08 elc4345 fall2013 pi controller

8/18/2019 08 ELC4345 Fall2013 PI Controller

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_08_ELC4345_Fall2013_PI_Controller.doc

Version Nov. 06, 2013

Overview

In this lab, you will add feedback to your buck/boost converter. he controller will hold theout!ut volta"e at a set !oint by auto#atically ad$ustin" the duty cycle control si"nal to the

%&'() firin" circuit.

Introduction* !ro!ortional+inte"ral controller i.e., -I with feedback can take the !lace of #anual

ad$ust#ent of the switchin" duty cycle to a + converter and act #uch #ore uickly than is

!ossible by hand. onsider the ransfor#er, 45, %&'() (irin" ircuit, +onverter, and oad as a !rocess shown below. In the o!en loo! #ode that you used last ti#e,

you #anually ad$usted duty cycle volta"e cont.

o auto#ate the !rocess, the feedback loo! is closed and an error si"nal 7 or 8 is obtained.he -I controller acts u!on the error with !arallel !ro!ortional and inte"ral res!onses in an

atte#!t to drive the error to 9ero.

et :Vout be a scaled down re!lica of Vout. ;hen :Vout euals Vset, then the error is 9ero. *

resistor divider attached to Vout !roduces :Vout, which is suitably low for o!+a#!s volta"e

levels.

-a"e 1 of 16

cont

0+3.


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The Circuit

* detailed circuit layout of the -I controller is "iven in (i"ure 3. * total of si= o!+a#!s are used 8 two as buffer a#!lifiers, one for

error, one for !ro!ortional "ain, one as an inte"rator, and one as a su##er. 'ince the o!+a#! chi!s are duals, three o!+a#! chi!s arereuired to i#!le#ent the -I controller. ;e use four to de+clutter the circuit. eft to ri"ht, o! a#!s >1 and >2 are in one chi!, o!

a#!s >3 and >? not used are in one chi!, o! a#!s >< and >6 are in one chi!, and o! a#!s >@ and >A not used are in one chi!.In!uts to unused o! a#!s are "rounded. 4o=es link this fi"ure to #easure#ent locations in (i"ure ?.

-a"e 2 of 16

(i"ure 3. &! *#! I#!le#entation of -I ontroller

5 i is a 4


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(i"ure ?. - 4oard I#!le#entation of -I ontroller with &ct. 26 (i=es

4otto# ayer Not 'hown Here

-a"e 3 of 16


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O#tainin$ I%olated 12& 'ro( 12& )all )art

he o! a#!s are !owered by a 2; dual out!ut + converter chi!, 12Vdc in!ut, isolated12Vdc out!uts. etails for the dual out!ut converter and its 'I- socket are shown below.

-a"e ? of 16

(ront View

;all wart &! a#!s

In!ut &ut!ut

Care'ull* #rea+ o'' two o' the ,la%tic %ection%

with lon$-no%e ,lier% or dia$onal cutter%


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The E,eri(ent

In this e=!eri#ent, you will !ower a buck/boost converter with a 45, and use the controller tohold re"ulated 100& to a 150) incande%cent li$ht #ul#. &!erate your buck/boost converter at

about100+/.

te, 1. The PC%• *ll chi!s I- and 'I- are double+socketed. &ne socket is soldered to the - board, and

the other socket re#ains connected to the chi!. Fee!in" chi!s in a socket hel!s !reserve

their leads for future use.

• -o!ulate your -I controller. It i% ver* i(,ortant that the 100+ Ω and 1.5+ Ω re%i%tor%

at the to, ri$ht o' the #oard are the correct oh(ic value% and are ,ro,erl* (ounted.

• Jse nylon hardware to !hysically connect a %&'() firin" circuit to your -I controller,

overla!!in" as shown in (i"ure ?.

• (or !ower, solder >22 red and "reen $u#!er wires fro# the %&'() firin" circuit 12V

su!!ly to the 12V in!ut of the -I controller.

•

4rin" a >16 red wire fro# the out!ut of a buck/boost converter to the -I controllerter#inal labeled &NV)5)5 V&J, *5)(J, ;I )K)) 100V.

• Jse short >16 red and black wires to connect the )=ternal uty In!ut ter#inal block of

the %&'() (irin" ircuit to the cont ter#inal block of the -I controller.

• %ove the '- switch of the %&'() firin" circuit to the left !osition for )=ternal

uty In!ut.

te, 2. The et Point

• O OT ,ower u, the in thi% %te,.

• 5otate the et Point6 Pro,ortional 7,6 and Li(iter ,otentio(eter% to the 'ull*

countercloc+wi%e !osition.

• 5otate the Inte$rator ,otentio(eter to the 'ull* cloc+wi%e !osition.

• )ITC/ OFF the Feed#ac+ and Inte$rator PT %witche%.

• -ower u! the co#bined %&'() (irin" ircuit and -I ontroller.

• heck the isolated 712V and E12V out!uts on the -I controller to #ake sure they are

&F. Volta"es below 11V indicate a short circuit in your wirin", which will burn out the

+ chi! in a few #inutes.

• View VC' on an oscillosco!e and confir# that the wavefor# is clean and has a switchin"

of about 100+/.

• ai%e the et Point Potentio(eter so that the set !oint volta"e 4o= 1 is 1.5&. his

will be the tar"et volta"e of the controller, and it corres!onds a!!ro=i#ately to the

fraction of Vout across the 1.


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te, 3. The Li(iter

• O OT ,ower u, the in thi% %te,.

• View VC' on an oscillosco!e.

• )ITC/ O the Inte$rator PT %witch to te#!orarily drive the inte"ratorLs out!ut

to its 12V rail.• ai%e the Li(iter Potentio(eter so that the duty cycle of VC' is a!!ro=i#ately 0.A0.

he ob$ective is to !revent the -I controller fro# risin" to the D 1 condition which

would short circuit the %&'(). he resultin" cont %hould #e a,,roi(atel* 3.1&.

• he i#iter -otentio#eter will re#ain at this value for the entire e=!eri#ent. If the

!otentio#eter knob is accidently bu#!ed later, then si#!ly re+ad$ust it as e=!lained

above.

• )ITC/ OFF the Inte$rator PT %witch.

te, 4. et the O,en Loo, ain to 9nit*

• %ake sure that the Inte$rator Potentio(eter is 'ull* cloc+wi%e.

• onnect a 1


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scales on the sco!e, two ti#e constants can be observed in the res!onse. he slow one, in

(i"ure


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-a"e A of 16

(i"ure 1

'lowly and asy#!totically

a!!roaches the tar"et Vout

(i"ure 6. he (ast i#e onstant of Vout durin" the &!en oo! 4u#! est

this is a < #sec/div scale 9oo#+in of (i"ure


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te, ". Clo%e the Feed#ac+ Loo, and Chec+ 'or O%cillation due to 7 ,

• ;ith the li"htbulb on, )ITC/ O the Feed#ac+ PT witch. he li"ht bulb will

di# because the feedback volta"e reduces the error si"nal.

• &bserve and take note of the knob !osition of F !

. hen, swee! F !

throu"h its ran"e,

startin" fro# full counter+clockwise to full clockwise. If an oscillation develo!s, such as

li"ht bulb flicker or flicker in VC', back u! on F ! until the oscillation subsides and then

a bit farther. In #y case, there was always oscillation, but it "ot #uch worse as I

increased F !. I settled for 0.1? as bein" the a!!ro=i#ate onset of si"nificant

oscillation, althou"h there was no clear boundary. I was also kee!in" in #ind the desiredvalue of 7 , fro# theory see *!!endi= and the ne=t two bullets. 5e#e#ber that the

theoretical euations a!!ly to linear circuits, but our circuit is nonlinear due to the

D

D

V

V

in

out

−=

1 relationshi!. Nevertheless, the -I controller will work well.

• %easure and deter#ine the uotient EV4o=< / V4o=? . ;e define this uotient as 7P2.%y values were EE?.16 / 1.30 D 3.2.

• o#!ute the uotient F-2 / F-1. Cain 7 , in ;,,endi uotient 7P2 :

7P1. %y value was 3.2 / 6.A? D 0.?@.

te, ?. Turn on the Inte$rator and Care'ull* wee, Inte$rator Ti(e Con%tant Ti to Find

the oundar* o' In%ta#ilit*

• )ITC/ O the Inte$rator PT %witch. he li"ht bulb will i##ediately bri"hten

because the controller uickly raises Vout to the 100V tar"et value.

• If needed, raise the variac so that the 45 out!ut volta"e is ?0V. *lso, if needed, fine

tune the 'et -oint !otentio#eter so that Vout D 100V.

• ;hile watchin" VC' on the sco!e, carefully lower i by slowly rotatin" the Inte$rator

Potentio(eter countercloc+wi%e until si"ns of oscillation occur in VC' and/or you

detect audible bu99in". 4u99in" was very noticeable in #y circuit. ;hen that ha!!ens,

)ITC/ OFF the to$$le %witch. his is the onset of instability.

• Turn o'' the 12& #* un,lu$$in$ the wall wart.

• eter#ine 5 i at the onset of instability as followsM %easure the Inte$rator

!otentio#eter resistance by connectin" an oh##eter between the #iddle and ri"ht+hand

!ron"s. *dd the series 10kO resistor to your readin". he su# is 5 i. %y 5 i was 20kO.

hus, #y co#!uted iii C RT = D 0.?? #sec at the onset of instability. ;e want to staywell above this value.

-a"e P of 16


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te, 8. et the Inte$rator Ti(e Con%tant Ti

• he inte"rator should be faster than the !rocess, but not so fast to create instability such

as bu99in". -I tunin" rules reco##end that inte"rator ti#e constant iii C RT = bea!!ro=i#ately 0.A. (or our case, with 2 #sec fro# 'te!


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te, 11. O#%erve en%itivit* to Tunin$ Para(eter%

&bserve the effect that variations in tunin" !ara#eters 5 i and F ! have on bu#! tests.

'lu""ishness indicates do#inant !ro!ortional control. oo #uch rin"in" indicates do#inant

inte"ral control. * !ro!er balance is !referred. Include observations in your re!ort.

It a!!ears that the -I controller works well over a fairly wide ran"e of 5 i and F !.

)=a#!le sna!shots follow.

-a"e 11 of 16


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-a"e 12 of 16

losed oo! 4u#! est, 5 i D @3kO, F ! D 0 Inte"ration only

losed oo! 4u#! est, 5 i D @3kO, F ! at the #a=i#u#

losed oo! 4u#! est, 5 i D @3kO, F ! D 0 inte"ral only


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-a"e 13 of 16

losed oo! 4u#! est, 5 i D 3?kO $ust above the bu99in" threshold, F ! D 0.?@

losed oo! 4u#! est, 5 i at the #a=i#u#, F ! D 0.?@ #ostly !ro!ortional


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;,,endi. ;nal*%i% o' the Tran%'er Function

he circuit in (i"ure 2 re!resents the standard ne"ative feedback block dia"ra# with transfer

function

.,.,1

.,

.,

.,

s H sG

sG

sV

sV

set

out

+= , with 1, = s H .

hus, we have

.,1

.,

.,

.,

sG

sG

sV

sV

set

out

+= , *1

where , sG is the o!en loo! transfer function. In our case, , sG is the !roduct of the two

transfer functions

,,, sG sG sG LOADTER DCDCCONVER NGCIRCUIT MOSFETFIRI DBRTRANS PI ++++•= . *2

he second ter# is the !rocess transfer function , sG process . (or the -I controller, the !arallel

!ro!ortional and inte"ral co#!onents yield

i P PI

sT K sG 1

., += , *3

where

iii C RT = .

(or the !rocess, 1.


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'ubstitutin" *


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-a"e 16 of 16

Response of Second Order System

(zeta = 0.99, 0.8, 0.6, 0.4, 0.2, 0.1)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10

0.99

0.1

0.4

0.2

08 elc4345 fall2013 pi controller

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