation of a stepper motor different from the operation of !onentiona# C or AC motors?

Answer: Conentiona# C and AC motors rotate !ontin$o$s#" %ased on a !ontin$o$s C or AC po+erso$r!e. A stepper motor rotates in dis!rete an)$#ar disp#a!ements, !a##ed step an)#es. 5a!h an)$#ar step isa!t$ated %" a dis!rete e#e!tri!a# p$#se. he tota# rotation of the motor shaft is determined %" the n$m%er of

p$#ses re!eied %" the motor, and rotationa# speed is determined %" the fre($en!" of the p$#ses.

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6.11 What is a so#enoid?

Answer: A so#enoid is an a!t$ator that !onsists of a moa%#e p#$n)er inside a stationar" +ire !oi#. When a!$rrent is app#ied to the !oi#, it a!ts as a ma)net, dra+in) the p#$n)er into the !oi#. When !$rrent iss+it!hed off, a sprin) ret$rns the p#$n)er to its preio$s position.

6.1* What is the differen!e %et+een a h"dra$#i! a!t$ator and a pne$mati! a!t$ator?

Answer: i# is $sed in h"dra$#i! a!t$ators, +hi#e !ompressed air is $sed in pne$mati! a!t$ators.

6.13 rief#" des!ri%e the three phases of the ana#o)-to-di)ita# !onersion pro!ess?

Answer: he three phases of the A/ !onersion pro!ess are &1' samp#in), +hi!h !onsists of !onertin) the!ontin$o$s si)na# into a series of dis!rete ana#o) si)na#s at periodi! intera#s8 &*' ($anti9ation, in +hi!hea!h dis!rete ana#o) si)na# is assi)ned to one of a finite n$m%er of preio$s#" defined amp#it$de #ee#s,+hi!h are dis!rete a#$es of o#ta)e ran)in) oer the f$## s!a#e of the AC8 and &3' en!odin), in +hi!h thedis!rete amp#it$de #ee#s o%tained d$rin) ($anti9ation are !onerted into di)ita# !ode, representin) theamp#it$de #ee# as a se($en!e of %inar" di)its.

6.14 What is the reso#$tion of an ana#o)-to-di)ita# !onerter?

Answer: he reso#$tion of an AC is the pre!ision +ith +hi!h the ana#o) si)na# is ea#$ated. Sin!e thesi)na# is represented in %inar" form, pre!ision is determined %" the n$m%er of ($anti9ation #ee#s, +hi!h int$rn is determined %" the %it !apa!it" of the AC and the !omp$ter. n e($ation form, reso#$tionRACL/&*n-1', +hereL f$## s!a#e ran)e of the AC and n n$m%er of %its.

6.1 rief#" des!ri%e the t+o steps in the di)ita#-to-ana#o) !onersion pro!ess?

Answer: he t+o steps in the /A !onersion pro!ess are &1' de!odin), in +hi!h the di)ita# o$tp$t of the!omp$ter is !onerted into a series of ana#o) a#$es at dis!rete moments in time, and &*' data ho#din), in+hi!h ea!h s$!!essie a#$e is !han)ed into a !ontin$o$s si)na# &$s$a##" e#e!tri!a# o#ta)e' $sed to drie theana#o) a!t$ator d$rin) the samp#in) intera#.

6.16 What is the differen!e %et+een a !onta!t inp$t interfa!e and a !onta!t o$tp$t interfa!e?

Answer: A !onta!t inp$t interfa!e is a dei!e %" +hi!h %inar" data are read into the !omp$ter from someexterna# so$r!e &e.)., the pro!ess'. t !onsists of a series of simp#e !onta!ts that !an %e either !#osed or open&on or off' to indi!ate the stat$s of %inar" dei!es !onne!ted to the pro!ess. A !onta!t o$tp$t interfa!e is adei!e that !omm$ni!ates on/off si)na#s from the !omp$ter to the pro!ess.

6.17 What is a p$#se !o$nter?

Answer: A p$#se !o$nter is a dei!e $sed to !onert a series of p$#ses into a di)ita# a#$e.

PROBLEMS

Sensors

6.1 $rin) !a#i%ration, an ron/Constantan thermo!o$p#e is 9eroed &set to emit a 9ero o#ta)e' at 0 C. At70C, it emits a o#ta)e of 3. m;. A #inear o$tp$t/inp$t re#ationship exists %et+een 0 C and 70C.etermine &a' the transfer f$n!tion of the thermo!o$p#e and &%' the temperat$re !orrespondin) to a o#ta)eo$tp$t of *.6 m;.

Soluton: &a'E mT 3. m; m&70C' m 3./70 0.0173 m;/Cransfer f$n!tion:E! "#"$%&' T

&%' AtE *.6 m;, T V/m &0.0173-1' &*.6' $&(C

6.* A di)ita# ta!hometer is $sed to determine the s$rfa!e speed of a rotatin) +or2pie!e in s$rfa!e ft/min.a!hometers are desi)ned to read rotationa# speed in re/min, %$t in this !ase the shaft of the ta!hometer isdire!t#" !o$p#ed to a +hee# +hose o$tside rim is made of r$%%er. When the +hee# rim is pressed a)ainst thes$rfa!e of the rotatin) +or2pie!e, the ta!hometer proides a readin) of s$rfa!e speed. he desired $nits fors$rfa!e speed are ft/min. What is the diameter of the +hee# rim that +i## proide a dire!t readin) of s$rfa!espeed in ft/min?

Soluton: Ci!$mferen!e of +hee# C 1 ft 1* in

C D D C/ 1*/ '#)%*& n

6.3 A di)ita# f#o+ meter operates %" emittin) a p$#se for ea!h $nit o#$me of f#$id f#o+in) thro$)h it. he

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parti!$#ar f#o+ meter of interest here has a $nit o#$me of 7. !m3per p$#se. n a !ertain pro!ess !ontro#app#i!ation, the f#o+ meter emitted 64 p$#ses d$rin) a period of 3.6 min. etermine &a' the tota# o#$meof f#$id that f#o+ed thro$)h the meter and &%' the f#o+ rate of f#$id f#o+. &!' What is the p$#se fre($en!"&9' !orrespondin) to a f#o+ rate of 7,000 !m3/min?

Soluton: &a' V 64&7.' '&$+&%' ,-'

&%' Q 37,713/3.6 %".+'6$ ,-'/-n

&!' Q 7,000 !m

3

/min 1*0 !m

3

/se!fp &1*0 !m3/se!' / &7. !m3/p$#se' *1. p$#se/se! (%#$* H0

6.4 A too#-!hip thermo!o$p#e is $sed to meas$re the !$ttin) temperat$re in a t$rnin) operation. he t+odissimi#ar meta#s in a too#-!hip thermo!o$p#e are the too# materia# and the +or2pie!e meta#. $rin) thet$rnin) operation, the !hip from the +or2 meta# forms a

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6.7 n the preio$s pro%#em, +hat is the po+er de#iered %" the motor at the operatin) point in $nits of &a'Watts and &%' horsepo+er?

Soluton: &a'P T

73.6 rad/se! from preio$s pro%#em

T 1.14 = 0.04 1.14 = 0.004&73.6' 0.1 -mP 0.1&73.6' . W

&%'HP .6/74.7 0.00 hp

6. A o#ta)e of *4 ; is app#ied to a C seromotor +hose tor($e !onstant 0.11 -m/A and o#ta)e !onstant 0.07 ;/&rad/se!'. Armat$re resistan!e 1. ohms. he motor is dire!t#" !o$p#ed to a %#o+er shaft for anind$stria# pro!ess. &a' What is the sta## tor($e of the motor? &%' etermine the operatin) point of the motor

if the tor($e-speed !hara!teristi! of the %#o+er is )ien %" the fo##o+in) e($ation: TLKL1@KL**, +here

TL #oad tor($e, -m8 an)$#ar e#o!it", rad/se!8KL1 0.00 -m/&rad/se!', andKL* 0.00033 -m/&rad/se!'*. &!' What horsepo+er is %ein) )enerated %" the motor at the operatin) point?

Soluton: &a'Ia *4/1. 1*.63 A T 0.11&1*.63' 1.4 -m

&%' Boad tor($e &)ien': TL 0.00 @ 0.00033 *

otor tor($e: T 0.11*4 0.07

1.

0.11&1*.63 = 0.01'

1.4* = 0.007Set T TL1.4* = 0.007 0.00@ 0.00033 *

1.4* = 0.0107- 0.00033* 0

earran)in), 0.00033*@ 0.0107- 1.4* 0

So#in) the ($adrati! e($ation, -16.47 6.3 1. rad/se! &ne)atie a#$e not feasi%#e'

&!'HP 1.14&1.' / 74.7 0.0 hp

6. he step an)#e of a !ertain stepper motor 1.. he app#i!ation of interest is to rotate the motor shaftthro$)h 10 !omp#ete reo#$tions at an an)$#ar e#o!it" of *0 rad/se!. etermine &a' the re($ired n$m%er of

p$#ses and &%' the p$#se fre($en!" to a!hiee the spe!ified rotation.

Soluton: 1. ns 360/1. *00 step an)#es

&a' o rotate 10 reo#$tions,Am 10&360' 3600np 3600/1. (""" pulses

&%' o rotate at *0 rad/se!,fp *0&*00' / * 6'6#6 H0

6.10 A stepper motor has a step an)#e 7.. &a' o+ man" p$#ses are re($ired for the motor to rotate thro$)hfie !omp#ete reo#$tions? &%' What p$#se fre($en!" is re($ired for the motor to rotate at a speed of *00re/min?

Soluton: 7. ns 360/7. 4 step an)#es

&a' o rotate reo#$tions,Am &360' 100np 100/7. (." pulses

&%' o rotate at *00 re/min,fpNns/60 *00&4' / 60 %6" H0

6.11 he shaft of a stepper motor is dire!t#" !onne!ted to a #ead s!re+ that dries a +or2ta%#e in an x-y

positionin) s"stem. he motor has a step an)#e . he pit!h of the #ead s!re+ is 6 mm, +hi!h means thatthe +or2ta%#e moes in the dire!tion of the #ead s!re+ axis %" a distan!e of 6 mm for ea!h !omp#etereo#$tion of the s!re+. t is desired to moe the +or2ta%#e a distan!e of 300 mm at a top speed of 40mm/se!. etermine &a' the n$m%er of p$#ses and &%' the p$#se fre($en!" re($ired to a!hiee this moement.

Soluton: /step ns 360/ 7* step an)#esit!hp 6 mm/re

x 300 mm at 40 mm/se!$m%er of reo#$tions 300/6 0 reo#$tions of the motor shaftN &40 mm/se!'&60 se!/min'&1 re/6 mm' 400 re/min 6.667 re/se!

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&a'Am &0 re'&360/re' 1,000np 1,000/ '6"" pulses

&%'fpNns/60 6.667&7*' .)" H0

6.1* A sin)#e-a!tin) h"dra$#i! !"#inder +ith sprin) ret$rn has an inside diameter of mm. ts app#i!ation is top$sh pa##ets off of a !one"or into a stora)e area. he h"dra$#i! po+er so$r!e !an )enerate $p to 3.* a ofpress$re at a f#o+ rate of 17,000 mm3/se! to drie the piston. etermine &a' the maxim$m possi%#e e#o!it"of the piston and &%' the maxim$m for!e that !an %e app#ied %" the apparat$s.

Soluton: Area of !"#inderA 0.*&'* 60* mm*

&a' V Q/A &17,000 mm3/se!' / 60* mm* ()#&& --/se,

&%'FpA &3.* /mm*'&60*' %*+.6( N

6.13 A do$%#e-a!tin) h"dra$#i! !"#inder has an inside diameter 7 mm. he piston rod has a diameter 14mm. he h"dra$#i! po+er so$r!e !an )enerate $p to .0 a of press$re at a f#o+ rate of *00,000 mm3/se!to drie the piston. &a' What are the maxim$m possi%#e e#o!it" of the piston and the maxim$m for!e that!an %e app#ied in the for+ard stro2e? &%' What are the maxim$m possi%#e e#o!it" of the piston and themaxim$m for!e that !an %e app#ied in the reerse stro2e?

Soluton: >or+ard stro2e areaA 0.*&7'* 441 mm*eerse stro2e area A 441 = 0.*&14'* 4*64 mm*

&a' >or+ard stro2e v *00,000 / 441 .$#' --/se,F &441' ((+"*" N

&%' eerse stro2e *00,000 / 4*64 .6#* --/se,F &4*64' (%+'(" N

6.14 A do$%#e-a!tin) h"dra$#i! !"#inder is $sed to a!t$ate a #inear

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.0 0 11

* 1

. & 'n

, &*n-1' 0.&11'/ 11., *n 1*.

n1n&*' 1n&1*.' n *.*6/0.63 3.64 Ese n! .

&%' 1 o#t max 0.RADC1

* * 1

an)en

1.0

0 11

* 1

. & '

n , &*n

-1' 0.&11'/1 7. *n

.

n1n&*' 1n&.' n 4.06/0.63 .7 Esen! 6

&!' 0.1 o#t max 0.RADC1

* * 1

an)en

0.1 0 11

* 1

. & 'n

, &*n-1' 0.&11'/0.1 7.0 *n 76.0

n1n&*' 1n&76' n 6.36/0.63 .17 Ese n! %"

6.17 A di)ita#-to-ana#o) !onerter $ses a referen!e o#ta)e of 1*0 ; d! and has ei)ht %inar" di)it pre!ision. none of the samp#in) instants, the data !ontained in the %inar" re)ister 01010101. f a 9ero-order ho#d is$sed to )enerate the o$tp$t si)na#, determine the o#ta)e #ee# of that si)na#.

Soluton: Vo 1*0F0.&0' @ 0.*&1' @ 0.1*&0' @ 0.06* &1' @ 0.031*&0'@ 0.016*&1' @ 0.0071*&0' @0.00306&1'G

Vo '*#). 3olts

6.1 A AC $ses a referen!e o#ta)e of 0 ; and has 6-%it pre!ision. n fo$r s$!!essie samp#in) periods, ea!h 1se!ond #on), the %inar" data !ontained in the o$tp$t re)ister +ere 100000, 011111, 011101, and 011010.etermine the e($ation for the o#ta)e as a f$n!tion of time %et+een samp#in) instants 3 and 4 $sin) &a' a9ero-order ho#d, and &%' a first-order ho#d.

Soluton: >irst samp#in) instant: 100000, Vo 0&0.' 40.0 o#tsSe!ond samp#in) instant: 011111, Vo 0&0.* @ 0.1* @ 0.06* @ 0.031* @ 0.016*' 3.7 o#tshird samp#in) instant: 011101, Vo 0&0.* @ 0.1* @ 0.06* @ 0.016*' 36.* o#ts>o$rth samp#in) instant: 011001, Vo 0&0.* @ 0.1* @ 0.016*' 31.* o#ts&a' Hero order ho#d: V5t ! '6#($%et+een instants 3 and 4

&%' >irst order ho#d: V&t' 36.* @ a t%et+een instants 3 and 4 a &36.* - 3.7'/1 -*.

V5t ! '6#($ 1 (#$t

6.1 n the preio$s pro%#em, s$ppose that a se!ond order ho#d +ere to %e $sed to )enerate the o$tp$t si)na#. he

e($ation for the se!ond-order ho#d is the fo##o+in):E&t' E0@ t@ t*, +hereE0 startin) o#ta)e at the%e)innin) of the time intera#. &a' >or the %inar" data )ien in the preio$s pro%#em, determine the a#$es

of and that +o$#d %e $sed in the e($ation for the time intera# %et+een samp#in) instants 3 and 4. &%'Compare the first-order and se!ond-order ho#ds in anti!ipatin) the o#ta)e at the 4th instant.

Soluton: t 0: V&t' 36.* 36.* @ a&0' @ &0't -1: V&t' 3.7 36.* @ a&-1' @ &1't -*: V&t' 40.0 36.* @ a&-*' @ &4'Sim$#taneo$s so#$tion "ie#ds a -3.1* and - 0.6*V&t' 36.* - 3.1*t- 0.6*t*

At the fo$rth instant, the se!ond order ho#d "ie#ds

V&t' 36.* - 3.1*&1' - 0.6*&1' '(#$ 3oltsAt the fo$rth instant, the first order ho#d "ie#dsV&t' 36.* - *.&1' ''#&$ 3oltshe a!t$a# o#ta)e #ee# at the fo$rth instant is 3*. o#ts. en!e, the se!ond-order ho#d more a!!$rate#"

pro

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