control systems prakticum

8/10/2019 control systems prakticum

1/12

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


2/12

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


3/12

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

-]


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


5/12

;

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


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


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


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.


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

-


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


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


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+

control systems prakticum

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