Tổng hợp bộ điều khiển PID bền vững cho đối tượng tham mờ đảm bảo độ dự trữ mờ về biên độ và pha

Theo xu hudng dd, difiu khidn bdn vung va dieu khidn md da dat dugc nhidu ket qua nghien ciiu dang ke Irong vai trd ky thudt xir ly cac bdi dinh cua md hinh hfi thd'ng ddc bifit la ddi v

Hd Noi, 11 - 2005

TONG HOP Bp DIEU KHIEN PID BEN V Q N G CHO DOI TUONG

THAM SO M d DAM BAO DO DU T R Q M d VE BIEN DO VA PHA

Le Hiing Ldn, Le Tin Tuyet Nhung Tnfdng Dgi hgc Giao thdng Van tdi

Tdm tdt:

Bdi bdo difa ra mgt pliifaug phdp thie't ke' hg diin khien PID hen vffng tren cff sd ky

thudt phdn rd D cho mgt ldi? ddi tifcmg co md td difdi dgiig tap md trong khdng gian tham

so ciia hdm truyen cd tre ddm bdo do dif tri'f md cho trifdc vi bien do vd pha Ke't qua nhdn

dtfgc tap cdc hg diiu khien bin vffng ddm bdo ddng thdi do dif trt'f tdt nhd't cho cdc tnfdng

hgp hay \dy ra vd do dtf trifkem han iho cdc tnfdng hgi) it xdy ia

Abstract:

This paper present a method to design the robust PID controllers for a fuzzy set in

the paiamefer spate of a lineai transfer fnncdon plus delay with gain and phase margins,

that obtained hy D-partition technique A set of lohnst PID controllers resulted has both

good margin in most of situation and more relaxed margin in infrequent cases

I DAT V ^ DE

Xu hudng chung cua ky thudl didu khifin tu ddng la lim cac bifin phap ndng cao chd'l

lugng didu khidn cua cac qua trinh phiic tap Theo xu hudng dd, difiu khidn bdn vung va

dieu khidn md da dat dugc nhidu ket qua nghien ciiu dang ke Irong vai trd ky thudt xir ly

cac bdi dinh cua md hinh hfi thd'ng ddc bifit la ddi vdi he phi tuye'n

Trong cac thifit kfi' he thd'ng didu khien ben virng cd mdt nhugc didm la do cd gang

lim ra bd didu khidn nhdm thda man yfiu cdu chdi lugng cho ca mdt Idp ddi tugng nfin cd

Ihd xay ra trudng hgp thdi bai do ldp dd qud rdng Cd hai hudng khdc phuc nhugc didm

nay: (a) Giam thidu yfiu cdu chdt lugng; (b) Sir dung ky thudt didu khifi'n thfch nghi

Tuy nhifin khi phdn ifch ky Idp ddi tugng, dfi nhdn thd'y rdng trong thuc te dii cho

Iham sd la khdng xac dinh nhung cd xu hudng thudng xud't hifin d mdt khoang nao dd va fl

xay ra d khoang khdc

Do dd cd the cd gdng tim ra giai phdp thifit ke he thd'ng dam bao chat Iugng cao nhd'l

ddi vdi ldp ddi tugng hay gap va dam bao chat lugng tfi'i thidu cho ldp do'i iugng ft xay ra

Ddy Id hifdng di nidi vd se difgc di cap chi tie't trong hdi bdo

Trong bai bao, lap md dugc su dung dd md la ldp tham sd dd'i tugng va md la cac

chudn chdi lugng trong mifin tdn s d c d dang ham thudc nhu hlnh ve (1)

Xet ha didu khifi'n vdi ddi tugng bat djnh P(s,q) trong dd q la vector cac tham sd bdt

dinh, mdc ndi lie'p vdi bd didu khien PID Irong mach kfn phan hdi dm don vj Ham iruyfin

bd difiu khidn

C(s) = K,-i-^ + K„s (1)

s Gpi 'P la tap mcr co chita doi tuong P va tap mcr,t cua tieu chua'n S

' P = {P,/i(P)}:rf={S, / " ( S ) ) (2)

tugng trong tdp P thda man lap md lifiu chuan S Ndi cdch khac cdn phai tim bd didu khifi'n

PID dam bao:

Vdi mpi P(x thda man tieu chudn S^^ (3) Trong dd chi sd a la lat cdt or cua tdp md

Pa={P,u(P)^a]-^^a = {S^M(S)>a] (4)

Vdi gia In xac djnh ciiaa bai loan dat ra cd the coi nhu mdt bai loan didu khidn bd

virng quen thudc: hay tim bfi didu khien PID dd he thd'ng vdi Idp ddi tugg khoang

IP(s,q),q' <q<q* ] thda man lifiu chuan khoang (S,.y^ < i ' < J* )

Trong danh gia chat lugng dieu khien, mdt dang tieu chuan quan trgng la dd du trQ' vd

bifin do va tdn sd Ky hifiu do du trQ bifin do la A^ va do du triJ tan sd la <p„, Djnh nghTa vd

do du trCr bien dd va tan sd dugc the hifin tren hinh ve (2) vd cdc cdng thdc sau:

/\CU0)^)PU0^,)\ = ~7f

\C(,jo,;,P{jo)^)\ (5j

|c(y^^,)P(7^^.)| = i

fp„,=z\C(^jw^)P{ja)^)\ + K

Cdn giai quyfi'l bai loan tim bd didu khidn PID sao cho vdi ddi tugng khoang

lP(s,q),(7" <q<q* ]\.a\> tifiu chudn [^yA^" <A^^ < A^^* ,<p~i <tp^, -fp,,* Idugc thda man

II TONG HOP BO DIEU KHIEN BEN V U N G PID THONG QUA PHAN R A D

Ban chd'l cila ky thudt phdn ra D kinh didn la dd dd thj Nyquist di qua diem (-l,jO) Ta

cd thd md rdng khai quat hda 6e dd thj Nyquist di qua mdt didm M bat V.^ md la bdi

phuong trinh:

C(jo})P(^jo)) = M (6)

De tao nen phdn ra D tdng qudt Didm M cd the ddng vai trd dd du tri? bien dd A^:

M(.AJ = (-^,J0) (7)

Hay do du IriJ pha <p^;

<p„ = - c o s ^ „ , , - y s i n ^ „ , (8)

Gia sir Ko=l thay vao (6) thu dugc:

K„-^^ h K„s \p{j6}) = M

>K^~j^ = M*P(jo>y~JK„a

(9)

Tir dd nhdn thd'y cd thd xay dung dugc cdc phuong Irinh phdn ra D tdng qudt trong

mat phdng Kp-K,:

K^{to,q,Aj=R4H{ja,,q.Aj ^Ij^j

K, (ffl, q, A,„) = -to lm{H{ja), q, A„ )]

Hijoy, q, A„,) = M(Jo), A„,) * P{jco)'' - jK„0} d 0

va

K,.{o},q,<pJ= Re{H{jo},q,^J] ^^^j Ki{co,q,^^,)= -o}lm{H{jfo,q,p^^)}

Vdi

H{jQ},q,A,„)= M(Jo),ip„,)* Pijo))' - jK„a> (13)

Vdi cac gia trj cu thd cua q hay A^,(p^, cdc phuong trinh tCr 10-13 khi 0<fo<^ bieu

difin thanh hai dudng cong trong mat phang K^-K, giao diem cua chiing thd hien gia trj

tham sd bd didu khien C(s) vira thda man ddng thdi cac tifiu chudn ve dd du trii bien do vd

pha

Khi cdc dd du triJ thay ddi trong khoang cho trudc thi hai dudng cong trd thanh hai

ddng hay hai tdp cd cac gidi ban dugc md la bdi cac dudng

Bddd

- Gidi hgn cua tap [KiX<^,q,A„,),K,{co,q,A„,),0<Q)<or:),,A~, < A,„ <A„*\

Id {K^(a),q,A\,],Ki(o},q,A\,)] trongdd A^ ={A'm,A*,]

- Gidi hgn cua tap [K^,{fo,q,<p„j,K/{o},q,tp„j,0<0}<<x),<p~^ ^<P,„ -<Pm*\

Id \K^\o),q,q}'m\Ki\o},q,fp\,J^ trong do v'm=W~"'-'^*^\

Bd dd tren the hien Irfin hinh hgc la /'(/(o)"' la mdt sd phdc vdi q,ti) xdc djnh do dd

M(j(i),A^) P{jo))~' hay M(Jco,(p„,)P{jfo)~ la cdc sd phdc nhdn dugc bdng each md rdng

thfim I/An, hay quay di mdt gdc tp^^ Nhu vdy khi thay ddi co cdc didm bifin se tao thanh cac

dudng gidi ban

Ne'u tham sd q thay ddi thi tbay vao 04 dudng gidi han ta se nhdn dugc cdc ddng cua

cac Idp gid tri H\JQ},q,A',„) hay H\jco,q^(p'm) quen thudc trong phdn tich dn dinh bdn

vung: ky ihuat xay dung cdc tdp gid trj nay dugc nfiu tdng quat trong

(KiselovO.N.etai.,1997)

Mifin ddng trong mat phdng Kp-K, gidi ban bdi bdn ddng ndi trfin se chiia td't ca cac

bd didu khidn bdn viJng can tim

III UNG DUNG TRONG GIAI BAI TOAN DAT RA

Vdi dd'i iugng md va tifiu chudn md cd the dp dung phuong phap trfin thdng qua tap

rdi rac cac lat cdt a ciia ddi tugng va tifiu chudn:

Sa(A~^,(p-,,):={An„ 9„, I A„,G A^„„ , tp , , E ^\^ } (14)

P a ( s , q - ) : = { P ( s , q ) | q e q l Trong dd - thd hifin bifi'n md

Ggi C° la tap ke't qua vdi lat cdt a Sa(A'',n,(p~^) va Pa(s,q~ ) Khf dd ldi giai bai todn

(2) se la

C : = n C « ; a e [ 0 , l ] (15)

Di thuc hifin ldi giai nay cdn rdi rac hda a Trudng hgp don gian nhd't la chgn

a e { 0 , l 1 (lifiu chu^n mdm ciing, dd'i lugng thudng xuyfin xay ra vd cd thd xay ra) vdi kfi't

qua thda man la

C = C°nC'

Vi du : Xet ddi tugng cd md hinh xd'p xi P{s,q) =

lugng thudng xuyen cdn cdc dd'i tugng ft gap Irong trudng hgp xdu nha't cung thda man tifiu chuan mem

Ke'^

(Ts-^l)

Cdc tham sd K, T,T cd ham Ihudc tren hinh (I) Trong dd hfi sd khuyfi'ch dai cd thfi ndm trong khoang [2.5,2.7) nhung hay ndm nhd'l trong khoang [2.55,2.65]

Do du trir bifin do va pha mong mudn

A;„ - lrap(\ 5,1.7,2.0,2.2) ^,„ = trap(7r / 6 ;r / 5, ;r / 4, ;r / 3)

Trong dd trap (Pi,P2,p.(,p4) la bidu didn tSp md hinh thang vdi gia (ddy dudi) [p,, p J va tdm (day tren) [pj.psj

Tfnh loan nhu tren thd'y khdng cd mot bd dieu khidn nao cd the dap ung loan bd lap cac dd'i lugng da cho (gid) Bai loan trfin cd thd giai dugc nfi'u chi ddi hdi tifiu chudn dd ra(lifiu chu^n ciiug) thda man cho cdc ddi tugng hay xay ra nhdt (tdm) Cdn vdi loan bd tap cac ddi tugng cd thd xay ra chd't lugng se bi giam di {tifiu chuan mdm)

Trfin hinh (3a) ke't qua ciia tap chinh hay xay ra (lieu chudn ciiug) Cdn trfin hinh (3b) kdt qua Id giao ciia hai tdp chfnh ung vdi cdc irudng hgp didn hinh : hay xay ra (tifiu chuan Cling) va cd kha nang xay ra(tieu chuan mdm) C = C"nC'

IV KET LUAN

Trong bai bdo da de cap den bai loan cd gdng dap ung chd't lugng td't nhat cho mdt Idp dd'i tugng bdt dinh trong khi vdn kidm tra dugc miic dd dam bao chdi lugng tdi thidu cho Idp ddi tugng rdng hon

Phuong phap dd ra sir dung cac md hinh ddi tugng md va djnh nghTa tdp lieu chu^n

md Hudng giai quyet mdi nay cd mdt sd uu diem trong dd ddc bifit la kha ndng md ta rd rang tdt ca cac bd didu khidn bdn viJng can tim va kha nang dp dung khdng chi cho bd dieu khidn PID ma vdi cac bfi didu khidn tuy y cd hai tham sd cdn tim

fi{K) a cut

/

\ ^

• — ^ — •

2.5 2.55 2.65 2.7

Hinh 1, a

/ /

a cut

\ ^

' ^^—• 10.7 10.75 10.85 10.9

Hinh 1, b

Hinh l,c

Hinh 3.a

Astrom K.J T Hagglund (1984) "Automatic Tuning of Simple Regulators with Specificadons ou phase and Gain margins " Automicat Vol20, no5.pp645-65I

Bliattacharyya.SP.H.Chapellat and L.H.Keel(1995) "Robust control The parametric Approach " Prentice-Hall

Kiselov O.N, Lan LH , Polyak B.T(]997)," The fieqiiency chaiatericstics with parametric uncertainty" Automation and Remote Control Vol.57, pp I55-I73lin mssiani Bondia J Pico J., (2003) "Analysis of linear systems with fuzzy parametric unceitainty F tizzy Sets and Systems", V.135 81-121

Le Himg Ldn Le Thi Tuyet Nhung, Ddnh gid do dif trff on diiih he thd'ng diiu khien dd'i tifgug md, Tuyen tap V1CA6