TRNG I HC K THUT CNG NGHIP KHOA C KH B MN: CH TO MY BI GING PHT CHO SINH VIN (LU HNH NI B) Theo chng trnh 150 TC hay 180 TC hoc tng ng S dng cho nm hc 2008 - 2009 Tn bi ging: K thut iu khin t ng S tn ch: 3 Thi Nguyn, nm 2008 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Tn cc tc gi: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. BI GING PHT CHO SINH VIN (LU HNH NI B) Theo chng trnh 150 TC hay 180 TC hoc tng ng S dng cho nm hc: 2008 - 2009 Tn bi ging: K thutiu khin t ng S tn ch: 3 Thi Nguyn, ngy.thng nm 200 Trng b mn Trng khoa (k v ghi r h tn)(k v ghi r h tn) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.MC LC I. Phn 1: Phn l thuyt Chng 1. CC VN C BN CA H THNG IU KHIN T NG 1.1Cc ni dung c bn1.2M hnh din t h thng iu khin 1.3M t ton hc cc phn t iu khin c bn 1.4Phn loi h thng iu khin1.4.1. H thng iu khin h v h thng iu khin kn. 1.4.2. H thng iu khin lin tc v gin on 1.5Tuyn tnh ha cc h thng phi tuyn 1.6ng dng MatLab Chng 2.HM TRUYN T 2.1 Hm truyn t 2.2S khi - i s s khi 2.3Graph tn hiu v qui tc Mason 2.4. Cc h thng ly mu d liu 2.5Hm truyn t ca h thng ri rc 2.6ng dng MatLab Chng 3. KHNG GIAN TRNG THI. 3.1Cc m hnh khng gian trng thi. 3.2M hnh khng gian trng thi v cc phng trnh vi phn 3.3Xc nh bin trng thi t hm truyn 3.4Xc nh hm p ng t phng trnh trng thi 3.5ng dng MatLab Chng 4. N NH CA H THNG IU KHIN TUYN TNH. 4.1 Khi nim chung 4.2 Khi nim n nh v cc nh ngha chnh 4.3 Tr ring v tnh n nh ca h thng 4.4 Cc tiu chun n nh 4.5 ng dng MatLab Chng 5. TNH IU KHIN V QUAN ST C CAH THNG IU KHIN. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.5.1 Tnh iu khin c ca cc h thng lin tc. 5.2 Tnh quan st c ca cc h thng lin tc. 5.3 Tnh iu khin c ca cc h thng gin on. 5.4 Tnh quan st c ca cc h thng gin on. 5.5 ng dng MATLAB. Chng 6. THIT K H THNG IU KHIN. 6.1M u. 6.2Cc khu ng hc ca h thng iu khin. Chng 7.THIT K H THNG IU KHIN BNG THU LC. 7.1. Cc phn t c bn7.1.1. Bm du. 7.1.2. Van trn, van an ton. 7.1.3. Van gim p 7.1.4. B iu chnh v n nh tc . 7.1.5. Van iu khin. 7.1.6. C cu chp hnh. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.I. Phn 1: Phn l thuyt I.1. Yu cu i vi sinh vin - Mc tiu: Ni dung c bn ca h thng iu khin t ng, Phn tch v tng hp c mt h thng iu khin. - Nhim v ca sinh vin: D hc l thuyt: y Tho lun:y . - nh gi:Chm im Tho lun: 20% Kim tra gia k: 20% Thi kt thc hc phn : 60% I.2. Cc ni dung c th Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Chng 1 CC VN C BN CA H THNG IU KHIN T NG 1.1- Cc ni dung c bn ca h thng iu khin. *iukhin:Ltcnglnitngitnglmvictheomt mc ch no . * H thng iu khin: L mt tp hp cc thnh phn vt l c lin h tc ngqualivinhauchhuyhochiuchnhbnthnitnghaymth thng khc. *Xungquanhtacrtnhiuhthngiukhinnhngcthphnchia thnh 3 dng h thng iu khin c bn. - H thng iu khin nhn to. - H thng iu khin t nhin (bao gm iu khin sinh vt). - H thng iu khin t nhin v nhn to. Trong cc h thng i tng iu khin c th l h thng vt l, thit b k thut, c ch sinh vt, h thng kinh t, qu trnh v.v... i tng nghin cu l cc thit b k thut gi l iu khin hc k thut. Mihthng(hocphntcahthng)kthut,uchutcngca bn ngoi v cho ta cc p ng. Gi tc ng vo l u vo, tc ng ra l u ra( hoc tn hiu vo, tn hiu ra). Hnh 1-1 * Nhim v ca l thuyt iu khin t ng L thuyt iu khin t ng gii quyt 2 nhim v chnh: -Phn tch h thng -Tng hp h thng Phn tch h thng: Nhim v ny nhm xc nh c tnh u ra ca h sau em so snh vi nhng ch tiu yu cu nh gi cht lng iu khin ca h thng . Mun phn tch h thng iu khin t ng ngi ta dng phng php trc tip hocgin tip gii quyt 2 vn c bn. -Tnh n nh ca h thng H thng (hoc phn t ca h thng) Cc tc ng voCc p ng Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.-Chtlngcaqutrnhiukhin-qutrnhxclptrngthitnhv trng thi ng (trng thi qu ). gii quyt vn trn dng m hnh ton hc, tc l cc phn t ca h thng iu khin u c c trng bng m hnh ton ca cc phn t s cho m hnh ton ca ton b h thng. C th xc nh c tnh n nh ca h thng qua m hnh ton ca h thng vi vic s dng l thuyt n nh trong ton hc. Tng hp h thng: Tng hp h thng l xc nh thng s v cu trc ca thit b iu khin. Gii bi tonny,thcralthitkhthngiukhin.Trongqutrnhtnghpny thng km theo bi ton phn tch. ivicchthng iukhintiuvthchnghi,nhimvtnghpthit b iu khin gi vai tr rt quan trng. Trong cc h thng , mun tng hp c hthng phixc nhAlgorit iukhintclxc nhlutiukhin(t).H thngiukhinyucuchtlngcaoth victng hpcngtrnn phctp. Trong mt s trng hp cn n gin ho mt s yu cu v tm phng php tng hp thch hp thc hin. 1.2- Cc m hnh din t h thng iu khin. tin vic nghin cu v cc vn iu khin cn sdng cc s (m hnh)dintccthnhphncahthngsaochorrngmimiquanhbn trong v ngoi h thng d dng phn tch, thit k v nh gi h thng. Thc t s dng cc m hnh sau l ph bin v thun tin: 1) H thng cc phng trnh vi phn 2) S khi. 3) Graph tn hiu. 4) Hm truyn t 5) Khng gian trng thi (S khi v Graph tn hiu l cch biu din bng ho din t mt hthngvtlhocmthphngtrnhtonctrngchoccphntcah thng - Din t mt cch trc quan hn). *Vmtlthuytmihthngiukhinucthdintbngcc phng trnh ton. Gii cc phng trnh ny v nghim ca chng s din t trng thicahthng.Tuynhinvicgiiphngtrnhthngkhtmnghim(c trng hp khng tm c) lc cn t cc gi thit n gin ho nhm dn ti cc phng trnh vi phn tuyn tnh thng H iu khin tuyn tnh lin tc. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.*Phnlnkthutiukhinhini,lsphttrincaccmhnh ton hc cho cc hin tng vt l. Sau da vo cc m hnh ton hc nghin cu cc tnh cht ca h thng iu khin. 1.2.1.Phng trnh vi phn Cchthngvtl(hocccqutrnh)cncdintchnhxcmi quanh gia nhng i lng bin ng bn trong ca chng. T ta d dng nghin cu c cc hin tng din bin ca h thng; cc nh lut c bn ca vt l c th gip ta gii quyt vn . Cc quan h ca cc i lng c bn ni chung c th biu din bng cc phng trnh vi phn ( gi l m hnh ton ca h thng). V d: Phng trnh ca nh lut II Newton F = m.a Trongphngtrnhisgitr cc ilngkhngthayitheothi gian,v thnchdinttrngthinnhcah.Nhngtrongthcthkhngtnh. u ra thng bin ng i vi cc thay i ca u vo, thm vo tc ng canhiucngthayitheothigian,nnhkhngnnhtcluradao ng. V th cn phi phn tch h trong cc iu kin ng lc hoc gi l trong trngthiqu,lcnyccbinskhngcnhmthayitheothigian. Phng trnh vi phn m t h trng thi ng lckhng ch cha bn thn cc bin s m cn cha tc thay i hoc gi l o hm ca cc bin s . * Cc ni dung c bn ca phng trnh vi phn: Phng trnh dng: an. nndty d + an-1.1 n1 ndty d + ... + a1.dtdy + a0. y = x(t) (1.1) x(t) v y(t) l cc bin ph thuc, t l bin c lp. * Cc tnh cht ca phng trnh vi phn: Mi h l tuyn tnh nu quan h vo- ra ca n c th biu th bng phng trnh vi phn tuyn tnh:

==iiiniiiidtx dbdty da . .0 Hoc mt h l tuyn tnh nu quan h vo ra ca n c th biu th bng tch phn: y(t) = } t t t d x t W ) ( ) , ( Trong W(t,t ) l hm th hin cc tnh cht bn trong ca h,y(t) l u ra v x(t) l u vo. Hm 2 binW(t,t ) l hm trng lng ca h. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.- p ng y(t) ca mt h tuyn tnh do nhiu u vo x1(t), x2(t), ...., xn(t) tc ng ngthilnhbngtngccpngcamiuvotcngringbit (nguyn l chng cht) y(t) ==niit y0) ( V d: Phng trnh vi phn thun nht: A.dtt dyBdtt y d ) (.) (22++ C.y(t) = 0 C hai nghimy1(t),y2(t). theo nguyn l chng cht thy1(t) + y2(t) cng l mt nghim ca phng trnh . - Ton t vi phn v phng trnh c trng: Xt phng trnh vi phn tuyn tnh h s hng cp n an nndty d + an-1.11nndty d + ... + a1.dtdy + a0. y = x(t) Gi ton t vi phn D = dtd, Dn= nndtd

Phng trnh trn c th vit thnh: Dny + an-1 D1 ny + ... + a1Dy + a0y = x (Dn + an-1 D1 n + ... + a1D + a0 )y = x (1.2) a thc Dn + an-1 D1 n + ... + a1D + a0 gi l a thc c trng. Phng trnh Dn + an-1 D1 n + ... + a1D + a0 = 0 l phng trnh c trng. Nghimcaphngtrnhctrngrtcnghakhixttnhnnhcah thng. 1.2.2- S khi. *Skhicbiuthbngcckhilinktvinhaudintmi quan h u vo v u ra ca mt h thng vt l. * S khi thun tin din t mi quan h gia cc phn t ca h thng iu khin. V d: a)b)

c) Vo A Phn t G Ra B G1 A G2 BC xd dt y = dtdx Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hnh 1-2 *Cckhicthl mtthit b hoc dngcvcth l mt hm(chc nng) xy ra trong h thng. Khi:K hiu thut ton phi thc hin u vo to u ra. ng ni:ng ni gia cc khi biu th i lng hoc bin s trong h thng. Mi tn: Ch tiu ca dng thng tin hoc tn hiu Cc khi ni tip nhau th u ra ca khi trc l u vo ca khi sau im t: Biu hin thut ton cng hoc tr k hiu bng mt vng trn u ra ca im t l tng i s ca cc u vo.

Hnh 1-3 *imtn:Cngmttnhiuhocmtbinsphnranhiunhnhti im gi l im tn, tc l ti u rap ln nhiu khi khc k hiu l mt nt trn en. Hnh 1-4 Cu trc s khi ca h thng iu khin kn Hnh 1-5 Hnh (1-5) din t mt h thng iu khin kn bng s khi. Cc khi m t cc phn t trong h c ni vi nhau theo quan h bn trong ca h thng. * Cc bin s ca h: (1) Gi tr vo V: tn hiu ngoi p vo h. (2) Tn hiu vo chun R: rt t gi tr vo V l tn hiu ngoi h p ln h iu khin nh mt lnh xc nh cp cho i tng. R biu th cho mt u vo l tng dng lm chun so snh vi tn hiu phn hi B. x + - y (x-y) x x x x CC C E G1 G2 MC GV V R+ H B - u x + + y (x+y) x + + y (x+y-u) - u Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.(3)Bins iukhinM(tn hiu iuchnh):l ilng hoctrngthi m phn t iu khin G1 p ln phn t (i tng) iu khin G2 (qu trnh c iu khin). (4)BinsraC(tnhiura):lilnghoctrngthicaitng (hoc qu trnh) c iu khin. (5) Tn hiu phn hi B: l mt hm ca tn hiu ra C c cng i s vi vo chun R c tn hiu tc ng E. (6)TnhiutcngE(cnggilsailchhoctcngiukhin)l tng i s (thng l tr) gia u vo l R vi phn t B l tn hiu p ln phn t iu khin. (7) Nhiu u: l tn hiu vo khng mong mun nh hng ti tn hiu ra C. CthvoitngtheoMhocmt imtrunggianno(mongmunp ng ca h i vi nhiu l nh nht). * Cc phn t ca h: (1) Phn t vo chun GV: chuyn i gi tr vo V thnh tn hiu vo chun R (thng l mt thit b chuyn i). (2) Phn t iu khin G1: l thnh phn tc ng i vi tn hiu E to ra tn hiu iu khin M p ln i tng iu khin G2 (hoc qu trnh). (3)itngiu khinG2lvtth,thitb, qutrnh mb phnhoc trng thi ca n c iu khin.(4)PhntphnhiH:lthnhphnxcnhquanh(hm)giatn hiu phn hi B v tn hiu ra C c iu khin (o hoc cm th tr s ra C chuyn thnh tn hiu ra B (phn hi). (5) Kch thch: l cc tn hiu vo t bn ngoi nh hng ti tn hiu ra C. V d tn hiu vo chun R v nhiu u l cc kch thch. (6) Phn hi m:im t l mt php trE = R - B (7) Phn hi dng: im t l php cng:E = R + B (iukhinkngmhaituyn:TuynthuntruyntnhiuttcngE n tn hiu ra C. Cc phn t trn tuyn thun k hiu G (G1 , G2, ...) tuyn phn hi truyn t tn hiu ra C n phn hi B cc phn t k hiu l H (H1 , H2 , ...). 1.2.3. Hm truyn t: Hm truyn t ca h thng. * Hm truyn t ca h thng i vi h thng iu khin lin tc mt u vo v mt u ra c nh ngha: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.-Ltscabin iLaplaceca uravibiniLaplacecau vovigithittonbcciukinungnhtbngkhng(iukin dng). G(s) = o 11 n1 nno 11 m1 mmma S . a ... S . a Sb s b ... S . b S b+ + + ++ + + +(1.3) i vi h thng vt l thc cc ch s trong hm truyn n > m. *Tronglnhvcthigianginon(iukhinrirc)vicbiniZ ng vai tr ca bin i Laplace: Hm truyn c dng sau: G(z) = o 11 n1 nno 11 m1 mmma z . a ... z . a zb z b ... z . b z b+ + + ++ + + + (1.4) *ivi hthng nhiu uvo nhiu u ravir uvo, p ura,cc hm truyn l cc phn t ca ma trn cp pr phn t , vi ch s i ca phn t th i ca u vo, ch s th j ca phn t th j u ra. G11(s)G12(s).....G1r(s) G21(s)G22(s).....G2r(s) G(s) =..........Gji(s).....(1.5) ....................GP1(s)..........GPr(s) y: Gji(s)= ) s ( u) s ( Yij;cc u vo khc ui(s) u coi l bng khng. (Nguyn l c lp tc dng). * Mt cch tng t vi h thng iu khin gin on ta c hm truyn ca h thng nhiu u vo nhiu u ra. G11(z)G12(z).....G1r(z)prG21(z)G22(z).....G2r(z) G(z) =..........Gji(z).....(1.6) .................... GP1(z)..........GPr(z) y:s - s phc -bin Laplace. z = eS.T- bin ca php bin i z. 1.2.4. Khng gian trng thi Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Khi phn tch v thit k h thng iu khin tuyn tnh thng s dng mt trong hai hnh thc sau: + i vi lnh vc thi gian s dng hm trng thi. + Trong lnh vc tn s dng hm truyn t. Nh trn, ta xt h phng trnh vi phn, sai phn o hm n bc n(h thng bc n); nthc chtltrngthicaccbin.Cctrngthica bin c mtnhlvectx.Ccphngtrnhtrngthicmtdidngsau(h thng tuyn tnh). .x (t) = A.x(t) + B.u(t); x(o)= xo y(t) = C.x(t) + D. u(t) (1.7) vx(k+1) = A. x(k) + B.u(k) ; x(o) = xo y(k) = C.x(k) + D. u(k) (1.8) y:A, B, C, D l cc ma trn h s hng c kch thc. Ann,Bnr,CPn,DPr Cc h phng trnh vit dng (1-11); (1-12) cc phng trnh trng thi ca h thng iu khin. * Khng gian trng thi:Mt h thng c r tn hiu vo u1(t), u2(t), u3(t) ... ur(t) m tn hiu ra: y1(t), y2(t), y3(t).... ym(t)Xc nh n bin trng thi: x1(t), x2(t)..... xn(t)Vy h thng c m t bi phng trnh khng gian trng thi nh sau:= (t) x1. f1(x1, x2,..., xn; u1, u2,..., ur; t) . . . = ) (.t xn fn(x1, x2,..., xn; u1, u2,..., ur; t) i lng ra: y1(t) = g1(x1, x2,..., xn; u1, u2,..., ur; t) . . . ym(t) = gm(x1, x2,..., xn; u1, u2,..., ur; t) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.++D(t)C(t)A(t)dtu(t) y(t)B(t)x(t) x(t).++= (t) x. ((((((((((

(t) x...(t) x(t) xn.2.1. f(x, u, t) = (((((

t) ; u ,..., u , u ; x ,..., x , (x f...t) ; u ,..., u , u ; x ,..., x , (x ft) ; u ,..., u , u ; x ,..., x , (x fr 2 1 n 2 1 nr 2 1 n 2 1 2r 2 1 n 2 1 1(1.9) Phng trnh trng thi: = ) (.t xf(x, u, t) y(t) = g(x, u, t) Hoc di dng ma trn: = ) (.t xA(t). x(t) + B(t). u(t) y(t) = C(t). x(t) + D(t). u(t) S khi: Hnh 1-6 1.3. M t ton hc ca cc phn t iu khin a. Phn t di ng thng: Tc dng vo l xo c chiu di L0 l xo di ng mt lng X th cn mt lc: PL = k .X(k: l cng l xo hay l hng s l xo) k = XPLAA O LPL PLL0 LX K = PL X Hnh 1-7. ng c tnhHnh 1-8. S khi 1/k R=XP V= PLGenerated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.i vi l xo thng thng tn hiu vo l lc PV = PL, tn hiu ra l lng di ng R = X. Vy m hnh ton c trng v s khi biu din chc nng nh hnh 1-8 b. B gim chn bng khng kh hoc bng du p:

di ng piston vi vn tc V, cn tc dng lc PV c gi tr: PV = C.V= C.dtdR p dng ton t Laplace: s = dtd

PV = C.V= C.dtdR = C.s.R Lc PV coi l tn hiu vo Tn hiu ra: Lng di ng R. T cc yu t trn thnh lp s khi th hin m hnh ton ca b gim chn. c. Trng khi Theo nh lut II Newton tng cc lc P bn ngoi tc dng vo mt trng khi s c biu thc: P= M.A = M. 22dtR d Dng ton t Laplace: s =dtdnnP = M. S2.R R =P . 2.1S M S khi th hin m hnh ton nh sau: d.Phn t quay nh lut II Newton: i vi chuyn ng quay gia tc gc ca vt th quay t l thun vi tng m men tc dng ln n. Dng ton hc ca nh lut: P V R Hnh 1-9 PVR 1/C.s Hnh 1-10Hnh 1-111/M.S2R PGenerated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. 22dtd = uM Mddt = .22u Trong : l gc quay u l momen qun tnh ca vt th M l momen bn ngoi tc dng vo vt th. Momenbnngoictoratngc,dotitrngtcdnglxohocgim chn. Xt mt a quay trong cht lng v ni vi mt bnh nh hnh v: -Phn tch xy dng m hnh ton: Quay a c phi tc dng mt momen xon Mx, trc quay i mt gc l jto mo men ca l xo: M1 = kx. j (1.10)Trc c ng knh D, chiu di l, h s l xo xon l: kx = lG D32. .4t (G: M un n hi) Momen cn thit thng lc ma st ca cht lng: Mm = C.w = C. dtd = C. p. j (1.11) w: l vn tc gc C: h s ma st ca cht lng Nu quay a vi momen xon Mx (momen xon ca trc l xo) v momen ma st s ngn cn s quay ca a do c th vit thnh: M = Mx M1 Mm = 22.dtdu= q. s2. j Thay cc tr s (1.10) v (1.11) ta c: Mx = q. s2. j + kx. j+ C. s. j = (q. s2 + kx + C.s). j T phng trnh trn ta c s khi ca h thng nh hnh v. e. Cc phn t in Cc phn t c bn ca cc mch in Hnh 1-12 M1 Mm Mx e Hnh 1-13 1( u.S2+ C.S + k x) M x Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.y = Rx =VC1A.Pb) uR = R. I I = R1.uR uL= L.dtdI = LP. I dtdI = p. I = dtd.I uC= C1.}dt I. = PC1.I f.Cc phn t thu kh Xt phn t du p: -Nu van trt c y ln pha trn , du c p sut P0 s vo bung trn ca xi lanh 3 v du ca bung di s qua van trt v b du. - Nu van trt c a xung pha di , du s qua bung di ca xilanh 1 v du bung trn s chy v b du. Vi hiu p khng i c hnh thnh ca van, tc l t l thun vi lng di ng x. Gi q l lng du chy vo xilanh, ta c: q = C1.x q ng thi cng l s thay i th tch ca xilanh: q = A.Py (A l din tch b mt ca xilanh) A.Py = C1.x+ uRuL + uC + RLC 1 R uRI I uL L p 1I uCC p 1 Hnh 1-14 x1 23 y P 0M Hnh 1-15 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. y = P AC.1.x T phng trnh trn tn hiu vo l x ( lng di ng ca xilanh 1) v tn hiu ra y lng di ng ca xilanh 2. g.Phn t phi tuyn Taxtmtphntphituynvtrncstinhnhtuyntnhhomhnh ton hc c trng cho chc nng ca c cu. Xt c cu nng vung gc bng c kh: Thanh nng vung gc ti im A (a + b = 900) v c th chuyn ng cng bc trong rnh thng ng. Mt nhnh ca thanh nng c th trt trn con trt im B , con trt ny di ng cng bc theo phng ngang. Nhnh kia ca thanh nng c th di ng trong bc ca khp ni c nh im C. - Phn tch: Tam gic AOB lun ng dng tam gic AOC nn: KXXY= KXY2=( K = const) NutnhiuvolX,thvtrca imB ltn hiuraYtlvibnhphng ca X. Cn tn hiu vo l Y v tn hiu ra l X s t l vi cn bc hai ca Y: X =Y K. vit phng trnh ton v xy dng m hnh ton hc ta cn tuyn tnh ho cc phng trnh phi tuyn trn. Phng php nh sau. 1.4- Phn loi h thng iu khin. *Vicphnloi hthng iukhin(Controller System)c rt nhiu hnh thc tu theo gc nhn nhn nh gi: phn loi theo tn hiu vo, theo cc lp phng trnh vi phn m t qu trnh ng lc hc ca h thng. Theo s vng kn trongh,v.v...Tuynhinychltngi.Xtvtnhchtlmvicvni dung c bn ca iu khin th h thng iu khin c 2 loi lm c s trong phn tch tnh nng (Phn bit tc ng vo h v p ng ra): H thng kn H thng h. Hnh 1-16 o |O YK X BC Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.*Theo c im m t ton hc th c cc h thng sau: H thng lin tcH thng gin on H thng tuyn tnh H thng phi tuyn H thng tuyn tnh ho * Theo dng nng lng tiu th: H thng iu khin bng in H thng iu khin bng du H thng iu khin bng kh p .... 1.4.1.Cc h thng iu khin h v h thng kn a. H thng iu khin h (Open- Loop Control Systems) *Khi nim: H thng iu khin h l h thng m tc ng iu khin c lp vi u ra (Hoc u ra khng c o v khng c phn hi so vi u vo) V d: Qu trnh hot ng ca my git hon ton t ng m chng ta ch cn tc ng trckhimyhotnglnginvnhncngtcsaukhimyhonthnh cng vic th chng ta ly sn phm ra. Trong my c din ra cc qu trnh nh sau: qutrnhlmtquno(Soaking),qutrnhgit(Washing),qutrnhvtkh (Rinsing) u lm vic vi mt thi gian tng chun (time basic) V cc qu trnh ny khng c o kt qu (Tc l khng c kim tra l lm sch qun o hay cha) S khi ca h thng (Control System in Washing Machine) t = ts + tW + tR = const T v d trn ta thy h thng iu khin h c dp ng ra khng so snh p ng vo. Mi tc ng vo c trng thi (hot ng) n nh, kt qu ca h thng c chnh xc phthuc hthngchia (hthng o).Trong qutrnhc nhiu,h thng khng thc hin nhim v yu cu. * c tnh ca h thng iu khin h: - chnh xc ca h quyt nh bi iu chnh (cn) v c duy tr chnh xc c lu hay khng. Hnh 1-17 SoakingWashingRinsingTurn on Finish Cleanliness Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.-Nhycmviccbinixungquanhnh:nhit, daong,xunglc,in th, ph ti... - p ng chm khi tn hiu vo thay i. * u im: - n gin - Gi thnh thp ( chnh xc va phi) - Vn mt n nh khng nghim trng. b.H thng iu khin kn Khi nim: H thng iu khin kn l h thng m tc ng iu khin ph thuc p ng ra. cn gi l h thng iu khin phn hi. E: Sai lch iu khin E = R B R: Tn hiu vo B: Tn hiu phn hi. Trong h thng iu khin kn sai lch iu khin l s chnh lch gia tn hiu vo v tn hiu phn hi. Qu trnh iu khin nhm gim sai lch v p ng ra t gi tr mong mun. V d: H thng iu khin nhit trong l l mt h thng iu khin kn. Nhit trong l in c o bi nhit k ( l thit b Analog(tng t)) Nhit didngtnhiutngtcbinithnhtnhiunhit dngsbib A/D. Tn hiu nhit c chuyn v my tnh trung tm qua Interface. v nhit c so snh vi tn hiu nhit m chng trnh ca my tnh lp, nu c bt k sai s no (discrepancy: s chnh lch, s khc nhau) th my tnh trung tm c tn hiu qua Interface v tn hiu ny c khuch i nh thit b Amplifier v tcnglnRelaylmchonhittrongltnghaygimtutheoyucuca chng trnh lp. E R +-G 1 H Hnh 1-18 G 2 C B L in (E.Furnace)A/DConverter Interface RelayAmplifierInterface Computer Programming inputHnh 1-19.Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.V d 2: iu khin mt bnh nc sao cho mc nc trong bnh lun l hng s khng ith caoct nctrongbnhslmttrong nhngthngskthut cn quan tm ca h thng. Gi tr v cao ct nc ti thi im t c o cm binvcbiu dinthnh mtilnginp didnghmsphthuc thi gian u(t) c n v Volt. i lng vt l y l in p c s dng truyntihmthigianu(t)mangthngtinvcaoctnc.(Phnmhnh ton hc) * c tnh ca h thng iu khin kn( h thng phn hi) c trng ca h thng iu khin kn l phn hi. - Nng cao chnh xc c kh nng to li u ra - Tc p ng nhanh - chnh xc ph thuc cc iu kin lm vic - Gim tnh cht phi tuyn v nhiu - Gim nhy cm ca ts u ra v u vo i vi s thay i tnh cht ca h. - Tng b rng di tn (dy tn s ca u vo) - C khuynh hng dao ng hoc khng n nh. - iu khin mm . 1.4.2.- Cc h thng iu khin lin tc v gin on. Cchthngthccmttrngthitnhhocnglchc.Cch thngtnhthngcdintbihthngccphngtrnhis.Trongiu khin kthutcc hthng tnhkhngdin tytrngthica h thng.V vy ngi ta dng cc phng trnh vi phn/sai phn m t trng thi ng lc hc ca h thng (c bit nh l cc h thng vi cc tham s cc b hoc tp trung) hoc cc phng trnh vi phn o hm ring (nh l cc h thng c cc tham s phn tn). Trong ni dung gio trnh ta nghin cu cc h thng c m t bi h cc phng trnh vi phn/sai phn tuyn tnh, ngha l cc tham s ca h thng c lp tuyn tnh.Vdhthngnglchccmtdidngccphngtrnhvi phn/sai phn v hng: x&(t)= fc(x(t)) ,x(to)= xo(1.12) x(k +1) = fd (x(k)) , x (ko) = xo(1.13) y:t : bin thi gian lin tc. k : bin thi gian gin on. Ch s e:(continuous- Time) - thi gian lin tc. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. d:(discrete - Time) - thi gian gin on. Nu h thng chu tc ng ca ngoi lc, haycc tc ng vt l khc. Ta ni nchu ti ngiukhinvphngtrnhvi phn/sai phnmt trngthi ng lc ca h thng. x&(t)= fc (x(t), u(t)) ;x(to)= xo (1.14) x(k+1)= fd (x(k), u(k)) ;x(ko) = xo(1.15) y:u(t);u(k)ngvaitrbiniukhin.Vimcchcaiu khin ta thay i bin iu khin nhn c cc p ng ca h thng k thut theo yu cu nh vy, nhn chung vn chnh ca iu khin c th m hnh ho theo dngsau:tmbiniukhinbngcchgiihthngphngtrnhviphnc trng ca h. Nu cc h phng trnh vi phn (1.12) (1.15) l tuyn tnh ta gi h thng ltuyntnh.Nulphituyntagilhthngphituyn.Vicnghincuh thngphituyntngikh.Trongthct,ngitatmcchtuyntnhho. Trongphmvigiotrnh ny,chngtachnghincu hthngiukhintuyn tnh. 1.5- Tuyn tnh ho h thng phi tuyn. Trong thc t khng c mt h thng vt l no c th m t tuyt i chnh xc bng phng trnh vi phn h s hng tuy nhin nhiu h phi tuyn c th xp xhoccoinhtuyntnhtrongtng onlmvic.C nhiu phng php c pdngchovictuyntnhhohthngphituyn.Phngphptrung bnhgn im lm vic. Phng php tuyn tnh ho iu ho v phng php sai lch nh. 1.5.1- Phng php trung bnh gn im lm vic. y l phng php n gin c dng trong thit k cc h thng khi c tnh trn khng th xp x ho c bng cc hm gii tch. Phng php ny p dng cho cc h c nhng phn t ch phi tuyn trng thi tnh, quan h gia u ra y vi u vo u l trng thi xc lp (n nh). Gi thit trong on: - uM < u < um c tnh phi tuyn c th xp x ho bng ng thng. Trong :y = K . u ;k = mmuy = tgo ; o l dc. 1.5.2- Phng php tuyn tnh ho iu ho. Phng php ny c dng khi h c mt phn t tuyn tnh ni sau mt phn t phi tuyn lm vic ch t dao ng. Cc tn hiu trong h l lm tun hontheo thi gian. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Phng php ny da trn c s khai trin hm sng thnh chui hm dng sin (chui Fonricr) iu ho c tn s l e, 2e, 3e, ... c bin v gc pha khc nhau. Gi thit cc hm iu ho bc cao khc (2e, 3e, ...) c bin nh b qua ch gi li thnh phn iu ho bc nht (e) (gi thit lc) ngha l: Hnh 1-20 Trong :u(t)= Um . sin (et + ) y(t) = Ym1 . sin (et + ) Trong Um = Ym1 v - = t c gi l iu kin cn bng iu ho. 1.5.3- Phng php sai lch nh. Theophngphpnyvictuyntnhhocthchinbngcchkhai trin hm phituynthnhchuiTaylortivnglncn im n nh(tngng vi ch xc lp). Ch kho st cc sai lch bc nht trong chui . Sai lch so vi trng thi nnhcng nhthvicnhgiccqutrnhca phnt phi tuyn c sai s cng b sau khi bin i tuyn tnh. a) H thng (bc nht) phi tuyn. x&(t) =f(x(t) , u(t) )(1.16) Gi thit rng h thng lm vic trng thi xc lp vi qu o xn(t) khi n ciukhinbitn hiu vo un(t).Chngtagixn(t)vun(t)lqu odanh ngha v u vo danh ngha theo phng trnh (1.16) ta c: x&n(t) =f(xn(t) , un(t) )(1.17) Bygitagithitrngthayicahphituyn(1.16)lncnquo danh nh mt lng nh (v cng b). x(t)= xn(t) + Ax(t)(1.18) Lng bin i v cng b ny l do thay i u vo: u(t)= un(t) + Au(t) (1.19) T cc phng trnh (1.16), (1.18), (1.19) ta c: x&n(t) + Ax&(t) = f(xn(t) + Ax(t), un(t) + Au(t))(1.20) S dng khai trin Taylor vi cc i lng Ax(t), Au(t) ta s c: x&n(t) + Ax&(t) = f(xn(t), un(t)) + xfcc(xn , un) Ax(t) + + ufcc (xn , un) Au(t) + cc thnh phn bc cao. (1.21) Nonlinear System u(t) Element Linearization y(t) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.(Cc thnh phn bc cao l cc i lng v cng b Ax2 , Au2, Ax.Au, Ax3...) c b qua, t y ta c: Ax&(t) = xfcc(xn , un) Ax(t) + ufcc (xn , un) Au(t)(1.22) Nh vy bng vic trnh by xp x vi Ax(t) ta tin hnh tuyn tnh ho theo sai lch bc nht c phng trnh xp x bc nht (1.22). t:ao= -xfcc(xn , un); bo = ufcc (xn , un) (1.23) Ta c phng trnh m t h thng tuyn tnh: Ax&(t) + ao(t)Ax(t) = bo(t). Au(t)(1.24) iu kin u ca h thng c tuyn tnh ho c xc nh. Ax(to) = x(to) - xn(to)(1.25) b) H phi tuyn bc 2: x& & = f( x,x&, u,u&)(1.26) Vi gi thit rng: x(t) = xn(t) + Ax(t); x&(t) =x&n(t) + Ax&(t) u(t) = un(t) + Au(t); u&(t) =u&n(t) + Au&(t) (1.27) Tng t ta c: x& &n + Ax& &= f (xn + Ax,x&n + Ax&, un + Au,u&n + Au&)(1.40) p dng khai trin Taylor ln cn cc im danh ngha: xn ,x&n , un ,u&nv ta c: Ax& &(t) + a1Ax&(t) + aoAx(t) = b1Au&(t) + boAu(t) (1.28) Cc h s xc nh theo: a1 = - xf& cc(xn ,x&n , un ,u&n ), ao = - xfcc(xn ,x&n , un ,u&n ) b1 = uf& cc(xn ,x&n , un ,u&n ), bo =ufcc(xn ,x&n , un ,u&n )(1.29) Cc iu kin u c xc nh. Ax(to) = x(to) - xn(to) ; Ax&(to) =x&(to) -x&n(to) V d:Cho h thng phi tuyn. u& & = Sinu - u.cosu = f(u, u) Trong : u= u(t) ; u = u(t) y l m hnh ton ca thanh thng ng cn bng, u: lc ngang; u l gc lch khi phng thng ng. y l h thng ng lc hc bc 2. Trng thi danh nh ca n: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.u&n(t) = un(t) = 0;un(t)= 0; s dng (1-42) ta c: a1 = - u cc&f = 0, ao = - nf|.|

\|u cc= - (Cosu + Usinu)0 ) t (nU0 ) t (n== u = -1 b1 =|.|

\|ccuf& = 0; bo =nuf|.|

\|cc= - Cosu0 ) t (n= u = -1 Vy phng trnh tuyn tnh ho: (1.30) dy: Au(t) = u(t) ,Au(t) = u(t)ng thi un(t) = 0,un(t) = 0 u& &(t) - u(t) = - u(t) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.OojeGxGyuG(s)OjeoojeSCHNG II HM TRUYN T Trc tin n tp li kin thc v s phc v hm phc. *Bin phc: s = o + jw o: Phn thc (Real part) e: Phn o (Imaginary part)Nu o, e l cc s thc th ta gi l s phc, cn thay i s l bin phc. Biu din bin phc s trn th nh sau: Hnh 2.1 * Hm phc: L hm ca bin phc S G(s) = Gx + j Gy Cng bao gm phn thc v phn o. ln ca) (s G = 2 2y xG G +Gc q = tan-1(Gx/Gy), Chiu dng theo chiu kim ng h tnh t trc thc-Biu din trn th: Hnh 2.2 Hm lin hp ca hm G(s) l: ) (s G= Gx - j Gy Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.OjeoS02j 416O-11 ReGImGG(S0)nh x GPhng SPhng G(S)Mt hm phc, c bin l s =o + je . Bin phc S ph thuc vo 2 i lng c lp: l phn thc v phn o ca s. biu din hm G(s) cn c 2 th, mi th c 2 chiu: - th ca je ng vis gi l phng S -thcaphnoG(S)(ImG)ngviphnthccaG(S)(ReG)gil phng G(S). Stngnggiaccimtronghaiphnggilmtnhxhaybini. Cc im trong phng S c nh x vo cc im trong phng G(S) bng hm G. V d: Hm phc G(S) = S2 + 1. im S0 = 2 +j 4 c nh x vo im G(S0) nh sau (S0) = G(2 + j 4) = -11 + j 16 Hnh 2.3 * Phng S (mt phng phc) Nu G(S) l hm hu t nh sau: G(S) = ==++niimii mp Sz S b11) () ( -Cc gi tr ca bin phc S = -zi lm cho G(s) = 0 c gi l cc khng ca G(s) (Zeros) -Cc gi tr s = - pi lm cho G(s) c gi l cc cc ca G(s) ( Poles) Ccccvcckhng cxc nh bi: mti din phnthcv mt i din phn o ca s phc. Biu dincc im trn mt phng phc(phngS)gilnh xcc khng ca G(s) V d: G(s) = ) 1 )( 1 )( 3 () 2 )( 1 ( 26 8 54 2 22 32j S j S SS SS S SS S + + + +=+ + + Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Phng Sojej-j-12-3PoleZeroPhng SoPhng G(S)ReGjeS1ImGG(S1)S2S3S4G(S4)G(S2)G(S3)nh x GG(s) c cc khng: s = -1 ; s = 2 v cc cc: s = -3; s = -1 j ; s = -1 +j Hnh 2.4 *Phng G(s): c biu din trong mt phng vi 2 thnh phn. Mt l phn thc ca G(s) ReG, v mt l phn o ca G(s)- ImG. nh x t cc im s0 sang phng G(s) l cc im G(s0). Hnh 2.5 * Nhn xt: Mi quan h gia phng S ( nh x cc khng)*Php bin i Laplace BiniLaplacelcscamtphngphpgiitchtmcpngn nhvpngqu mccphngtrnhviphntuyntnh hskhngi. Nn php bin i Laplace ch dng bin i cho phng trnh vi phn tuyn tnh. BiniLaplacechuynphngtrnhviphnthnhccphngtrnhisnn tmnghim ca phngtrnhi s nginhnv tnghimcaphngtrnh i s tm c nghim ca phng trnh vi phn. Mt uiml phngphp nycth xltrctipcciukin uca h thng nh mt phn ca p ng.- Bn cht ca php bin i Laplace: L cc php tnh o hm v tch phn gc c chuyn thnh cc php ton i s thng thng i vi cc nh, min xc nh rng. - Hm gc: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Oq(t)tOtq(t).sint Gi hm f(t) ca bin thc t l hm gc nu n tho mn cc iu kin sau: 1. Hm f(t) lin tc trn tng on thucmin xc nh mt> 0. Gii thch: Ly [a; b] trnt> 0, lun chi c trong [a; b] mt s hu hn khong nh [e; x] sao cho trong mi khong f(t) lin tc v ti cc mt ca mi khong nh th f(t) c gii hn mt pha: 0;a >0 sao cho:te t f.) (os ; mi t >0 agi l ch s tng ca f(t). 3.f(t) = 0 khi t < 0. iu kin ny c a ra v trong ng dng bin s t thng l thi gian, hm f(t) biu din mt qu trnh no m ta ch kho st lc t > 0. Mt s v d: a)Hm h(t) =0 khi t < 0 1 khi t > 0 L mt hm gc : 1 ) ( s t qtho mn iu kin hm f(t) khng tng nhanh hn mt hm m. t0 >ta ly t thuc trong [-1; 1] th 1 ) ( lim1=+ ttq( tho mn iu kin 1) h(t) =0 khi t < 0(tho mn iu kin 3)

Hnh 2.6 b)Hmf(t) = h(t). sint = 0 khi t < 0 sint khi t > 0 te M t toq . 1 sin ). ( = s( M = 1; a= 0)t t sin ). ( qlin tc trn t> 0t t sin ). ( q= 0 khi t 0 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Oq(t).tt2te t t . 2 ). (2s q ( M = 2; a = 1)

Hnh 2.8 - Ton t Laplace: Nu f(t) l mt hm gc c ch s tng l a th yu cu ca f(t) chuyn i c l: 0 Bin i Laplace: [ s2Y(s) s y(0) ] + 4[ s Y(s) y(0) ] + 3 Y(s) = 2 R(s)Thay R(s) = s1 v y(0) = 1 ta c: s2Y(s) s + 4 s Y(s) 4 + 3 Y(s) = s2 Y(s) = 3) 4s (s4 s3) 4s s(s22 2+ ++++ + Trong : q(s) = s2 +4s + 3 = ( s + 1)(s +3) = 0 l phng trnh c trng v d(s) = s Y(s) = [s2/3]3) (s1/31) (s1[ ]3) (s1/21) (s3/2++++++++ = Y1(s) + Y2(s) + Y3(s) Bin i Laplace ngc: y(t) = 32] .e311.e [ ] .e21.e23[3t t 3t t+ + + Trng thi n nh l:32y(t) limt= V d 2: H thng c kh nh hnh v ( c m hnh ho) Hnh 2.9 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.+-Armatureif(t)FieldInertia = JFriction = fLoadRaLa RfLfTrong hnh v: K: cng l xo ( hng s l xo) f1, f2: l cc h s ma stV1(t), V2(t): Vn tc di chuyn ca cc trng khi M1 v M2. M1sV1(s) + (f1 + f2)V1(s) f2V2(s) = R(s)M2sV2(s) + f1(V2(s) V1(s)) + Ks(s) V2 = 0 Tng ng vi: (M1(s) + (f1 + f2)) V1(s) + (- f1)V2(s) = R(s) (-f1)V1(s) + (M2(s) + f1 + sK) V2(s) = 0 Hoc di dng ma trn sau: ((

=((

(((

+ + + +0R(s)(s) V(s) VsKf (s) )......(M f .........() f ........( f f (s) (M211 2 11 2 1 1.) Vn tc di chuyn ca M1 chnh l i lngra, vic tm V1(s) bi ma trn nghch o hoc nguyn tc Cramer l: V1(s) = 21 1 2 2 1 11 2f (K/s)) f s ).(M f f s (M) (K/s)).R(s f s (M + + + ++ + Hm truyn t ca h thng: G(s)==R(s)(s) V121 1 2 2 1 11 2f (K/s)) f s ).(M f f s (M(K/s)) f s (M + + + ++ += s ss21 122 2 1 1122f K) f s ).(M f f s (MK).R(s) f s (M + + + ++ + Ti mt thi im no m xc nh x1(t), th hm truyn t l: sG(s)sR(s)(s) VR(s)(s) X1= =V d 3: Hm truyn t ca ng c dc ng c dc l thit b pht ng m chuyn t dng nng lng in sang chuyn ng quay. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.my(t)cu(t)dFc FmFdHnh 2.10 V d 4: Cho h c hc gm mt l xo c h s c, mt vt vi khi lng m v b gim chn c h s d c ni vi nhau nh hnh v. Xc nh hm truyn t cho h c nu tn hiu u vo u(t) c nh ngha l lc bn ngoi tc ng ln vt v tn hiu ra y(t) l qung ng m vt i c. Gi Fc, Fm, Fd l nhng lc ca l xo, vt v b gim chn sinh ra khi vt di chuyn nhm cn s dch chuyn th: Fc = c. y(t) Fm = m. 22dty(t) d

Fd = d . dtdy(t) Theo tin v cn bng lc ta c: u(t) = Fc + Fm + Fd = c . y(t) + m. 22dty(t) d + d . dtdy(t) Bin i Laplace: U(s) = ( c + ds + ms2 ). Y(s) Hnh 2.11 Hm truyn t ca h thng l: G(s) = U(s)Y(s) = c ds ms12+ + Gi g(t) l hm gc ca hm truyn t G(s), tc l: g(t) = L-1{G(s)} Theo tnh cht ca ton t Laplace ta c:Y(s) = G(s). U(s) y(t) = g(t). u(t) = }+ t t t )d .u(t g( )= }+ t t t )d .u( - g(t )Hm g(t) c gil hm trng lng ca h thng. Vi u(t) =) (t oDo U(s) = 1 nn ta c y(t) = g(t)* Hm truyn t trong lnh vc Laplace Trn y mi ch gii thiu hm truyn t gii hn trong quan h t l vo ra n gin, l mt hnh thc m t c trng ca phn t hoc h thng. Tuy nhin c nhiu phn t c p ng thay i theo thi gian. Trong lnh vc thi gian c tnhcmtbngphngtrnhviphn,phngtrnhnykhngtrctip dng lm hm truyn t c. Nu dng mt hm truyn t vi bin s Laplace S, din t c c tnh ng lc ca phn t hoc h thng v phng phpphn tch trong lnh vc thi gian ( tc Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.l qu trnh qu )s tng i n gin gip ta xc nh p ng ca phn t hoc h thng i vi mt tn hiu vo xc nh. ctrngcamththngiukhin,tacphngtrnhviphntngqutsau y: (pn + bn-1pn-1 + ... + b1p + b0). y(t) = ( ampm + am-1pm-1 + ... + a1p + a0 ). x(t)(2.11) y(t) =.x(t)(p) L(p) L.x(t)b p b ... p b pa p a ... p a p anm0 11 n1 nn0 11 m1 mmm=+ + + ++ + + + Trong : a0, ..., am v b0, ..., bn l nhng hng s x(t) hm kch thch, n l tn hiu tc ng vo lm kch thch h thng y(t) hm phn ng. N l hm chuyn tip (tn hiu ra) di tc ng ca tn hiu vo x(t). Ln(p) = pn + bn-1pn-1 + ... + b1p + b0 Lm(p) = ampm + am-1pm-1 + ... + a1p + a0 Bin i Laplace tng s hng ca phng trnh (2.11) ta c L[pn y(t)] = sn Y(s) I(s)n bn-1 L[pn-1 y(t)] =bn-1. sn-1 Y(s) I(s)n-1 ... am L[pm x(t)] = am sm X(s) I(s)m am-1 L[pm-1 x(t)] =am-1 sm-1 Y(s) I(s)m-1 Vi I(s)n,...l nhng iu kin ban u tng ng vi cc bin i. Thay vo phng trnh:Y(s) = (s) L I(s) (s).X(s) Lb s b ... s b sI(s) X(s) a s a ... s a s (anm0 11 n1 nn0 11 m1 mmm+=+ + + ++ + + + +). I(s) = I(s)n + I(s)n-1 + ... - I(s)m - I(s)m-1 l tng nhng iu kin u. T phng trnh trn thy rng: - cc a thc Lm (s); Ln(s) trong min bin i s vn gi nguyn nh trong min ton t p. - T s ca chng cng c dng ging nhau, ch khc l min s c cc iu kin u I(s). -Nucc iukin u bng 0thtacth bin iLaplaceca phngtrnh vi phn bngcchthaysvovtr p,thayY(s)vovtry(t)vX(s)vovtrx(t). Tc l: Y(s) =) ( . s X(s) L(s) Lnm V hm truyn t l G(s) = (s) L(s) Lnm Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Vy c mi quan h trong h thng iu khin: Hm phn ng = Hm truyn t x Hm kch thch Nu cho mu s ca hm truyn t bng 0 ta s c phng trnh c trng: sn + bn-1sn-1 + ... + b1s + b0 = 0 trn c s phng trnh c trng ta suy ra cc c tnh chuyn tip ca h thng. - Hm phn ng (hm chuyn tip) y(t) c th xc nh vi vic bin i ngc hm Y(s)y(t) = L-1[ Y(s)] = L-1 [(s) L I(s) (s).X(s) Lnm+] Tm y(t) theo 2 cch: 1) Dng bng xc nh cc hm thi gian tng ng 2) Phn tch hm bin i thnh tng nhng hm n gin hn v sau dng bng bin i ngc tng s hng. Thngdngphngphp2vtkhigpcchmngin.Vytatmhiu phng php 2 nh sau: Y(s) = (s) L I(s) (s).X(s) Lnm+ Hm kch thch X(s) hay tn hiu vo c th vit di dng sau y: X(s) = xxDN Y(s) = ) () (s Bs A=+x nx x m(s).D L I(s).D (s).N L y A(s) v B(s) l nhng a thc ca s. cthchiaY(s)thnhccphnthc,taphntchmusB(s).Giscc nghim ca B(s) l r1, r2, ..., rn. Cc nghim ny c th l nghim n, nghim bi hay l s phc. - Nghim n: Y(s) = nn2211r sC...r sCr sCB(s)A(s)+ ++=Xc nh C1, C2, ..., Cn ta dng phng php sau C1 =).Y(s)] r [(s lim1r s1 C2 =).Y(s)] r [(s lim2r s2 ... Cn =).Y(s)] r [(s limnr sn Bit c C1, C2, ..., Cntm c bin i Laplace ngc trong bng: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. L-1 [nnr - sC] = Cn. et rn ( t0 > ) Vy,y(t) = L-1[ Y(s)] = C1. et r1 + C2. et r2 +... +Cn. et rn

Hm chuyn tipy(t) mong mun l hm tt dn nn tng phn Cn. et rn l hm tt dn, tc l tt c cc nghim r1, r2, ..., rn cn phi l s m. - Nghim bi: B(s) = (s-r)q.(s-r1).(s-r2)...(s-rn)Y(s) =nn11 11 q1 qqqr sC...r sCr sKr) (sKr) (sKB(s)A(s)+ +++ ++=...Xc nh Kq: Kq =.Y(s)] r) [(s limqr s Cn cc h s cn li xc nh xc nh bng cch: ) r (sr) (sqC ...) r (sr) (sqC ... r) (s 2K K Y(s)] r) [(sdsdnqni1 q1 2 q 1 qq+ ++ + + = Kq-1 =Y(s)]} r) [(sdsd{ limqr s Kq-2 =Y(s)]} r) [(sdsd21{ limq22r s .... Kq-k =Y(s)]} r) [(sdsdk!1{ limq(k)(k)r s Vy: y(t)=+ + + ++rt1rt2rt 2 q1 qrt 1 qq.e K1!.t.e K...2)! (q.e .t K1)! (q.e .t KC1.et r1+C2.et r2+...+Cn. et rn -Nghim phc lin hp: Y(s) = nn11 0r sC...r sCjb a sCjb - a sCB(s)A(s)+ +++ +=Xc nh cc hng s C, C0 tng ng vi cc nghim phc lin hp: C= ]) r )...(s r (2jb).(sA(s)[ lim ]) r )...(s r jb).(s a jb).(s a (sA(s)jb). a [(s limn 1jb a sn 1jb a s = + + + =jb) .K(a2jb1+Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.K(a+jb) = jb a s + lim) )...( 1 () ( 4nr S r ss = [(s2-2as+a2+b2.s Bs A//)]jb a S + = Co = jb a s lim [(s-a+jb)) )....( ).( ).( () (1 nr s r s jb a s jb a ss A + ] = jb a s lim [) ).( .( 2) (1 nr s r s as A ] = -a 21.K.(a-jb) K(a+jb)= jb a s lim [) ).( () (1 nr s r ss A ] = -a 21.K.(a+jb) = [(2- 2as + a2+b2)) () (s Bs A]jb a s = Cc tr s k(a+jb) v k(a-jb) l cc s phc lin hp Ta cn th hin cc s ny trn hnh v: K(a+jb)= [k(a+jb)]eo j K(a+jb)= [k(a+jb)]eo j [k(a+jb)] = [k(a-jb)] ( di ca vc t ) C v Co cng l cc s phc lin hp . C = jb 21.[k(a+jb)].eo j Co = -[k(a+jb)]eo j T bng laplace ta xc nh hm chuyn tipy) (t=c.et jb a ). ( ++Co.et jb a ). ( +C1.et r1+.....+Cn.ernt

) (ty = jb 21[k(a+jb)].et jb a ). ( +.eo j + -jb 21[k(a-jb).et jb a ). ( .eo j +... = jb 21[k(a+jb)].et a..e) ( o + bt j- e) ( o + bt j = b1[k(a+jb)].eat.je ebt j bt j2) ( ) ( o o + + = b1[k(a+jb)].eat.sin( ) ( bt + o +C1.et r1+...+Cn.ernt Phngtrnhtrnthhinhmiuhosinttdntheohmm,xutpht tnghim phc lin hpPhn o b l tn s dao ng tt dn . Thi gian ca mi dao ng l bt 2 . ng bao hnh sin l b1[k(a+jb)].eat . hm m gim dn th a Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Ojt(1/b).[K(a+ jb)] (1/b).[K(a+ jb)].eOjtatOat(1/b).[K(a+ jb)].etjtObja>0a0a 0)i|= Tng cc gc ca cc vect t cc khng n pi tr i tng cc gc ca cc vect t cc cc ti pi + 1800 ( nubm < 0) -Phng php th ny khng p dng cho trng hp c cc cc trng nhau ( nghim lp). Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.G1 G2 G1xG2R C R C* Hm truyn t trong lnh vc tn s Vic phn tch h thng nm trong hai lnh vc: Lnh vc thi gian v lnh vc tn s. -Trong lnh vc thi gian: ni dung ch yu l cc c tnh ng lc ca h th hintrngthiqu(pngqu).Tadngphngtrnhvi phnvbini Laplace nghincu cc nghimca phngtrnh (tclcc p ng ca h). p dng bin i Laplace gii cc phng trnh vi phn tuyn tnh l phn quan trng nht trong nghin cu trng thi qu ca cc h tuyn tnh thuc lnh vc thi gian. Tuy vy gii phng trnh vi phn phn tch trng thi ng lc ca h thng (tc l trong lnh vc thi gian) kh phc tp i vi cc h khng n gin. Nhng phng php phn tch p ng tn s ( thuc lnh vc tn s) c th nh gi c tnh nng ca h m khng cn gii phng trnh vi phn. Phng php p ng tn sphntchcctnhnngcahxemnhmthmcatnscatnhiuvo dngsinmkhngphilkhostpngthigianthct.Cngcthni phng php p ng tn s phn tch p ng dng sin n nh ca hm truyn ca h.Phng php ny c nhiu u im: -Cho php ta c lng c dy tn s nh hng n tnh nng ca h -D ch cho ta bin php thay i h t cc tnh nngyu cu trong vic thitkcchthngiukhin.Bngthcthchchotabinphp phn onvn bngcc phngtrnhvi phn.Nucc phngtrnh cgiinhngpngkhng tyucuthkhngdquytnhc bin php thay i h thng t cht lng mong mun. Phng php tn s vt qua c hn ch . -pngcthxcnhbngthcnghimcngttkhngthuakmtnh ton gii tch. u im ny rt quan trng khi m t cc phn t ca h bng cc phng trnh vi phn. 2.2. i s s khi S khi l mt trong cc dng m hnh ton ca h thng iu khin, trn s th hin i lng vo ra ca h thng v cc tnh cht ca h thng. Mt s chuyn i c bn rt gn cc s khi phc tp. 1.T hp cc khi ni tip

Hnh 2.14 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.++

RG1G2CRCG1+G2R++CGAB

++ CGGBAABG1/G++

BGC+ACGC

BGC1/GCBBBCG G GB CCCChng minh : C= R.G1.G2 = G1.G2.R 2.T hp cc khi song song

Hnh 2.15 Ti im t C = R.G2 + R.G1 = ( G1+G2).R 3.Di chuyn im t v bn phi mt khi : Hnh 2.16 Ti im t R = A + BNn C = G. ( A + B)S tng ng l: C = A. G + B. G = G. ( A + B)4.Di chuyn im t v bn tri mt khi Hnh 2.17 5.Di chuyn im tn v bn phi mt khi Hnh 2.18 6.Di chuyn im tn v bn tri mt khi Hnh 2.19 7.Rt gn h thng Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

R G1+GHCBCHGR +-EE-+ RG1HCBG2+E+ RGHCB+- Hnh 2.20 Chng minh: S ban u: G = ECC = E. G ; E = R - B ; B = C. H ;E = R C. H = R E. GHE. ( 1 + GH ) = R E = G.H 1R+

Hm truyn ca h thng l: RC = G.H 1R+.RG = GH 1G+

T biu thc ta thy: Nu gia lng tuyn thun G ln th tch GH> 1, lc ny gia lng mch kn cn l RC = H1 -Ktlun:Trngthicamchkn phthuctnhchttuyntnhcaphn hi H v c lp vi tuyn thun ( v tnh cht ). Nu tuyn thun c mt vi thayi do mtvildo no thtuynphnhistrkhhiu qus thay i ca u ra. V th khng cn iu chnh h thng, nhng phi iu chnh phn t phn hi H.-Nu mch kn b ct t nh hnh v: Hnh 2.21 Hm truyn ton mch cn G1. G2. H c xem nh hm truyn ca mch h. G1. G2. H = E.H .G E.GEC.HEB2 1= =* S khi dng chnh tc: Hnh 2.22 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.B EH GCCc i lng sau cn xc nh r:G: Hm truyn tuyn thun H: Hm truyn tuyn phn hi GH: Hm truyn mch h. Hnh 2.23 RC: Hm truyn mch kn (t s iu khin) RE: T s tn hiu tc ng ( t s sai lch ) RB: T s phn hi c bnTa c lin h sau: RC = GH 1G * H phn hi n v: Mt h phn hi n v l mt h trong tn hiu phn hi c bn B bng u ra C. y l mt trng hp c bit hay gp trong thc t v l s so snh trc tip giaurav uvochun.Vlcnykhi phnhic gitr nvl 1 nn hm truyn mch kn l:

RC = G 1G+ Trng hp ny xy ra khi u ra m phng li u vo chun. Bt k h phn hi no nu ch c cc phn t tuyn tnh trong tuyn phn hi u c th t di dng mt h phn hi n v bng cch dng chuyn i 4, ta c s khi sau:

E+ RGHCB+- -+BCG.HR +E1 H E = R B E = HR B B = C.hB = C Hnh 2.24 RC = GHG 1

Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.BCG2+G1R+-+HUC(R)G2 G1R +-H E = GC E= H GC. H GC.= HR C C (H G.1 1) = HR * H c nhiu tn hiu vo ra : Nhiu h c nhiu U, hoc c nhiu tn hiu vo ( nhiu kch thch ) ng thi vi tn hiuvochunR,chngpln hticcimkhc nhauv manglicho h nhng tnh nng khc nhau. Khitrong mt htuyntnhc mt nhiutn hiuvotaphixltngtn hiu c lp vi nhau, sau da trn nguyn l chng cht cng i s cc p ng c bit ca tng tn hiu vi nhau ta s c tn hiu ra tng cng ca h khi mi tn hiu ng thi tc ng ln h. C ngha l ta gi thit tng tn hiu vo tc dng ring bit n h ( cc tn hiu vo cn li gi thit bng khng ) ln lt lm nh vy vi tng tn hiu vo, sau thc hin mt php cng i s cc p ng ni trn, tm p ng ring ca tng tnhiuvo,ikhi cnnththutrtgn skhivdng chnhtcbng cch dng mt trong by chuyn i trn. * MT S V D V d 1 : Xc nh du ra C ca h thng: Hnh 2.25 Cho U = 0h thng n gin ho thnh : Hnh 2.26 Xc nh u ra : C) ( R = 2 . 1 12 . 1G GG G+.R + Cho R = 0 , ch c u vo U ta c s sau Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.C(U)G2U +-G1.HH++ UG2CG1-G2-+ R1G1C1G3G4+ -C2 R2 Hnh 2.27 Tiimt,trckhiG1c dum nn phn hilphn him(i du phn hibanu)

Hnh 2.28 C) (U= H G GG. 2 . 1 12+.U Vy u ra tng cng khi c 2 tn hiu vo R, U tc ng l: C = C) (U = C) ( R = ( H G GG G. . 12 12 . 1+).R + H G GG. . 12 12+.U * Nhn xt :T C) (U = H G GG. . 12 12+.U Nu G2 1.G .H> 1 th C) (U~H G .11.U Tc dng ca nhiu U vo h thng b gim ng k khi hm truyn ca mch h tng.VthvigialngG1lncthchomturachnhxc(urart khng nhy cm vi nhiu) . V d 2 : H c nhiu u vo, nhiu u ra Tm C1, C2 = ?

Hnh 2.29 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.C1G1R1 +-G2 G3.G4-G2.G3.G4++ R1G1C1C1G1R1 +-G2 G4 G3R2+-C12G2R2 +-(-G1).G3.G4G2-+ R2G4C12G1 G3- + Trc ht b qua C2, h thng ch cn mt u ra C1 u tin b qua R2=0 :

Hnh 2.30 C11 = 4 3 2 11.G .G .G G 1G.R1 B qua R1= 0, h thng cn R2v C12. Hnh 2.31 C12 = 24 3 2 14 3 1.R.G .G .G G 1.G .G G Vy u ra C1 do R1 v R2 tc ng l: C1 = C11 + C12 = 4 3 2 11.G .G .G G 1G.R1 +Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.-G1 G4C2G2R1 +-G3G1.G2-+ R1G3C21+R2-G4Cho R2 = 0C21G3R1 +-G1.G2.(-G4)G3C22G4R2 +-G1.G2-G1.G2.G3++ R2G4C22+ 24 3 2 14 3 1.R.G .G .G G 1.G .G G = 4 3 2 12 4 3 1 1 1.G .G .G G 1.R .G .G G .R G * B qua C1 tm C2 ta c:

Hnh 2.32 C21 = 14 3 2 14 2 1.R.G .G .G G 1.G .G G Cho R1 = 0: Hnh 2.33 C22 = 4 3 2 12 4.G .G .G G 1.R G Vy u ra C2 do R1, R2 tc ng l: C2 = C21 + C22 = 14 3 2 14 2 1.R.G .G .G G 1.G .G G + 4 3 2 12 4.G .G .G G 1.R G= 4 3 2 11 4 2 1 2 4.G .G .G G 1.R .G .G G .R G V d 3: Rt gn s khi v dng chnh tc Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.+H1G3G4+G1-+ RH2C-G2G2-CH2G3R +-G4+G1G3H1+CG4+G1-+ RH2G3G2.G31 + G2.G3.H1 Hnh 2.34 Hm truyn ca h thng:2 2 4 1 1 3 23 2 4 12 3 2 4 1 3 1 3 2 1 3 21 3 2 3 2 4 1.H ).G G (G .H .G G 1.G ).G G (G] .H .G ).G G (G ).G .H .G G ).[(1 .H .G G (1) .H .G G .(1 .G ).G G (GRC G+ + ++==+ + + ++ += = * Nguyn tc rt gn s khi phc tp v dng s chnh tc - T hp cc khi ni tip theo chuyn i 1 - T hp cc khi song song theo chuyn i 2 - Trit tiu cc mch phn hi ph theo chuyn i 7 -Dichuynimtsangtrivimtnsangphicamchchnhtheocc chuyn i 4 v 5. - Lm li t bc 1 n 4 cho n khi nhn c dng chnh tc vi 1 tn hiu vo ring bit. - Lm li t bc 1 n bc 5 i vi mi tn hiu vo. 2.3. Graph tn hiu v qui tc Mason 2.3.1. Graph tn hiu CchthngiukhincncmtbngmhnhtonlGraphtnhiu. Graph tn hiu th hin bng th s truyn tn hiu trong h thng, nhng d dng hn cc dng m hnh ton khc. Xt phng trnh n gin: Xi = Aij. Xj

Cc bin Xi, Xj : l hm thi gian, hm bin phc hoc hng s, hoc l hng s. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Nt Nt NhnhXj Xi AijAin Xi X2X1XnAi2Ai1Aijlmt tontnhxXjvotrongXinnAij gilhmtruyn(hmtruyn t). Khi Xi, Xj cc hm ca bin Laplace S ( bin phc). Mi bin s trong Graph c Mi bin s trong Graph c k hiu bng mt nt mi hm chuyn c k hiu bngmtnhnh,ccnhnhuchngkhiubng mitndintdngtn hiu. Hnh 2.35 * Quy tc hi t ( cng vo): Tng cc tn hiu i vo mt nt bng gi tr cc nt . Tng qut: Xi = =n1 jj ij.X A

Hnh 2.36 *Quy tc phn k ( chuyn ra): Gi tr ca mt nt c th chuyn ra tng nhnh ri khi nt . Nu ta c: Xi = Aik ; i = 1,2,..., n. Th Graph nh hnh v:

AjkXk X2X1XnA2kA1kXnAnk

Hnh 2.37 *Quytcnhn:Nhiunhnhnitipnhaucththaybngmtnhnhchm chuyn bng tch cc hm chuyn ca cc nhnh . Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.A21Xn-1 X2 X1 XnAn(n-1)X1 XnA21.A21...An(n-1)=A43X4 X1 X2 X3A21A33A32A23A23A32A21X3 X2 X1=X1 X2 X3A21A32A231X4X3=X4Xn = A21. A32. A43... An(n-1) .X1

Hnh 2.38 * Cc thnh phn trong Graph tn hiu: Cho mt Graph tn hiu nh hnh v sau Hnh 2.39 -Mttuyn:Lmttrnhtnitip,nhngcaccnhnh,trong khng c nt no b xuyn qua qu mt ln. X1 n X2 n X3 n X4 X2 n X3 v tr v X2 X1 n X2 n X4. -Nt vo: L mt nt ch c cc nhnh i khi n ( X1). -Nt ra: l mt nt ch c cc nhnh i ti n ( X4) C th thm mt nt gi vi hm chuyn bng 1 tho mn nh ngha ny. Hnh 2.40 -Tuyn thun: l tuyn i t nt vo n nt ra ( bng bt c ng no) X1 n X2 n X3 n X4; X1 n X2 n X4 -Tuyn phn hi: l tuyn xut pht v kt thc ti cng mt nt. X2 n X3 n X2 -Tuyn n: L tuyn phn hi ch c mt nhnh. -Hai tuyn ( hoc hai vng kn) gi l khng chm nhau nu chng khng c nt chung. -Hmtruyncatuynhoccavngknbngtchhmtruyncacc nhnh nm trong tuyn hoc vng kn . Tuyn thun X1 n X2 n X3 n X4 c gia lng A21. A32. A43 Tuyn phn hi: X2 n X3 n X2 c gia lngA32. A23 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.x2x1x3x3 dt22d-1 dtd1x1A32A23A21A31A33x4 A43A42x1x2x3x4A21A23A31A32A42A43A33

x2x3G1G2 G3G4 G5G7G6-H1-H2u y11Cc v d: V d 1: Dng Graph tn hiu cho h thng c m t bi phng trnh vi phn sau: x3 = 11222xdtdxdtx d + T phng trnh ta thy c 3 bin s x1, x2, x3 nn cn c 3 nt ( khng k nt gi). Cc ton t trong phng trnh l dtd v 22dtd Vit li phng trnh trn: x3 = 1 22xdtddtd + ) ( ) (1 2x x S Graph tn hiu:

Hnh 2.41 V d 2: Dng Graph tn hiu cho nhm phng trnh xt ng thi sau: x2 = A21. x1 + A23. x3 x3 = A31. x1 + A32. x2 + A33.x3 x4 = A42. x2 + A43. x3 Nhn xt: Phng trnh trn c 4 bin s x1, x2, x3, x4 ta c s Graph tn hiu sau

Hnh 2.42 2.3.2. Quy tc Mason T s Graph tn hiu c th rt gn s v tm hm truyn t ca c h thng. tm hiu v quy tc Mason ta c v d minh ha sau: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hnh 2.43 Bc 1: Xc nh tt c nhng tuyn thng Pk c th c ca h thng. lnhng ng ni lin nhau khng cha ng phn hi i t im nt ngun u(t) ti im nt ch y(t) v Pk c gi tr bng tch cc gi tr cc ng ni c trong Pk.H trn c 3 tuyn thng: P1 = G1. 1. G2. G7 P2 = G1. 1. G6. G4. G5

P3 = G1. G2. G3. G4. G5

Bc2:XcnhttcnhngvnglpLkcthcca hthng.lnhng ng ni lin nhau to thnh mt vng kn. H trn c 4 vng lp: L1 = -1. G4. H1 L2 = -1. G2. G3. G4. G5. H2 L3 =-1. G6. G4. G5. H2 L4 = - 1.G2. G7. H2

Bc 3: Tnh ... .L .L L .L L L 1 n m, l,n m lj i,j ikk+ + = (2.3.2.1) Trong : Li, Lj l nhng cp hai vng lp khng trng nhau ( khng c chung mt nhnh no) Ll, Lm, Ln l b 3 vng lp khng trng nhau,... Htrnchc2vnglpL1,L2lkhngtrngnhau(khngconnoging nhau).... .L .L L .L L L 1n m, l,n m lj i,j ikk+ + = = 1 ( L1 + L2 + L3 + L4) + L1. L4 = = 1 + G4. H1 + G2. G3. G4. G5. H2 + G6. G4. G5. H2 + G2. G7. H2

Bc 4: Xc nhAk tA bng cch trong cng thc (2.3.2.1) ta b i tt c nhng vng lp c on ni chung vi Pk . Tc l: A1= 1 L1 = 1 + G4. H1 ( tt c cc vng lp u khng c on ni chung vi P1) A2 = 1 ( tt c cc vng lp u c on ni chung vi P2 ( c G1) A3 = 1 ( Vng lpc on chung vi P3 ) Bc 5: Xc nh hm truyn t G(s) theo cng thc Mason: G(s) =) . (P1kk k Vy G(s) =1. ( P1.A1 + P2.A2 + P3.A3)=Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.-uG2yG3 G1-H2H11uG3G2 G1-H2H1-1y

h1h2A1 A2 qu(t)y(t)r1 r2,p1,p2=H . G . G H . G . G . G H . G . G . G . G H . G 1G . G . G . G . G G . G . G 1. . G ) H G .(1 G . G 1. . G2 7 2 2 5 4 6 2 5 4 3 2 1 45 4 3 2 1 5 4 6 1 1 4 7 2 1+ + + ++ + + V d 1: Cho h thng c s khi nh sau, s Graph tn hiu tng ng nh hnh v Hnh 2.44 H ch c mt tuyn thng l:P1 = G1. G2. G3

H c 3 vng lp tng i mt c on ni chung: L1 = G1. G2. H1

L2 = -G2. G3. H2 L3 = -G1. G2. G3

Vy,... .L .L L .L L L 1n m, l,n m lj i,j ikk+ + = = 1 ( L1 + L2 + L3)==1 - G1. G2. H1 +G2. G3. H2 + G1. G2. G3

Do tt c cc vng lp cng u c tuyn thng P1 nnA1= 1Hm truyn ca h thng l: G(s) = ) . (P1kk k = 1. P1. A1 = 3 2 1 2 3 2 1 2 13 2 1G . G . G H . G . G H . G . G - 1G . G . G+ + V d 2: Xt mt h thng gm 2 bnh cha cht lng nh sau Hnh 2.45 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.A1s11r11A2sr21u(t)y(t)h2 p2qp1h11A1s r11 1A2s r21-1-1-1u(t) y(t)Cht lng c bm vo bnh th nht vi lu lng u(t). Nu cht lng trong bnh th nhtc cao h1,psut p1, hschuyn ipsut,lulngr1, hsp sut, cao g. lu lng chy sang bnh th hai l q v h2, p2, r2 l cao, p sut, h s chuyn i p sut, lu lng ca cht lng trong bnh th 2. Theo cc nh lut vt l, gia nhng thng s k thut c quan h: A1.dtdh1 = u(t) q q =.r11(p1 p2) A2.dtdh2 = q y(t) y(t) =.r12p2 ( p sut ti u ra c xem nh bng 0) p1 = .h1 p2 = .h2 Trong y(t) l lu lng cht lng chy ra khi bnh th 2. T nhng hiu bit l thuyt ban u ca h thng ta c s khi v s uGraph m t tn hiu m t h thng. Hnh 2.46 T s trn ta thy h ch c mt tuyn thng: P1 = 22 1 2 12.s .A .A .r r

H c 3 vng lp: L1 = -.s .A r1 1 L2 = -.s .A r2 1 L3 = -.s .A r2 2 Trong c 2 vng lp L1 v L2 khng c nhnh no chung. NnGenerated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.H thngKu(t)y(t)K... .L .L L .L L L 1n m, l,n m lj i,j ikk+ + = = 1 ( L1 + L2 + L3) + L1.L3 = 1 + ( .s .A r1 1+ .s .A r2 1+ .s .A r2 2) + .s .A r1 1..s .A r2 2 = 22 1 2 12 2 1 2 1 122 1 1 2.s .A .A .r r.A r .A r .A r .s .A .r .A r2). .( + + + + s V c 3 vng lp trn u c nhnh ni chung vi P1 nn 11 = A Vy hm truyn t:G(s) = . P1 1 = 22 1 2 12.s .A .A .r r.2). .( + + + + s2 2 1 2 1 122 1 1 222 1 2 1.A r .A r .A r .s .A .r .A r.s .A .A .r r= = 2). .( + + + + s2 2 1 2 1 122 1 1 22.A r .A r .A r .s .A .r .A r 2.4. Cc h thng ly mu d liu Nh bit, h thng lin tc l h c cc bin s vo v ra c truyn i v bin i lintctheothigian,cth quanstvo bt cthi im no.Nhngtrong iukhincncnhiuhthngmccbinschcavovxlgin on, n cho p ng ti cc thi im gin on l cc h thng ri rc m cc tn hiu truyn i khng lin tc. C cc dng h thng gin on: -Cc h thng ly mu gin on t cc h lin tc, bin i tn hiu lin tc thnh gin on gi l lng t ho -Cc h thng lm vic theo chu k -Cc h thng c cu trcc chu k H ri rc, gin on c nhng u im: -Lm vic t tn nng lng, c tnh kinh t -C th iu khin nhiu knh ng thi, chng nhiu tt -Truyn v gi tin c lu -V l thuyt khng cn php tnh tch phn v vi phn nn n gin hn -C nhiu tnh cht ging nh h lin tc -M hnh ton l cc phng trnh lp ( phc hi li) * M hnh ton ca h thng ri rc Xt h xung ly mu gin on: Hnh 2.47 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.0y(kT)tT 2T 3T 4T 5T 5T 4T 3T 2T T1 2 3 4 5 5 4 3 2 1ky(k)0f)Chui ri rc0u(k)ku(1)u(2)u(3)u(4)u(5)y(1)y(2)y(3)y(4)y(5)e)Chui ri rctu(kT)0tTn hiu vob)c)Tn hiu ratng v m b ngt K theo chu k mch ca n khng lin tc c na; ta s cccxungginonlintipnhautothnhmtchuitnhiuxung.Mi xung ko di mt thi gian t . Gi s thao tc b ngt K sao cho t cng nh ( t 0) vi mt chu k ly mu c nh T th cc xung cng thu hp li v ta chn t l thi gian sao cho chu k ly mu T = 1, tc l u(kT) = u(k) y(kT) = y(k)k = 0, 1, 2, 3,... l cc s nguyn Phng trnh lp i s c dng sau: any(k+n) + an-1y(k + n -1) +... + a1y(k + 1) + a0 y(k) = bm u( k+m) + bm-1u(k + m -1) + ... + b1 u(k + 1) + b0 u(k) Trong phng trnh trn khng c vi phn, cng khng c tch phn gi l phng trnh lp li din t h ri rc ( ly mu) tng ng vi phng trnh vi phn ca h lin tc. k: l bin c lp vi cc gi tr 0, 1, 2, 3,... u(k): l mt chui ri rc m t tn hiu vo y(k): l mt chui ri rc khc m t tn hiu ra. Hnh 2.48 * Ton t gin on: H thng gin on cng quy nh mt vi ton t vi hm cn tm. -Ton t cng thm 1: E (k) = k + 1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.f(k+1)f(k)k k+1f(k)kf(k)0E[f(k)] = f( k+ 1) Ef(k) f(k+1)E[f(k)] = f(k+1)k+m kEm nEk+m+n Tnh cht ca ton t E: Tnh lp li:En(k) = k + n Tnh nghch o:E-n(k) = k n Tnh gp:Em. En = Em+n E[Cf(k)] = C.f(k+1) = C. E[f(k)] ; C l hng s E[f1(k) + f2(k)] = f1( k+1) + f2(k + 1) = E[f1(k)] + E[f2(k)] E[C1.f1(k) + C2.f2(k) + ... + Cn. fn(k)] = = == +n1 ii in1 ii i(k)] .E[f C 1) (k .f CHm truyn t: Phng trnh lp: any(k+n) + an-1y(k + n -1) +... + a1y(k + 1) + a0 y(k) = = bm u( k+m) + bm-1u(k + m -1) + ... + b1 u(k + 1) + b0 u(k) an.En[y(k)] + an-1.En-1[ y(k)] +... + a1. E[y(k)] + a0 y(k) = bm. Em[u(k)] + + bm-1. Em-1[u(k)] + ... + b1. E[u(k)] + b0. u(k)Ta c : D(E).y(k) = N(E) u(k)Trong : D(E) = an.En + an-1.En-1 +... + a1. E + a0

N(E) = bm. Em+ bm-1. Em-1 + ... + b1. E + b0 Hm truyn ca h thng: H(E) = D(E)N(E) = 01 n1 nnn01 m1 mmma ... E a E ab ... E b .E b+ + ++ + + *Ton t sai phn A[f(k)] = f(k+1) f(k) Hnh 2.49 Cc tnh cht: 1. A[Cf(k)] = Cf(k+1) C f(k) = CAf(k) 2. A[f1(k) + f2(k)] = [ f1(k+1) + f2(k+1)] [ f1(k) + f2(k)] =Af1(k) -Af2(k) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.0f(t)tT 2T 3T 4T 5Tty(kT)0f(T)f(2T)f(3T)f(5T)0y(kT)t5T 4T 3T 2T Tf(0)f(kT) f(t)y(kT)3. A[C1f1(k) + C2f2(k) + ... + Cnfn(k)] = = = =A = +n1 ii in1 ii in1 ii i(k) f . C (k) .f C 1) (k .f C4. A[f(k)] = f(k+1) f(k) = E f(k) f(k) = ( E 1)f(k) ;A= E 1 5. A[f(k)] = f(k+1) f(k) 6. A2[f(k)] =A[ Af(k)] =Af(k+1) -Af(k)7. An[f(k)] =A[ An-1f(k)] =An-1f(k+1) -An-1f(k) An[f(k)]=(E-1)n[f(k)]=[En- = + = + + + + + + = + ++ + = + + ++n0 rrnr rnr rnr1 n n r n rnr 2 n 1 nr) n f(k C 1) ( ... r) n f(k C 1) ( .... 1) n nf(k n) f(k ... [f(k)] C 1) (... [f(k)] E1!n[f(k)] E ...].f(k) E .C 1) ( ... .E2!1) n(n.E1!nTrong : r)! r!.(nn!Crn=8. Amn[f(k)] =Am. An[f(k)] =An.Am[f(k)]

Cn dng ton t sai phn ngc: Vf(k) = f(k) f( k- 1); V = 1 E-1 * Bin i Z: TrongcchtuyntnhlintctadngbiniLaplace;cchnyctnh nhnqu(tchphnmtphat0n);VinhnghabiniLaplaceca hm f(t) l: L {f(t)} = }+0). ( dtste t fGia bin i Laplace ca h tuyn tnh lin tc v bin i Z ca h tuyn tnh ri rc c mi lin quan cht ch. Phpnhn2tnhiucththchincbngmtsbin iu(modulation). Cc xung ly mu gin on t mt tn hiu lin tc f(t) c th xem nh kt qu ca mt s bin iu ca mt chui ri rc Y(kT) theo bin ca tn hiu lin tc v c cng chu k vi chu k ly mu gin on. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.y(k)1 2 3 4 5k01d(k) d(k-1)d(k-2) d(k-3) d(k-4) d(k-5)Hnh 2.50 Ta c : f(kT) = f(t). Y(kT) Chui ri rc Y(kT) c th l chui Kronecker hoc chui Dirac. Chui Kronecker nhn qu ( 1 pha) l mt chui xung c bin bng 1, tc ng ti cc gi tr bng 0 hoc nguyn dng ca k ( k> 0): Y(kT) = =0 jj)T d(k , vi T = 1 ta c chui nh hnh v sau: Hnh 2.51 Y(k) = =0 jj) d(kTrong : d( k-j) = ==j k nu ; 0j k nu ; 1 vi j l s nguyn, j> 0 Ta c cc xung ly mu gin on ca f(t): f(kT) = f(t). Y(kT) f(t)

}=0st0skT -dt f(t).e f(kT).e t esT = Z vi T = 1 nn Z = es

Vy bin i Z ca chui f(k). Y(k): Z[f(k).Y(k)] = F(Z) = =0 kk -f(k).ZVi k = 0,1, 2, 3,... Bin i Z l mt thut ton qua mt chui a vo f(k) s cho ra mt chui v tn f(k).Z-k. Tc l, nu f(k) = [ f(0), f(1), f(2), ..., f(k),...] Z[f(k)] = f(0), f(1).Z-1, f(2). Z-2,.... Bin i Z ca mt chui f(k) ch tn ti nu chui bin i Z tuyt i hi t: [Z] > Rc : Chui hi t [Z] < Rc : Chui phn k. Rc l bn knh ca vng trn hi t ( Tm ca vng trn l gc ca mt phng phc. Cc im ngoi vng trn din t tnh hi t ca chui F(k), cc im trong vng trn din t tnh khng hi t, cn cc im nm trn ng trn l im c bit phi xt ring. 2.5. Hm truyn t ca h thng ri rc a) p ng xung ca h ri rc Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.0d(k-k0)kk0iu kin u bng 0 k0kh(k,k0)0kH thngCng nh h lin tc, p ng xung ca h ri rc, v hng ( 1 bin) l p ng ca h vi xung Dirac ( Kronecker). H lc u trng thi dng, iu kin ubng 0 x(0) = 0; tn hiu xung Dirac p ln h vo thi im k0T v p ng c xt thi im kT ( k > k0). p ng xung l mt chui [ h(kT, k0T)] Gi s T = 1: Hnh 2.52 V vy vi mt h ri rc, v hng , nhn qu, tuyn tnh, h s c nh ta c: Tn hiu vo l xung d( k- j ) th tn hiu u ra l p ng xung h ( k- j). Tn hiu vo l chui u(k) = =0 jj) d(k (j). uth tn hiu ra l chuiy(k) = =0 jj) h(k u(j).Do : y(k) = =0 jj) h(k u(j).vi i, j = 0, 1, 2, 3 ,... y(k) = u(k). h(k) Nu u(k) = d(k) l tn hiu xung n v ( Dirac hoc Kronecker) th u ra p ng xung l h(k). Nh vy p ng ca mt h ri rc, v hng , nhn qu, tuyn tnh, bt bin l tch chp ca tn hiu vo u(k) vi p ng xung h(k) ca h . b) Hm truyn ca h ri rc y(k) = u(k). h(k) Ta c bin i Z l: Z[y(k)] = Z[h(k)]. Z[u(k)] Y(Z) = H(Z). U(Z) H(Z) l hm truyn ca h ri rc, l bin i Z ca p ng xung h(k) ca h. H(Z) = U(Z)Y(Z) 2.6. ng dng MatLab Nhp m hnh ca h thng iu khin trong MatLab: G(S) = o 11 n1 nno 11 m1 mmma S . a ... S . a Sb s b ... S . b S b+ + + ++ + + += ) () (S denS num Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.>> num = [ bm bm-1. . . b1 b0 ] >> den = [ 1 an-1. . . a1a0 ] >> sys = tf (num, den) Kt qu: Tranfer function ) () (S denS num Hoc: >> S = tf(s) >> G(s) = ) () (S denS num M hnh im khng - im cc: >> [z, p, k] = residue (num, den) >> z = zero (sys) >> [p,z] = pzmap (sys) ( Hin th th cc - khng) >> p = pole (sys) Tm nghim mu s ca hm truyn t: >> c = [ 1 an-1. . . a1a0 ] >> p = roots (c) th p ng ca h thng iu khin: >> impulse (num, den,t) >> Step (num, den, t)>> Lsim (num,den,u, t)Chuyn t hm truyn t sang phng trnh trng thi: >> [A, B, C, D] = tf2ss (num, den) V ngc li: >> [num, den] = ss2tf ( A,B, C, D) Chuyn sang m hnh h thng gin on: >> sysd = c2d (sys , Ts) >> sysc = d2c (sysd) p ng ca h thng gin on: >> dimpulse (num, den) >> Dstep(num, den) >> dlsim(num, den) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Chng 3 PHNG TRNH TRNG THI * t vn : - Cc h thng tuyn tnh lin tc c m t bi h n phng trnh vi phn cp mtm t n trng thi ca h thng m hnh ton h thng vit di dng ma trn. x&(t)= A. x(t) + B. u(t) ; xo = x(o)(3-1) v y(t) = C. x(t)+ D. u(t) (3-2) y:x e 9n,u e 9r,y e 9Ptng ng l cc vect trng thi, cc u vo, cc u ra. MatrnhsAnnmtccmilinhbntronghthng.Ccmatrn Bnr , CPn , DPr , c trng cho mi lin h vi bn ngoi ca h thng. Nu khng c ng dn trc tip gia cc u vo vi u ra th DPr l ma trn zero. *Mhnhkhnggiantrngthicahthngiukhinginon(tuyn tnh) l cc phng trnh sai phn. x(k+1) = Ad . x(k) + Bd.u(k) , x(o) = xo(3-3) y(k) = Cd x(k) + Ddu(k)(3-4) 3.1- Cc m hnh khng gian trng thi. M hnh khng gian trng thi ca h thng ng lc hc lin tc u c th din t h thng trong lnh vc thi gian bng cc phng trnh vi phn hoc hm truyn di bn dng (form) sau: - Dng iu khin (khng gian pha). (Controller canonical form). - Dng quan st (khng gian quan st). (observer canonical form). - Dng modal (khng gian modal). (Modal canonical form). - Dng Jordan (khng gian Jordan). 3.2- M hnh khng gian trng thi v cc phng trnh vi phn. H thng ng lc hc cp n c m t bng phng trnh vi phn cp n. nndt) t ( y d + an-1 1 n1 ndt) t ( y d +... + a1 dt) t ( dy + aoy(t) = = bn nndt) t ( u d + bn-1 1 n1 ndt) t ( u d+... + b1 dt) t ( du+ bou(t) (3-5) Ta gi thit cc iu kin u ca h thng Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. y(o-) ,dto dy ) ( , ... , 1 n1 ndt) o ( y d ng thi bng khng, ta tin hnh bin i phng trnh vi phn cp n thnh h n phng trnh vi phn cp 1. + Xt phng trnh vi phn cp n sau:

nndt) t ( y d + an-1 1 n1 ndt) t ( y d + ...+ a1dt) t ( dy + aoy(t) = u(t)(3-6) i bin theo: x1(t)= y(t) x2(t)= dt) t ( dy

x3(t)= 22dt) t ( y d(3-7) . . . . . . . . xn(t)= 1 n1 ndt) t ( y d

Tin hnh ly o hm hai v cc phng trnh (3-7).

dt) t ( dx1=x&1 = dt) t ( dy= x2(t)

dt) t ( dx2=x&2 = 22dt) t ( y d= x3(t)(3-8) . . . . . . . . ) t ( d) t ( dxn =x&n = nndt) t ( y d= - ao(y(t) - a1dt) t ( dy - ... - an-1 1 n1 ndt) t ( y d+ u(t) = - aox1(t) - a1x2(t) - ... - an-1 xn(t) + u(t) Vy khng gian trng thi (3-8) vit di dng ma trn x&1 010AA0x1(t)0 x&2 001AA0x2(t)0 x&3 MMOOOMMM M=MMMOO0M+Mu(t) x&n-1 00AA01xn-1(t)0 x&n -ao -a1AAA-an-1 xn(t)1 (3-9) u ra c vit theo (3-7). y(t) = [1 0 0 ... ... 0] [x1(t) x2(t)...xn(t)]T(3-10) (3-9) v (3-10) c gi l dng chnh tc ca khng gian pha. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.+ i vi h thng c m t bi phng trnh (3-5) ta c: y(t) = [(bo - aobn) (b1-a1bn) ... ... (bn-1 - an-1)] [x1(t) x2(t) ... xn(t)]T + bn u(t) (3-11) Vi:bn = 0ta c: y(t) = [bo b1 ... ... bn-1] [x1(t) x2(t) ... ... xn(t)]T (3-12) 3.3- Xc nh cc bin trng thi t hm truyn. Phn ny gii thiu cc k thut hnh thnh m hnh khng gian trng thi t hm truyn ca h thng thng c p dng trong thc t. l k thut chng trnh trc tip v k thut chng trnh song song. n gin ta xt vi h thng mt u vo mt u ra. 3.3.1- M phng HT theo dng iu khin chnh tc. Kthutnycsdngthunlikhihmtruyncathitbdnga thc khng phn tch ra tha s c. ) s ( U) s ( Y = o 11 n1 nno 11 n1 nnna S a ... S a Sb S b ... S b S b+ + + ++ + + +(3-13) y ta s dng bin ph V(s). (Tnh iu khin c ca h thng l vi mt tc ng vo liu c chuyn ctrngthicahtthiimutonthiimcuitrongkhongthi gian hu hn khng?). ) s ( V) s ( Y = bnSn + bn-1Sn-1+ ... + b1S + bo (3-14a)

) () (s Us V = o 11 n1 nna S a ... S a S1+ + + +(3-14b) S khi m t h thng c s dng bin ph V(s). Hnh 3.1 Phng trnh (3-14a) c vit li nh sau: Y(s) = bnSnV(s) + bn-1Sn-1V(s) + ... + b1S.V(s) + boV(s) (3-15) iu ny ch ra rng y(t) l s chng cht ca V(t) v cc o hm ca n v tacthtrnhby(3-14a,b)didngphngtrnhviphnkhiiukinu ng nht bng khng bng cch thay: S dtd;Si iidtd ; V(s) v(t),V(s)/U(s) Y(s)/V(s) U(s) V(s) Y(s) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Xy dng m hnh khng gian trng thi ca h thng t cc hm truyn bng cch s dng s m phng rt thun tin. Trong cc trng hp h thnglin tc s m phng cc my tnh tng t gii cc phng trnh vi phn m t cc h thng ng lc hc s dng cc b tch phn, b cng b tr v nhn cthchinnhlbkhuchithutton.Skhitchphnphthucvo cp ca phng trnh vi phn. + S m phng (3-14a, b) nh sau: S dngkthutchngtrnhtrctip: tnkhitch phn nitipvi u vo tng ng l V(n)(t) ,v(n-1)(t) , ...,V(1)(t) ,v(t). p dng (3-15) xc nh y(t) bng cch nhn u vo vi(t) vi cc h s bi v cng bng b cng . + T (3-14b) ta c: v(n)(t) = u(t) - an-1 v(n-1)(t) - ... - a1v(1)(t) - aov(t)(3-16) Cc php tr m phng bng mi lin h ngc trn s ta c:

Hnh 3-2: S m phng k thut chng trnh trc tip (dng iu khin chnh tc). Theohnh 3-2tac mhnhkhnggiantrngthicah thngdngiu khin chnh tc. 010AA00 001AA00 x&(t) =MMOOOMx(t)+0u(t) MMMOO1M -ao -a1 -a2AA-an-1 1 1/S K 1/S 1/S bo U(t)x&n V(n-1) xn x&2 x2 x&1 x1 y(t) b1 b2 bn -an-1 V(n) -a1 -ao v(1) v(0) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.(3-17) Vy(t) = [(bo-aobn) (b1 - a1bn) ...(bn-1 - an-1 bn)] x(t) + u(t) . bn(3-18) ** ( chuyn t hm truyn sang dng khng gian trng thi trong Matlab s dng hm tf2ss). V d: Cho hm truyn. G(s) =S 811 S 12131 85 . 97 S 463 S 996 . 0 S19080 65 . 90 S 576 S 331 . 0 S 65 . 12 3 4 5 62 3 4+ + + + ++ + a) V s m phng h thng (dng iu khin). b) Dng m hnh khng gian trng thi ca h thng. 3.3.2- M phng HT theo dng quan st chnh tc. Cng vi dng iu khin, dng quan st chnh tc l quan h quan trng i vi l thuyt iu khin hin i. * Quan st c ca mt h thng l vi cc to o c bin ra y(t) ca h thng liu ta c th khi phc c cc vect trng thix(t) trong thi gian hu hn khng? Khng gian trng thi ca h thng v dng quan st chnh tc ca n c xc nh c cu trc rt n gin. Xut pht t hm truyn (3-13) ta c: Y(s)(Sn + an-1Sn-1 + ...+ a1S + ao) = U(s) (bnSn + bn-1Sn-1 + ...+ b1S + bo) (3-18) Y(s) = -nS1 (an-1.Sn-1 +...+ a1S + ao) Y(s) + nS1 . U(s) (bnSn ++ bn-1Sn-1 + ...+ b1S + bo)(3-19) Khai trin ra ta c: Y(s) = - an-1 . S1 Y(s) - an-2 2S1 Y(s) - ... - a11 nS1 Y(s) - ao nS1 Y(s) + + bnU(s) + bn-1S1 U(s) + ...+ b1 1 nS1 U(s) + bo nS1U(s) Mi quan h (3-20) c th hin trn s m phng qua n tng tch phn. Nhncacctnhiutqutngtchphnvdmtkhi S1chmttngtch phn. Tn hiu an-2y(t) v bn-2U(t) ch vt qua hai tng tch phn, aoy(t) v bo u(t) vt qua n tng tch phn. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Hnh 3-3: S khi m phng dng quan st chnh tc. + Cc bin trng thi nh l u ra ca cc khi tch phn quan h u ra vi cc bin trng thi theo s trn ta c: Y(t)= xn(t) + bnu(t)(3-21) x&1(t)= - aoy(t) + bou(t) = - aoxn(t) + (bo - aobn) u(t) x&2(t)= - a1y(t) + b1u(t) + x1 = x1(t) - a1xn(t) + (b1 - a1bn) u(t) x&3(t)= - a2y(t) + b2u(t) + x2 = x2(t) - a2xn(t) + (b2 - a2bn) u(t) x&n(t)= - a1-1y(t) + bn-1u(t) + xn-1 = =xn-1(t) - an-1xn(t) + (bn-1 - an-1bn) u(t) (3-22) T(3-21)v(3-22)taddngvitdidngmatrncadngquanst chnh tc: 00AA-aobo - aobn 10AA-a1b1 - a1bn x&(t) =01AA-a2x(t)+b2 - a2bnu(t) M01AA. 000A-an-2 . 000 1-an-1 bn-1 - an-1bn (3-23) vy(t) = [ 00......0 1] x(t) + bn u(t)(3-24) V d:G(s) = S 11 , 8 S 12131 S 8 , 94 S 463 S 996 , 0 S19080 S 6 , 90 S 576 S 331 , 0 S 65 , 12 3 4 5 62 3 4+ + + + ++ + Hy vit dng quan st chnh tc di dng ma trn. 3.3.3- K thut m phng chng trnh song song. i vi k thut ny ta phn ra lm hai trng hp: a thc mu c nghim thc ring bit v c nghim lp. + bo - ao + b1 - a1 + bn-1 - an-1 1/S + b1 - a1 1/S1/SA 1/S + bn U(s) y(s) x&1 x&n-1 x2 xn-1 x&n xn Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.a) a thc mu c hm truyn, c nghim ring bit. Dngkhnggiantrngthinythuntinchoccngdngkiunybt ngun t vic khai trin hm truyn thnh tng cc phn thc. Mt cch tng qut m < n th: ) s ( U) s ( Y = ) p S )...( p S )( p S () s ( Pn 2 1m+ + + =11p Sr+ + 22p Sr+ + ... + nnp Sr+ + k(3-25) yp1,p2,..., pnccnghimringbit(cccc)caathcmuca hm truyn.-S khi m phng dng ny nh sau:

(Dng modal chnh tc) Hnh 3-4: S khi m phng k thut lp trnh song song. M hnh khng gian trng thi theo s khi ny nh sau: -p1 0AA01 0-p2AA01 x&(t) =01AAAx(t)+Mu(t)(3-26) AAAA0 M 000 0 -pn 1 y(t) = [ k1 k2 ... ...kn ] x(t) (3-27) b) a thc mu c nghim lp. y(t) + 1/S r2 x&2 x&2 x2 - p2 + 1/S r1 x&1 x1 - p1 + 1/S rn x&n xn - pn M u(t) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Khi hm truyn c cc thc lp. Gi thit cc p1 lp r ln. ) s ( U) s ( Y = ) p S )...( p S ( ) p S () s ( Nn 1 rr1+ + ++ Dng khai trin ca n l:

) s ( U) s ( Y = 111p Sk+ +2112) p S (k+ +...+ r1r 1) p S (k+ + 1 r1 rp Sk+++ +...+ nnp Sk+ Hnh 3-5: S m phng dng Jordan chnh tc. 3.3.4- Cc m hnh ca h thng gin on. (tng t trong s ch thay khi S1 Z-1 ). 3.4. Xc nh hm p ng t phng trnh trng thi 3.4.1. H thng iu khin lin tc Phng trnh trng thi ca h theo (3.1) v (3.2) Nghim ca (3.1): x(t) = eAt. x(0) + }tAtd u B e0) ( . . t t (3-28) y(t) = C. eAt. x(0) + C.}tAtd u B e0) ( . . t t+ D. u(t) (3-29) y(t) = yq(t) + y(t)+ 1/S kr+1 x&r+1 xr+1 - p1 M u(t) + 1/S kn - pn + 1/S k1r+1 x&r xr - p1 K + 1/S - p1 x&2 x2 + 1/S - p1 x&1 k1r y(t)x1 k1r+1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. p ng qu : L p ng ca h thng khng ph thuc vo kch thch u(t) m docciukinucah(trngthibanu).Gildaongtdocah thng. p ng n nh: p ng ph thuc vo u(t). c trng cho qu trnh cng bc ca u(t) lm cho h thng n nh.3.4.2. H thng iu khin gin on Phng trnh trng thi c biu din (3-3) v (3-4) Nghim ca phng trnh (3-3): x(k) = Ak-k0. x(k0) + = 110) ( . .nk jj kj u B A (3-30) y(k) = C. Ak-k0. x(k0) + C.= 110) ( . .nk jj kj u B A+ D.u(k)(3-31) 3.4.3. Cc phng php tm p ng Tm ma trn trng thi: eAt - Ton t Laplace: p dng cng thc: eAt = l-1 [ (SI - A)-1] - Phng php Sylvester: Da vo tr ring ca ma trn A: Tm tr ring bng cch tm nghim ca phng trnh saudet (I - A) = 0, gii phng trnh c cc nghim: 1, 2, ..., n. Ta c: eAt = o0(t).I + o1(t).A + o2(t).A2+ ... + on(t).An

Trong : Cc h s o0(t), o1(t), o2(t), ..., on(t) xc nh t h phng trnh sau o0(t)+ o1(t).1 + o2(t).21 + ... + on(t).11 n= e1t o0(t)+ o1(t).2 + o2(t).22+ ... + on(t).12 n= e2t . . . o0(t)+ o1(t).n + o2(t).2n+ ... + on(t).1 nn= ent Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Chng 4 N NH CA H THNG TUYN TNH 4.1- Khi nim chung. Cc chng II v III trnh by m t ton hc ca h thng ca h thng iu khin truyn ng. Chng ny s s dng cc t liu ca cc chng trnh by trc y gii quyt nhim v u tin khiphn tch h thng iu khin t ng l xc nh tnh n nh ca n. Thcravicnimt hthng nnhlnin mts ilng no c iu khin n nh.Mt h thng thng biu din bng phng trnh vi phn tng qut: nndt) t ( y d + an-1 1 n1 ndt) t ( y d + ... + a1dt) t ( dy + aoy(t) = = bm mmdt) t ( u d + bm-1 1 m1 mdt) t ( y d + ... + b1dt) t ( du + bou(t)(4-1) Hoc phng trnh sai phn: y(k+n) + an-1y(k+n-1) + ... + a1y(k+1) + aoy(k) = = bmu(k+n) + bm-1u(k+m-1) + ...+ b1u(k+1) + bou(k)(4-2) S bao gm hai qu trnh: Qu trnh xc lp v qu trnh qu .c trng bng nghim: y(t) = yo(t) + yq(t) (4-3) Hoc y(k) = yo(k) + yq(k)(4-4) Trong :- yo l nghim ring ca (4-1) hoc (4-2) c trng cho qu trnh xc lp. - yql nghim tng qut ca (4-1) hoc (4-2) khi khng c v phic trng cho qu trnh qu . Qu trnh xc lp l mt qu trnh n nh vn ch cn xt qu trnh qu yq. 4.2- Khi nim n nh v cc nh ngha chnh. i vi h thng tuyn tnh, n nh ca h thng c mi lin h ti ma trn A ca h thng. C th ni i khi rng n nh ca cc h thng ny l tnh cht ca ma trn h thng A. i vi h thng lin tc hay gin on khi khng c u vo (u vo bng khng). x&(t) = A. x(t) ;x(to) = xo (4-5) x(k+1) = A.x(k) ;x(ko) = xo(4-6) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Theo iu kin bin nghim ca (4-5) v (4-6): x(t) = eA (t-to) xo ;x(k)=Ak-ko xo(4-7) h thng n nh i hi: ) t ( xsConst 0.+ Phn tch tng t i vi h thng gin on: x(k+1) = Ax(k) ;x(ko) = xo (4-14) C nghim: x(k) = Ak.ko xn ,vi k - ko > 0(4-15) Gii hn: as 1; nua< 1khi x(k) 0 khi k . V h thng trong vng n nh, ngc li nu c mt vi |i| > 1 h thng khng n nh. nh l 4.2:i vi h thng gin on tin nh c cc tr ring phn bit l trong vng n nh nu |i| < 1 , i .l n nh nu |i| s 1, i v khng n nh nu c mt vi i m |j| > 1. 4.3.3- n nh ca h thng c cc tr ring lp. *Cccclpnmbntrimtphngphc(namtphngphctri)l vng n nh. a thc c trng ca h thng mi n1 cc lp. A() = ( + a)n1 . A1() , a > 0 ,n > n1 > 1 Hm truyn ca h thng trong lnh vc Laplace. H(s) = 1n) a S (1+. H1(s) S dng bin i ngc Laplace vi S = -a. L-1 =1 n0 i11ni n) a S (k+ = =1 n0 i )! i 1 n (k1i n1 tn1-1-i . e-at ng thi: { ) e t imat i 1 nt1 0 ,i = 0, 1, 2, ..., n1 - 1. + Mt cch tng t nu cc cc lp l s lin hp phc mt phng tri ca mt phng phc. Hnh 4.1 nh l 3: Na mt phng vng n nh Im(s) Re(s)Vngn nh Re(z) Im(z) 1 1-1 -1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.H thng tin nh tuyn tnh c cc tr ring phn bit hoc lp l thuc vng n nh, nu ton b cc tr ring ca ma trn A na tri ca mt phng phc. Khng n nh nu c ch mt tr ring nm trn na phi ca mt phc. Cc tr ring trn trc o l n nh. n nh ca cc tr ring lp trn trc o gii hn ca n nh. Trongthctngin,ngitasdngccphngphpgintip nh gi n nh ca h thng da trn cc tiu chun n nh. Cc tiu chun n nh gm hai loi: 1- Cc tiu chun i s tm iu kin rng buc gia cc h s ca phng trnh c trng xt n nh h thng tiu chun n nh Routh - Hurwitz. 2- Tiu chun n nh tn s thng qua c tnh tn s ca h thng xt n nh. Tiu chun Mikhailv v tiu chun Nyquyrtz. * Kho st nghim ca phng trnh c trng. Hm truyn ca h kn dng chnh tc.

G(s).H(s) 1G(s)U(S)Y(S)+=(1) )] .[G(S).U(SG(s).H(s) 11Y(S)+= (2) Y(s) - hm p ng. Hnh 4.2 G(s).U(s) - hm kch thch. ) s ( H ). s ( G 11+ - hm ca h. * Hm kch thch ch nh hng ti p ng n nh ca h m khng nh hng ti dng ca p ng qu v th c th cho G(s) . U(s) = 0. Hay:Y(s) . (1 + G(s) . H(s)) = 0 (3) 1 + G(s) . H(s)) = 0(4) (4) phngtrnh ctrngca hkn.(s dng phngtrnh nynhgi n nh ca h). Ta bit: G(s). H(s) - hm truyn mch h ca h l mt t sgia cc a thc ca bin (S). GiN(s) : a thc t s. D(s) : a thc mu s. Ta c:0D(s)N(s) D(s)D(S)N(S)1 G(S).H(S) 1 =+= + = + (5) D(s) + N(s) = 0 (6) G(s) H(s) U(s) Y(s) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Phn tch phng trnh (6) ra tha s: D(s) + N(s) = (S - r1) (S - r2) ... (S - rn) = 0 Trong :ri nghim ca phng trnh c trng (i = 1, ..., n) *hn nh minghimca phngtrnhctrng uc phnthc m. V d: Mt h chnh tc c cc hm truyn sau: G(s) = ) 4 S ( S3+ ; H(s) = 1 Xc nh phng trnh c trng v nh gi n nh ca h: 1 + G(s) . H(s) = 1 + ) 4 S ( S3+ = ) 4 S ( S3 S 4 S2++ + = 0 Nghim ca phng trnh c trng l-1 ;-3 nghim qu cha cc s m c h s m h n nh. 4.4. Cc tiu chun n nh i s Routh - Hurwith. 4.4.1- iu kin cn h thng iu khin t ng n nh. Trc khi xt cc tiu chun n nh ta cn tm du hiu phn on tnh n nh ca h thng. iu kin cn h thng iu khin t ng tuyn tnh n nh l cc h s ca phng trnh c trng u dng. T phng trnh (6):D(s) + N(s) = 0. Ta c th vit: ao.Sn + a1Sn-1 + ... + an-1 . S + an = 0 (phng trnh c trng vit di dng khai trin). Tacthkimchngliiukin trn, nu gishthngn nh:Nh th nghim ca phng trnh c trng s l: S1 = - o1 ;S2 = -o2 + j|2 ;S3 = - o3 - j |3 ; ... ; Sn = -on

Trong : oi > 0( i = 1, 2, ..., n) Gi s phng trnh c n nghim ta c th vit: ao (S - S1) (S - S2) ( S - S3) ...(S - Sn) = 0 hayao (S + o1) (S + o2 - j|2) (S + o2 + j|2) ... (S + on) = 0 ao (S + o1) [(S + o2)2 + |22] ... (S + on) = 0 V cc s hng u l dng nn ta c th khi trin thnh: aoSn + a1S(n-1) + ... + an-1S + an= 0 Vth khihthng n nh btbuccc h sca phngtrnh ctrng phi dng (iu kin cn). V d:1) H thng iu khinc phng trnh c trng: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.0,04.S3 + 0,4S2 + S + 50 = 0 Vai > 0 nn c th n nh. 2) S4 + 2S3 - 0,5 S2 + 3S + 20 = 0 khng n nh. V khng tho mn iu kin n nh cn thit. 4.4.2.Tiu chun Routh:(khng chng minh). * iu kin cn v h thng n nh (tuyn tnh) l tt c cc s hng trong ct th nht cu bng Routh dng. * Gi s vi phng trnh c trng bc 5. aoS5 + a1S4 + a2S3 + a3S2 + a4S + a5 = 0 Bng Routh c lp nh sau:

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1occ 32cc Error! Not a valid link. 1odd hai hng u c dng cc h s ca phng trnh c trng xp theo chiu mi tn. cc hng sau c cc s hng tnh theo biu thc: bo = 13 12 oaa aa a = 13 o 2 1aa a a a ;b1 = o2 o3 1bb ba a = o2 1 3 obb a a b b2 = 15 14 oaa aa a = 15 o 4 1aa a a a ;b3 = o4 o5 1bb ba a = o4 1 5 obb a a b b4 = 17 16 oaa aa a = 17 o 6 1aa a a a ;b5 = oo7 1b0 ba a Nhn xt: - Mi s hng trong hng th ba ca bng Routh l mt thng s: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.+ T s: nh thc cp hai mang du m vi ct th nht ca n cng l ct th nht ca hai hng ng st trn hng c s hng ang tnh. Cn ct th hai ca nh thc chnh l ct ng st bn phi s hng ang tnh ca hai hng trn. +Mus:Trongttcs hngca mt hngcchung mus chnhls hng ng ct th nht v hng st ngay trn hng ang tnh. V d:1) Cho phng trnh c trng ca h thng: S4 + 2S3 + 8S2 + 4S + 3 = 0 Lp bng Routh: 183 240 630 30 3 H thng n nh v tt c cc s hng trong ct th nht u dng. V d 2: Cho phng trnh c trng ca h thng: S5 + S4 + 3 S3 + 4S2 + S + 2 = 0 Lp bng Routh: 131 142 -1 -1 32 -31 2 H thng khng n nh v cc s hng trong ct th nht khng cng du i s. V d 3:Cho phng trnh c trng ca h thng. S3 + K.S2 + 2S + 3 = 0 Xc nh K h thng n nh: K > 0 Bng Routh: 12 K3 (2K-3)/k 2K - 3 > 0 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.3 4.4.3- Tiu chun n nh Hurwitz. Pht biu: iu kin cn v cho h thng tuyn tnh n nh lcc nh thc Hurwitz dng. * Cch lp nh thc Hurwitz: Cc h s ca phng trnh c trng: ao , a1 , a2 , ..., an A0 = a0 ; A1 = a1 ; A2 = 2 o3 1a aa a ...tng qut An c nct , nhng . ng cho chnh ca An bt u t a1 n an cc s hng trn cng mt ct nm trn ng cho chnh c ch s tng dn, di ng cho chnh ch s gim dn. Cc s hng c ch s b hn 0 v cao hn n u ghi 0. V d:Phng trnh c trng bc 3. ao S3 + a1S2 + a2S + a3 = 0 ao > 0;A1 = a1 > 0 A2 = 2 o3 1a aa a = a1a2 - aoa3 > 0 A3 = 3 12 o3 1a a 00 a a0 a a = A2 . a3> 0 Nhn xt: 1- Tiu chun Routh c th p dng xt cho h thng bt k. 2- Tiu chun Hurwitz c th ng dng cho cc h thng c phng trnh c trng bc thp. 3- C tiu chun Routh v Hurwitz u dng xt n nh cho c h thng h v kn. 4.5. ng dng MatLab Kim tra n nh ca h thng iu khin bng phn mm MatLab - Theo tiu chun Routh: Tnh nh thc cp 2,3 , ... xc nh cc h s trong bng Routh >> det ( [a0a2]; [a1 a3 ])- Theo tiu chun Hurwitz: Tnh cc nh thc Hurwitz 3/2 < K Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.>> det ( [ a1 a3 a5]; [a0 a2 a4]; [0 a1 a3]) Kt qu: A3 - Theo tiu chun Nyquist: >> Nyquist (sys) Hoc >> Nyquist (sys,e ) Trong : >> sys = tf( num, den) Hoc: >> sys = zpk ([z], [p], k) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Chng 5 TNH IU KHIN C V TNH QUAN ST C CA H THNG IU KHIN Khinimviukhincvquanstc(controllabilityand Observability) do R - Kalman a ra 1961. *iukhinccamththnglvimttcngvoliucth chuynctrngthicahtthiimutonthiimcuit1trong khong thi gian hu hn (t1 - to) hay khng. * Tnh quan st c ca h thng l vi cc to o c u ra ca h liutacthkhiphcc(Reconstrucbility)ccvecttrngthix trongmt khong thi gian hu hn hay khng? 5.1- Tnh iu khin c ca h thng tuyn tnh lin tc. H thng tuyn tnh m t bi phng trnh trng thi cp n. x&(t)= A x(t) + B u(t)(5-1) cgiliukhinchontonkhivchkhimatrnsauyc hng bng n. P = [BABA2B...An-1B] (5-2) Rank (P) = n V d:Cho h thng m t bi s sau: Hnh 5.1 Ta c: ) s ( U) s ( Y= 4 S S 2202+ + t: x1=y x&1 = x2 x&2 = - 2x1 - 0,5 x2 + 10 u. Phng trnh trng thi tng ng. 10 1/S 1/S Y(t) U(t) 0,5 0,2 +x&2 x&1 x2 x1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. ((

21xx&& = ((

5 , 0 21 0 ((

21xx + ((

100 u Ta c: B = ((

100 ; AB = ((

5 , 0 21 0 ((

100 = ((

510 P = ((

5 1010 0 det (P) = - 100 = 0Rank (P) = 2 H cp hai trn iu khin c hon ton. 5.2- Tnh quan st c ca h thng lin tc. H tuyn tnh lin tc c m t bi h phng trnh: x&(t) = A x(t) + Bu(t) y(t) = C x(t)(5-3) c gi l quan st c hon ton khi v ch khi ma trn sau c hng bng n. L = {C AC (A)2C ... (A)n-1C } (5-4) Rank (L)= n V d:Cho h c phng trnh trng thi: )`) t ( x) t ( x21&& = ((

2 31 0 )`) t ( x) t ( x21 + ((

31 u(t) y = { 10 } )`) t ( x) t ( x21 C = )`01; A =((

2 13 0

A.C =((

10 L= ((

1 00 1 ; det (L) = -1 = 0 Rank (L) = 2 H thng quan st c hon ton. 5.3- Tnh iu khin c ca h iu khin gin on. Mt hiukhingin ongil iukhin c nutacthtm c mt vect iu khin u(k) chuyn h thng t trng thi ban u bt k n trng thi cui bt k trong mt khong thi gian gii hn. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Vy ta cn tm iu kin xc nh chuyn h thng t trng thi x(o) n trng thi cui x(n) cho. Gi s ta c phng trnh trng thi: x(k+1) = Ad x(k) + Bd u(k) y(k)= Cd x(k)(5-5) Ta vit li (5-5): x(1) = Ad x(o) + Bd u(o) x(2) = Ad x(1) + Bd u(1) = A2d x(o) + AdBd u(o) + Bd u(1) ............... x(n) = Adx(n-1)+Bdu(n-1) = Andx(o)+A1 ndBdu(o) +...+ Bd(u(n-1) hoc l:x(n) - Andx(o) = [ A1 nd BdA2 nd Bd ... Bd ] )` ) 1 n ( u) 1 ( u) o ( uM(5-6) V:x(o) , x(n) v Ad l bit nn (5-6) ch tn ti duy nht nghimu(k) khi hng ca ma trn sau l n. M = [A1 nd BdA2 nd Bd...Bd ] Rank (M) = n V d: Cho h thng cp II sau: ((

++) 1 k ( x) 1 k ( x21 = ((

951 , 0 0488 , 0 1 ((

) k ( x) k ( x21 + ((

00488 , 000123 , 0 u(k) y(k)= [ 1 0 ]((

) k ( x) k ( x21 Theo tiu chun Kalman: Ad . Bd = ((

951 , 0 0488 , 0 1 ((

00488 , 000123 , 0 = ((

00464 , 000361 , 0 M = ((

00488 , 0 00464 , 000123 , 0 00361 , 0 det(M) = 0 Rank(M)= 2 H iu khin c. 5.4- Tnh quan st c ca h thng iu khin gin on. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hthng gilquan st c nutheosliu o c u ray(k)tac th xc nh c trng thi x(k) ca n. y(k) = Cd x(k) y(o) = Cd x(o) y(1) = Cd x(1) = CdAd x(o) ........... y(n-1) = CdA1 nd x(o) Hay:N = [Cd Ad(n) Cd (Ad)(n-1).Cd ]c hng bng n. 5.5. ng dng MatLab - Kim tra tnh iu khin c: >> C0 = Ctrb (A,B) Hoc >> C0 = Ctrb (sys) Kt qu: Rank (C0) = k (hng s) k: l s trng thi iu khin c. - Kim tra tnh quan st c: >> Ob = Obsv (A,C) Hoc >> Sys = ss (A,B,C,D) >> Ob = obsv (Sys) Kt qu: Rank (Ob) = k. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Chng 6 THIT K H THNG IU KHIN 6.1. M u Thitkhthngiukhinbaogmccbcnhbitontnghphthng iu khin, v tun theo mt s nguyn tc thit k sau: Nguyn tc iu khin t ng: Cc h thng iu khin thng tun theo 3 nguyn tc iu khin ch yu sau: 1) Nguyn tc gi n nh Tc l duy tr u ra c nh, theo nguyn tc ny nu cc tc ng bn ngoi c th o c, cn c tnh i tng c xc nh trc th s dng phng php b tcng bn ngoi, nh hnh v nguyn tc ny cn o nhiu v tnh c tr s ca n tc ng vo thit b iu chnh. Trong thit b iu chnh ngoi phn t chuyn i v c cu chp hnh cn c cc thit b o G4 tc ng ti phn t chuyn i G1, to ra lnh cho c cu chp hnh G2. Phng php th 2 ca nguyn tc ny l iu khin theo sai lch (nguyn tc phn hi) c s dng khi tc ng bn ngoi khng o c v c tnh i tng cng khng xc nh c. l h thng phn hi m tn hiu ra C c a v so vi tn hiu vo chun R to nn sai lch E tc ng i vi phn t iu khin. Phng php th 3 gi n nh u ra l hn hp hai phng php trn. G 1G2 G3 G4 URHnh6-1Hnh 6-2 R G 1G 2H U G 3 B C+ - - + R B G 1 Hnh 6-3H U G 2G 3C G 4 E Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.V RTBKc TKTBK1TBK 2) Nguyn tc iu khin chng trnh Tc l nguyn tc iu khin tn hiu ra thay i theo mt chng trnh mong mun no theo thi gian: C = C(t) Tn hiu iu khin ph thuc quy lut thay i theo thi gian ca u ra, ta c th xc lp c quan h . Rt nhiu h iu khin theo nguyn tc ny, v d thay i nhit trong mt l nung, thay i cng nh sng trong phng tu theo gi gic trong ngy, thay i tc , bc tin dao ca mt my tin khi chuyn t ch gia cng th sang gia cng tinh... 3) Nguyn tc thch nghi Hnh 6-4 -Khi cn iu khin nhng i tng phc tp hoc nhiu i tng ng thi, m phi m bo cho mt tn hiu c gi tr cc tr, hoc mt ch tiu ti u no .... -H thng t thch nghi bao gm hai phn ch yu: i tng iu khin Thit b iu khin H thng ny l h thng nhiu vng: mch vng c bn c i tng iu khin v thit b iu khin c bn. Mch vng: H thng iu khin thng thng. L nguyn tc iu khin to ra tn hiu ra (i lng ra) theo s bin i ca tn hiu vo (i lng vo). 6.2. Cc khu ng hc ca h thng iu khin Phm vi ca mn hc cp n cc khu ng hc c bn thng s dng trong ngnh c kh. a. Khu khuch i (P) Hnh 6 -1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.C cu n by hnh 6-1 hot ng nh b khuch i vi h s khuch i Kp. Hoc lc qun tnh v gia tc quan h l F = m.a; in p v dng in quan h l U = R.I ... u l cc khu khuch i, c th gi l cc phn t P. b. Khu qun tnh (P- T1) M hnh tnh ton ca khu qun tnh (P- T1) c dng: T.dtdXa + Xa = K.Xe (6.1) V d xylanh thy lc c pittong mang khi lng m chuyn ng vi vn tc v th phng trnh cn bng lc l:m. dtdv = F - f.v , vi f l h s ma st nht(6.2) Hnh 6-2 a)S v d b) c tnh c) K hiu c. Khu tch phn (I) M hnh ton ca khu tch phn th hin l u ra bng tch phn ca u vo: Xa = KI. }dt t xe) ((6-3) KI l h s khuch i ca khu tch phn. V d 1: Hnh trnh ca pittong - xy lanh tnh theo lu lng vo l S = A1.}dt Q. = KI. }dt Q. (6-4) Vi A l din tch ca pittong v KI l h s khuch i ca khu tch phn. V d 2: B truyn vt me ai c bi c quan h nh sau S = tx. }dt n. (6-5) Nu s vng quay n khng i th S = tx.n.t Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Hnh 6-3 d. Khu vi phn (D) M hnh ton ca khu vi phn th hin u ra t l vi vi phn u vo: xa = KD. dtdXe(6-6) V d: quan h gia dng in v in p qua t in C th hin theo cng thc l Ic = C.dtduc = KD. dtduc(6-7) KD = C l h s khuch i ca khu D Ic: l tn hiu ra Uc: l tn hiu vo Hnh 6-4 e. Khu iu chnh PI

SKKs Xs XIpea+ =) () ( (6-8) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Hnh 6-5 f. Khu iu chnh PD S K Ks Xs XD pea.) () (+ =(6-9) Hnh 6-6 g. Khu iu chnh PID S KSKKs Xs XDIpea.) () (+ + =(6-10) Hnh 6-7 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Chng 7 THIT K H THNG IU KHINTHY LC 7.1. Cc phn t thy lc c bn7.1.1. Van iu khin a. Van trt c mp iu khin dng, trung gian v m Hnh 7-1. S cc loi mp iu khin ca van a- Van c mp iu khin dng (+x0) b- Van c mp iu khin trung gian (x0 = 0) c- Van c mp iu khin m (- x0) d- c tnh l thuyt Q - x(Q-I) Khi x0 > 0 gi l van trt c mp iu khin dng, con trt di chuyn trong vng x0 lu lng vn bng 0 v vng ny c th gi l vng cht. Khi x0 = 0 gi l van trt c mp iu khin trung gian. Khi x0 < 0 gi l van trt c mp iu khin m, ti v tr trung gian ( con trt cha di chuyn) hnh thnh tit din chy v lu lng du qua van. b. Van solenoid Cu to ca van solenoid gm cc b phn chnh (hnh 7-2). Con trt ca van s hot ng hai hoc ba v tr ty theo tc ng ca nam chm. C th gi van solenoid l loi van iu khin c cp. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only. Hnh 7-2: Cu to v k hiu ca van solenoid a- Cu to v k hiu ca van solenoid iu khin trc tip (1,5 - vt hiu chnh v tr ca li st t; 2,4 - l xo; 3,6 - cun dy ca nam chm in) b- Cu to v k hiu ca van solenoid iu khin gin tip ( 1- van s cp; 2- van th cp). c. Van t l Cu to ca van t l nh hnh 7-3 gm: Thn van, con trt, nam chm in. thayititdinchycavan,tclthayihnhtrnhcacontrtbng cch thay i dng in iu khin nam chm. C th iu khin con trt v tr bt k trong phm vi iu chnh nn van t l c th gi l loi van iu khin v cp. Hnh 7-3 d. Van servo Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.* Nguyn l lm vic: Hnh 7-4: S nguyn l ca b phn iu khin con trt ca van servo B phn iu khin con trt ca van servo th hin trn hnh 7-4. Hai nam chm vnh cu t i xng to thnh khung hnh ch nht, phn ng trn c hai cun daayvaf cnh chn du ngm vi phn ng, to nn mt kt cu vng. nh v phn ng v cnh chn du l mt ng n hi, ng ny c tc dng phc hi cm phn ng v cnh chn v v tr trung gian khi dng in vo hai cun dy cn bng.Ni vi cnhchn dulcng n hi,cng nynitrctipvicontrt.Khi dng invo haicun dylchnhauth phn ngb ht lch,dos ixngcacc cc nam chm m phn ng s quay. Khi phn ng quay, ng n hi s bin dng n hi, khe h t cnh chn n ming phun du cng s thay i ( pha ny h ra v pha kia hp li). iu dn n p sut hai pha con trt lch nhau v con trt c dch chuyn. Nh vy:-Khidnginiukhinhaicundybngnhauhocbng0thphnng, cnh, cng v con trt v tr trung gian. - Khi dng i1= i2 th phn ng s quay theo mt chiu no ty thuc vo dng incacundynolnhn.Gisphnngquayngcchiukimngh, cnh chn du cng quay theo lm tit din chy ca ming phun du thay i, khe h ming phun pha tri r