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Frrrtl-rer
Ccntrnl
cf
tlre
ftC
Motc,r l+lnclr-rle
Chapter
5,3
I
ntegraI
S1:eer1
[--lrrtrr:l
#
Fxrr"eis e
72
Construct
lhe s,;stlm
ir-:
:- 3
r.1
,cet
ProOort;cnal
lLtr
Derivative
Ot-lT
lntegrallN
ki
.-
G
Fllter
Cl,.lT
*
f
P.*rr
Coan..li$r
ur
Shrn
Far
Clrrilv
?
Apply
an input
cf
*2V at
0.1
l'lz
?nd
cbser.rq
boih cr:mrnand
VOltaOe
1n{ llro
l?f
l-r1qo6qlntnr_c
f
oc4brCk
r.,a i?Oo 1tpr*gf,nri;19
0utP il.
(r'i
D-4. f,trla. C.nr:.1
u.xtult
Fuq l3a
Ctntr.lo.
E
(>-
0v
voL.l
ovO
vour
O
ovO
F-C
E11
ovO
Dfo
or
c)
orO
030
ovO
pro
oy
(l
Crm-'
ll
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8/10/2019 control systems prakticum
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lntegral
Speed
Coriirol
Cliaptcr"S,s
f
l'rc
ierpoi
ise tr
a
'sluil'
unJeidarilped
f
eSLrCnSe
i$.e
f
ig
o.i
lrt;;ut
_--*.
Ou iptr
t
&
lnc;
ease
k;
to
t
2.
Ooser-ve
tfie
overs[ioJt
anO
osciilation
incrcases.
3
flecord
the
iime
taken
to
reach
lhe
p;ak
ovrsricct.
3 fieouca
k;to
1.
Oi.,Serv'e
tl-re reSponSe iS
riorv
O.r,erOampecl_
We
have
thus
created
a
fiew
speed
contrul
syst.c,ri tvltrI
predominantly
second
ordei'characteristics
tnat
ere
cor
rriuricrl
r.:;
k;.
5
Set k1
lc
ci.
3
Heouce
the
inpur
frequency
to
zero
so that
ille
r.lrive
rtin:
at a
constarrt
speed.
I
Fleouce
the input
ampiitlrde
to
give
an uuiput
speao
oi ar;i,t
i
100 rev.
min
I
i;ii
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8/10/2019 control systems prakticum
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Chapter
5"3
lntegral
Speed
Cnnircl
SuCCenlv
ar:nlv
llte
f.rr:r,.g
3p1rt
cls9r.,,.
1h.,i15p.r1r,..
Ren-nt
fcr
: i,-r.dder r: r::.:
Cb;tr:,'a
a
lransieni
lika
Fir:
ES b'-,1
n.,to
il-a tIr,
as;11i1
rq,q.i.,,,o.-r
e
F:ooat
at
r:?[rcr
otin"
Ensure
that
the inpul
a.nd
cutr:u
lsc;tlcscc:no
titces
e.,,
rl:i
each
ciher
w,iih
zere
innut.
F
l'Jor^r
chanoe
to
a FA,lu4Fr
inprrt
a 0 1l-Jz.
lF
Set ki tr:
10 an.1
Shrer-;e
lhat
thr:
foltny.,inrl
error
lerrris
to
ztr,:
These
a.spects 4ll
cr
lpgrnrf
ll-'e p;n;-r1,qi,ls
r.f
lht
Drel.ri(rl.
Ch?r.: er
F
'F
\
f
I
{
Brake
,n'
n1-'lierl
-]
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8/10/2019 control systems prakticum
4/12
Furtl"rer
Contral
of the
DC
Mntnr
l;1r.,rJtrle
Chapter
5.21
Propoiiic;,at
+
fr"r;i
sp-eec,;i6l
The
pre'rious
exercise
has
sufrpcrteC
our
nroccsals
of
elirninafinn
steadv
state
errtr.s.
lt r^",i t
also
supoorl th,l
corlept
cf
a
s o,.v.,
resooqse.
When
you
recorded
the
time to
peak
lor
a
lZy input
and
k
i
-.
1
2
it
i.
likely
to
be
around 6CCms.
This
is
mLrch
mcre
th2n
r.ye
had
y.,irh
prcforlionalcontrol.
You
may
have
noticec
thai
the
RlsE
Trr\"' E (usu
r:ilv
crf
rnec
3
ihs
time taken
bythe outputtochanoe from
r0?i
to
90%
oliis
tinar
steady
va.lue) is
actually relaiivelv
short vrith
inteqrat
coniror
birt
lhe
trarrsient
oscillations
are
al a relatir,,ely
lcw
fr.equency
thus
extending
the
lime
taken
to
seiile
lf
these
roulC
be
da:r:ne-,C
lirr
:
f
aster
everal
re:p3ns?
",'.f
ui(,J
resull
The
adtJitien
of
nrc'pc. icnal
ccntrr.:l
',vill
ha,,
+
g,1c-jccry
r -riq
of
fnr...l
+
trXorCiSF
T3
PrcceeC
aS
per
lhe
early
staqes
cf Exsrcise
2?,
jbtair;r:,:
ll-r.
steD
resncnse
to
a :t2\.r'inprll
al
0.
1
H.:
w,ith
k;
=
.l
?
lJorv
set
lh:
prcpct'-iicnal
glin
tr:
0.
1
er"rC
s,.,ritr;h il
irr"
lncrease
the
prcportiona
c':in
end
cbser;e
lh:trhl
c,",errlr:c.l
is
eventually
darnr-red
cut.
This
leaves
a
response
that
-se[les
in
a
much
shcrier
trme.
r.br:r-rt
half
that
with
in'1,.:cra
alcne,
but
relains
iire
at-*,.ilitv
f
c
cl,rntq:r
ce
lcrr:::t
Cisturbances"
Run
a.t 75
rev
and
verif't
lhe
above
bv
ryino
lo
slo.*,ihe
3.,,q ern
h,,,
min
orippipq
the
output shaii.
ProportionalActian
provi
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8/10/2019 control systems prakticum
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;
ftrurthsr
Contrr:l
of
the
DC
Mctor
Mor-tule
Cfiapter
5"5
-p;;F,t
fi;i
ptt-;;
Trr*s;efpil;
[]e
ri,.,a
lirze
Posi
ric
r"r-
Crn
trcl
\Ve
p'c.oseC
that
intenrlrrontrSl
alinq,r,,c'l,i
pit;1,-rcl
;;r 1
q115f
:iIf
.
cosition
contrrl
action.
This
cccurs
because
of
the
excessil,e
nhase
ra?
that ic
r_-riiirrcef
?:
irrfcrmatien
pass?s
areund
lhe
cenircl
locp.
A
simple
sinusoid
entering
the
ccnlroller
y/ould
come
oul
vrif
l
gf
.1l
lag'
the
inherent
inteqrarion
to
oesiricn
gives
ar.:other
30.
anr:lrho:
basic iirsl order iime
lag can
give
up to
Jncther
90.. We
cirnsl
rcrl.,.
expect
anythinO
other
than
chaos
and
that
is
whar
r,re
oEf
T hi
mechani-qm
cf
insiability
is
disrr.:sse.d
laler
on
Horvever
we
have
jusi
disco,rered
lhat
a
Frrcpcrtional
action
is
caCable
of
reducing
Chase
l;1g5
u;ho1
il
i5
66,,n1-ri1ed
uriih
inr.n-.t
As
such
P
* I
conlrol
of
pnsition
reoresenls
a
means
ci
cf
rsinlpa
our
_qr:als.
lf
ther.
is
ntt
enr*..u h prcctiional
inf
luence
11.1e
;,,.3i.f",
,,.;r1
ho
t rnclrhla
lf
yOU
u;CndereC,,,;hat
insil[,.iii1,,.
lr:lksd
lii,.9
r.,nr1c?r,]
rr-1 .,,
denrnslrate
it.
E
.:
;
,
{
G
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8/10/2019 control systems prakticum
6/12
F'ropcirtional
Plus
lntegral
Plus
Derivative
Pusiiiorr
Contrcl
Clrapter
S"L
I
Ixer
cisu
2{
Construct
Fig
BrJ.
Set
Proponionai
ll.j
lntegrallN
Derivative
OUI-
FiiterOUT
I
a
kp:
2
ki
=1
PS.i
Syrirm
Powrr
i0
rl2V
.l
2V
Vlf,
ovB
Vout
Q
ovo
O.a,llorCJpa
t*__*l
Molo(
Conlral liodult
(
--
As{
P.r.o.
co,rrrorr.r
-
$*-tr-
t;f1""'"'"*il;fr"*'t
".|
fB,,
,r;,*"3"'Il
L--
rfl:::":-'::
::lJ
::trs
",sl)
;:::::"::;:
w
.,.31
I
-*---:)
".u*'---_.
Pcw.r
Connrcttali.
a{ot
5hq{a
ro; C.did,
l,E
i3
Apply
a
+0.5V
square ware
ar 0.2H2.
Tire
response
snuuld
be
unoerdariiped,
wilr,out
muclr os,illaticr-i
&
lil,:rea:e
tiie
integal gain
ki
one
positior,;r
a tirne
ar'o
jtudy
it,,;
respoflse.
Wrur ki
arourrd
6 or 7 the
ciecay
oi
oscillation
is
iairly
small.
o lleduce
the
input frequericy'ro
0.11-lz.
t
It,crease
kr.
Furtlan
Grnrrrr;r
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8/10/2019 control systems prakticum
7/12
Chapter
5,5
P*p";il*;l
r,,l*
trl-"gr=l
n*
Derivative
Position
Cr:ntrnl
A
virtually eonstant
arnplituce
of
escil ,eiicn
m?y
he
obt:rintc{
at
som*
staoe.
rf
you
can
achieve
this
then
yori*'ri
n.*
rhrt
it
continues
even
if
you
rmove
the
innLrt.
This
is
a
cfl
TlcA
LlY',
S
ra
gq..r
sYsrFt,t.
f;
Furher
increase
ki
^
the
sysf?m
beccmes
lrprrq.| o.
Yc'u
will
f;nd
the
intagraf
res+t
butinq
r:sefr_rt frr
rqIrrnin,:l
the
svstem
tc
a
-qtahle
stata.
Having
demonskaled
that
rhis
system
can
becorne
unstat.:r,
,*o
r,r.ill
return
tc
ths
eriqinal
tasi
rf
nr:sition
ccntrcl"
s
-set
kp
to
'r
l,
ki
to 10.
(r.lnr^
-
you
mFv
h;ra
tr:
v,..rk
.rr,
t^
theSe,/?lL,qs
e,?Crltil,,,),
The
system
is
now
rnuch
slif{er,
staile
h,.lt
-,.,ery
c, i:irr:t^r:,
{'i
Exert
a
bad
an the
ourpsl
3[311.
Cbserve
the
inl*gral
ac,tir:n
trvinc
tr
realign
the
s,"rttern.
$/+
are
FCw
progTussine
t-.rt
nred
more
darnpino.
There are
l'r'*: ch+ices,
ver.::ihr leedback
en,J
rJcrivativg
r:ri^ri
Derivative
action
is
not
nar-ticurarry
weil
suited
to
th+
characterist'cs
of
he
serv,
and ir
a" sn
;.ospnncs
badry
ra
lhe
noise
generated
t'y
the
servr:"
Nevertheless
a
useful
resutt
can
be
ohtained.
t-i
Switch
in
the low
pass
filter
at
3,{l_t;
lc filtrr
eut
tha
noise
generp-te
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8/10/2019 control systems prakticum
8/12
Proporiional
Plus
lntegral
Plus
Derivative
Position
Contrc;l
Cfiapler
r.,
i.
Suriuiiary
$tttdertt
Assessnrent
5
,
I
{.
1.
c
Proportic;ral aciioit
is
ti-re luncjarriental fiiurls.
inteEral
action
is
capaole of renroving tiie
iotlowiri
rroi
;,,-j
oilset
due
to
an
external torque
but
its
inclusion
slows
& o7
i,li
,.
dovrn and
increases the tendancy
to be
unstabie.
lt
can
De
.',i
,.,
alone
to
control
a
basic lirst order system
but
not
a
systeni
tr;ri
already contains
an
inherent integration.
Proportional acticn
adds
a
oamping
eiiect
tirisn
cori
rcrr,
rud,,
i.,,
integral. This occurs
because
the combined
terms ifiti'ocr-rc"
,
phase
lead
er{ect
that
helps counter
the
inherent systern
lag.
Settling
time
can
be
irnproved
by its
adcjition.
Derivatrve
action can
provide
lurtner
stabilisatrorr
btit
it i.,
extremely sensitive
to noise. lvlcre
sophisticated
circuitry;,*,,
,.
used
to
partly
overcome this
but the
only
real
solution
is
trr
remove
the
noise
at source. Derivative
acttctr
is
very
coflrr,,.,,, ,
in
process
ccntrol bui
in
rnost
servo systems
veiocity'ano
transient
velocity teedback
is
preterred.
Wnat
is
a series
cotr,periscrlcr
?
Describe
in
your
owri
v,'orciS the
t,asic
corliuepi
r.rf ir'r.,i,;iiri.,
integral
and derivative
terms.
Explain
the ternis lntegralGair,
and
Derrvoitvs
Girtri.
\ruhy
can
derivative
action
be
very tioubiesoni'.;?
Discuss
the steps
tnat
might
[:e
taken
to
reduce
trr&
problems
inherent
in
derivative
action.
Vr'nal
eiiect ooes
the adcjition
ct
prc;porironcl
cofltii;t
t
i.
'.
.-.
on
the
system
when integralaction
is
used?
Wlry can't
tlertvative cor:trol
De
used
orr
its own'?
Discuss
the
response
of integial
arrcl derivailve
elii,,-,,,--
when
fed
with
step,
ramp
and
sinusoidal
inputs.
l{ny
can't
integralcontrolbe
useo
ori
its orvn
ior
tire
p;;ii.,
corltrol?
l3d
(
7.
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8/10/2019 control systems prakticum
9/12
_
Furth*r
control
of
the
frc
Motor
tv arju *
Cha;:ter
6.d
lnstabi ity
in
l:he
DC
Motor
Morjr-rl*
we
cannot
usefullv
test
a.n
unsfabre
svstem
and
iherefore
it
is
apOropriale
tC
test
Oper-r
IncO
sysls,-rs
arcj
see
if
ihe conditicr]S
ilr.
insta
bilitv
are
present.
Contrary
to
lvhat
you
may
think
f
rcm
readino
text
hrooks
ma
ny
real
-
-
8/10/2019 control systems prakticum
10/12
lnstability
in
tl-ie DC Motor Mociule
Ctrapter.
6.+
*'
[.,.ercise
25
t,
C.:;rsi.ruit
liie
crrcutl
rr', Flg
96
fuettoo C.o.r.{d,
PS{ iy.l.6 Po*rr i0
,l?v
OV
.l
2v
vcF
lnpat
o
Vln
E
0v
Vout
Q
ovO
V0ul
e
ovO
P*O
Ec)
ovO
o00
oro
ozO
o30
ovO
P00
0vo
A5{ P,l-O. cJntroll.(
do
0-o
6o
+l2V
0V
'11V
liP
Q
crr'
Cr
Ou
C mr*0(,
)up
rror
C,P
Vollrc.
C
f
O
-
i
Cc,rl.cllrr
O
^.
uJr(rcll,i IP
q
O,p
/\t)
rnnrr
Locp
^
\*
t..dcrci
Pg
Aui.
F.rdDdr
P
(yO
M.in i.ndosk li?
lt?
c'
P
Po(.f
Corinr;llurr ho{ 5no ,1 for
airiity
Fig
5o
frtS I
5 O.C.
Molor
Cqntrol
Modul.
Set rhe
follcwing Proponir,nal
lN
l.p
=
lntegrallN
ki
=
.l
Derivitive
OUI'
FilterOUT
c
are
going
to
use P
+
I
positicln
co{ttrci
arrd
aie
ioli.rrvtr ,g
tt,.;
procedure
of
Exercise
24
conducted
earlier.
$
Apply
a
-r0.5V
squ
are
lvave
at 0.
1
Hz ano otrse
i^r'e
titr=
ilolr
i,
r,-,
,
input
ano
potentio.neter
output
on tha
cscilloscope.
*
increase
ki until the
syslefi
goes
unstaole,
usuaily
irroUrir;
ki
=9toki=
Il.
I'Jote lhe
value
of
kijust
befoie
this
occurs,
t'lpically
c
to
10.
S''henever
the
syslem
runs
avJay
hoid
th.,
iirtegral
reset
outi.rr,
iir t,.
return
it.
t";
Oicilbr:op.
Qou
o
_,1
l
-
8/10/2019 control systems prakticum
11/12
Chapter
6.4
lnstaL"rility
in
tire
DC
ltlotor
MccJr_rle
G
G
Havino
established
lhis
ccndition
r,,,q
no,,v
w?nl
to
v*r.ify
thal
the
eiemenls
in
the
loop prorluce
a
lain
clesr
t.: i.rnitv
,rriih
gQ-,.
1,t::
tc
f
:6
G
Suzilch
off
the
siqnal
0eqeralcr,
G
Remove
theoscilloscoF,e
lead
monitor.ing
the
cornnrar.rd
lrrr-j
connect
it
ln
reaC
lho
rrrlpr.itcl
lhe
eri.cr
dgter:ror.
Return
kito
j
G
round
the
cscillosccce
input channe
is
mcrnen
taril,v
a nrJ
oyerlav
the
hva
li.ares
Set
hoth
gain_*
lc
O
,I_
C
I-T1
tri
select
a
sinrrsoicJar
innur
at
1r-lz
and
s,,vitch
on
the
gencr?ior.
1
t-{z
is
selected
because
loiver
f
reqs6ncies
will
shr-rrr
sionif
ii:frr-rt
i-lcn
l'l:,,'l'?:,lit
fhe
systern
andin
qcr?re
,r.,.,.,r..,,11-,.,,,,,.=.^^,i,r,-,,,=
tcr
instabilityoccur
at
I
-
t.3t-tz,
C)bsen,e
the
hvo
sinuseiCs.
The feedback signal,
u",hich
won'l
be
a
truc
sinusoid,,,;ill
be
:-:.:ll,1r
than
the
error
and
laocino
by
120"
or
5a
lncrease
kiin
sleps
3it3winQ
the
system
to
s_-tlte
each
rinre
Observe
thatthe
pt,.ass
lag
is
increasino.
ryl't':
hapgening
is
that
ihe p.eviousry
mentionec
phase
iead
rfrecl
of
the
tr
*
I
ter"ms
becornes
ress
at lhe
il-lz
freoLrerrcv
as
ki
increas.o
G
V/hen
ki
reaches
around
g
-
10
you
shcutrj
havq
clole
lt
1gn.
phase
with
a
oain
less
than
ur:ity.
t
Very
slo,*ly
increase
lhe fTeouency.
The
anrnlitLr;i9
5l-1ny16
inrr?a"o
anrj
he
qvs an-r
,,,.ill
L,ecnme.n
-
8/10/2019 control systems prakticum
12/12
lristability
in
ti're
tJC
fi,4cior
ivlociule
Cha[-,tt;l
o
-i
Studerr
t
Assesslt
ierrt
S
I
.
Erietly
ois:uss
lne
ierin
stabie
and
gi"'e
a
E'nsral
oo'ilr-rlit-'
r
of
it.
ldentiiy
any
non
linearities
in
tne
systcrn'
Y/lrat
is a
iirnit
cYcie?
What
concirion
in the
operi
toop'
i':equ:ncy"
r-ispoirsc
r\vulo
icjentify
a
systern
as
being
unstabie
in
closed
loop
ft.iiiit
even
though
eacn
element
is
itsetf
stable?
Why
is
the
position
controlsystem
o:sicalty
t',tnslabls
rviilr
2"
3"
4
+.
integral
control?
6.
'vYrry
oces
proponion;,i
action
impror':
tr'e
st;iriliiy?
7
.
lf
a
close,J
loop
system
nas
a
pure cjeoo
time
Ji
10rris
''
'c
a
toop
Eain
of
10
oescrioe
tn*
output
oeriaviour
otrCg
EXCitu:
by
an
imPulse.
i3+