control technique

8/18/2019 Control technique

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PRINCIPLES OFSTEADY STATE

CONVERTERANALYSIS

ANJANA SAP, EEE


2/26

REVIEW

• A simple dc-dc converter e!mple

•

Inp"t so"rce#$%%V• O"tp"t lo!d#&%V' $%A' &%%W

• (o) c!n t*is converter +e re!li,ed


3/26

REVIEW• .se o/ ! SPDT s)itc*

Vs0t1 2 V34 S $Vs0t1 2 % 4 S 5


4/26

REVIEW• S)itc* c*!n3es dc volt!3e level• D"t6 c6cle D 4 /r!ction o/ time s)itc* is in position

$


5/26

REVIEW

• Fo"rier !n!l6sis#

• S)itc* red"ces dc volt!3e +6 ! /!ctor o/ D


6/26

REVIEW• Insertion o/ lo)-p!ss 7lter to remove s)itc*in3

*!rmonics !nd p!ss onl6 dc component

• S)itc* is desi3ned to p!ss t*e dc component o/ Vs0t1 '!nd to re8ect components !t Vs0t1 !nd its *!rmonics

• C*oose 7lter c"to9 /re:"enc6 / % m"c* sm!ller t*!n

s)itc*in3 /re:"enc6 / s;


7/26

REVIEW

• O"tp"t volt!3e v 2 dc component o/ Vs0t1

Control c*!r!cteristics o/ t*e converter

•


8/26

REVIEW

• Feed+!c= s6stems constr"cted to !d8"st t*e d"t6c6cle D to re3"l!te converter o"tp"t volt!3e


9/26

REVIEW

•


10/26

REVIEW

(o) to solve converters e!ctl6

• L!pl!ce tr!ns/orm to )rite epressions /or)!ve/orms o/ t*e circ"its

• Invert t*e tr!ns/orms' B!tc* +o"nd!r6 conditions'

7nd t*e periodic ste!d6 st!te sol"tion o/ t*ecirc"it

• C!n 7nd !ver!3e v!l"es' pe!= v!l"es

•


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IND.CTOR VOLT-SEC


12/26

• Act"!l o"tp"t volt!3e v0t1 consists o/ desiredcomponent V' !nd ! sm!ll "ndesired !c componentVripple0t1 d"e to incomplete !tten"!tion o/ s)itc*in3

*!rmonics +6 t*e lo) p!ss 7lter;

• In ! )ell-desi3ned converter' t*e o"tp"t volt!3eripple is sm!ll; (ence' t*e )!ve/orms c!n +e e!sil6

determined +6 i3norin3 t*e ripple#

• T*er/ore o"tp"t volt!3e v0t1

SMALL RIPPL APPR!"IMA#I!$/ LI$ARRIPPL APPR!"IMA#I!$


13/26


14/26


15/26

IND.CTOR VOLTAE AND C.RRENT S.


16/26

Ind"ctor volt!3e !nd c"rrent )!ve/orms

Inductor current begins )ith some initial value iL%&


17/26

Determin!tion o/ ind"ctor c"rrent ripple m!3nit"de

Pea0 inductor current ' dc value I ( pea0 toaverage ripple 1iL

Ripple magnitude can be calculated asSince )ave2ormis s,mmetrical

about I31iL' pea0 to pea0 ripple


18/26

• T6pic!l v!l"e o/ 1iL ' * 4 to 3 4 o2 2ull load

value o2 I

•

1iL too large 5 pea0 current o2 L andsemiconductor device increase5 increase si6eand cost

• So b, design+ 1iL should be small

•

Small ripple approximation iL%t&≈

I is 7usti8ed

• Inductance value chosen such that desiredcurrent ripple ΔiL is attained9


19/26

Ind"ctor c"rrent )!ve/orm d"rin3 st!rt-"p tr!nsient

• G"st seen t*e ind"ctor c"rrent )!ve/orm /or ste!d6st!te conditions )it* t*e converter oper!tin3 in

e:"ili+ri"m;• :hat happens to inductor current )hen

converter is 8rst turned on;

• Initi!l ind"ctor c"rrent il0%1 2 %O"tp"t volt!3e v0t1 2 %4 Appl6 V3

• D"rin3 s"+interv!l $ 0S$1 → ind"ctor c"rrent

incre!ses )it* slope 0V3-v1>L 4 initi!ll6 v 2 % 4essenti!ll6 const!nt slope V3>L

• D"rin3 s"+interv!l 5 0S51 → ind"ctor c"rrent

decre!ses )it* slope -v>L 4 initi!ll6 v 2 % 4essenti!ll6 H% slope → const!nt


20/26

• Net incre!se in iL0t1 over $st s)itc*in3 period;

• iL0t1 Jo)s to c!p!citor' c!p!citor c*!r3es' v )ill

incre!se sli3*tl6

• Process repe!ts 4 incre!ses d"rin3 $st s"+interv!l4decre!ses d"rin3 5nd s"+interv!l

• As c!p!citor c*!r3es' slope d"rin3 S$ decre!ses4

d"rin3 S5 +ecomes more ne3!tive


21/26

• A point is re!c*ed )*en

incre!se in iL0t1 d"rin3 S$ 2 decre!se in iL0t1 d"rin3 S5

No net c*!n3e in ind"ctor c"rrent over ! completes)itc*in3 period

• Converter oper!tes in ste!d6 st!te


22/26

T*e principle o/ ind"ctor volt-second +!l!nce#Deriv!tion

I;e;' initi!l !nd 7n!l v!l"es o/ ind"ctor c"rrent !ret*e s!me


23/26

• I;e;' in e:"ili+ri"m !pplied ind"ctor volt!3e m"st*!ve ,erp dc component;

Inductor volt-second balance< =uc0 converterexample

. ( .>'*


24/26

Adv!nt!3e

C!n +e !pplied to derive epression /or dc volt!3eo/ !n6 converter;

S=etc* t*e !pplied ind"ctor )!ve/orm !nd e:"!tet*e !ver!3e v!l"e to ,ero;


25/26

T*e principle o/ c!p!citor c*!r3e +!l!nce#Deriv!tion


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control technique

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