W)fXq:H@8 Vol.7 No.7 485J8 3~VlL)fh~AoNmP9H9Y)f P 6 > ' &Y @ o &f < Robust Tmpratur Control of a Rformr by Using Stabl Continuous-Tim Gnralizd Prdictiv Control Naohio Ishibashi Mingcong Dng and Aira Inou A tmpratur controllr dsign using a stabl continuous-tim anti-windup gnralizd prdictiv control (CAGPC) systm is applid to a rformr of a ful cll systm in this papr. Th controlld procss includs uncrtain tim dlay and input constraints. Th controllr is dsignd by using coprim factorization rprsntation and Youla-ucra paramtrization to b robust to th uncrtain tim dlay and th input constraints. Th ffctivnss of th proposd dsign schm is confirmd by a ral application to th ful cll systm tmpratur control. y Words: stabl continuous-tim prdictiv control anti-windup robustnss rformr ful cll. O8a a Jq;&CO SPLo:NW-i3<8'M l<7gs79f`naz T5lF*j HmQ*hS.OH3QN.On*$FO GNbRA3AE SJPolymr Elctrolyt Ful Cll: PEFCE79F` Na BQ>^lF$. 3AESOGH@GrX?~5;r8.9axG E9?a$j<sJ(M.<r@3HG-. 77$9~VNEr@?aO3*JGN!_ wwhjj$ugob4-*hs$suindji JON!_wN_VO$qG. N?a$lL.L7F$:GO3AJTT9$LPG$t}JI rgjcaj~a9~a9x?~oj~aor V3HG$9~Vo?Er@F$. 33G$~A 9fNH.rBj]D3HBj7?E*hS PEFC NQW-N]R$N?aO~Aob<67? (^9Yr\89YBj*)f7$X?~rBj5; W. ~AoN)fO () EON)f$() EON)fN o`$:lb$~aobgn~ AWm;9OTNJ`@~Vr}A$A(<?N nooo)b. D^j~O)srbC?`@~VW IEEE Intrnational Confrnc on Industrial Tchnology (6 ) ( ) G! n )E)H t 3gX Mitsubishi Havy Industris LTD. Oayama Univrsity Rcivd January 4 8 J m;9h@$9(3hg-. \@8GO$EON~O)sr<$TNJWm; 9P7$Bj3~VlL)fJCAGPC79F `r_w9. C$~AoQ9?a$>h$L9 M!5lF-?$) `@~VNTN5mP9HJ)f O$) ~O)smP9HJ)fONDNj!rH_go ;. sf9_wj!o{srh Youla QiaHj <<7gs rq$$d.nj_wj!rsf9. ()`@~VNTN5mP9HBjJ)fOraa? a$~o)sr57?~a)fop7 3sHm< iobjgj DD<WObBj$9JoA$ BjJ)for_W9. ()D<WC-*$F ~O)smP9HBjJd ~o (sao$icw3shm<i ) HJ?aNr oraa$() Gaa?)fororUC9. \j!go$- ) NTNJ`@~VP9mP9H -P7FO$`@~V`Naw rq$$`@~vntn 5Hawm9r)fONTN5H7$TNJWm;9 P9Bj3~VlL)fN_Wj!rQ$. - ) N~O)sXNmP9H-O$~O)srTNJ s~awgh_j7$3shm<ibjnh-tn5 rbc?d<woomp9hbjg3h hj$() G@?roUC5lroH7Faa. 3) 8) 5) 6) 6). bghdj_j 3AESQ~Ao79F`NJJ$r Fig. (9. ~ Ao (Rformr) O(^r<67?(^X (Rforming CatTR 7877 48 c 8 SICE
W)fXq:H@8 h 7 h 7 f 8 49 )f~o u(t) OD.N)srubNH9. u(t) σ(u (t)) σ(v) umax v umin if v > umax if umin v umax J J3 if v < umin 33G u (t) O~O)sruN.fGj3sH m<inpor(9. Fig. *$F$w OH~OG j$p O)fP]r9. \*O Fig. G T r\89y )f93shm<i C r_w93hg. Fig. Th rformr sub-systm alyst) $6AH7F:GO3AHr!7$GjC AJ~A9 (H Rich Rformd Gas) ~A9. ~A 9O3AES (Ful Cll) NG&wil$@Gw il?u$h&$el~8f~a9fngcq 5l$DC?G9O3Fo (Combustor) G3Fu$H Hb3F5l$SP5l. ~A9H.fNl@:G (CO) r [ppm] J<)f7JlP3AESNEPO Oc<9?a$~A9fNH.OBj7F)f5lF$ JlPJiJ$. ~A9NH.)fGO () EON)fi$() EON)fZj9(FTJ&. C$() NEO N)fGO$3AES~A9r!9O~Aob N~A?~9Y\89YBj7F)f5lF$W j$eo*~aob9yn\89yxnj ~V;LO$3AESNEO~VN;LDJj$ ~*?>z(n~ro3hg-$ewg. hcf$\@8goeon~aon9y)fdjr M!9. 9JoA$~A9O4L3Fo!5lF$ uvrm(. Fig. (9H*j~AobN9Y T r$ )fo C rp7f3a!lhcf)f7$.lol jh9. ~AobN~A?~O[.?~G?a$?~ WJ.LO3FoGN3F.hjEol. 7?C F$C hcf3a!lr)f93hhcf3f. )f5l$~ao9y T r)f93hg-.!3a!lh~ao9yvo!(9h*j$tn J`@~Vr<C? n!ylwm;9h>j9. B[s] }U (s) V (s) J Y (s) { A[s] 33G A[s] B[s] OBjJ?`H9. Y (s) U (s) * hs V (s) Ol>lPO (Fig. fn9y T ) ~O (P<J 3A!L) pr9. Y (s)$u (s) Ol>l y(t) u(t) NiWi9XtG. A[s] B[s] Ol>l n! m!n {s?`g. T OTNJ$NN`@~VG < T T T N<BM T T O{NH9. ^? dg() n HJh& rja. A [s] O `@~VawiI87?`@~V`Gj!aGaa. 33G$-fH7F$A[s] O s N?`r(7 A(s) O s N -}Xtr(9. BjGmP9HJ3sHm<iN_Wj! 3. BjGmP9HJ3sHm<iN4j:` 3. Fig. Th stabl control systm r{nn`@~vnn_jmh 7F!(9 ℓ! Pad awrq$. B [s] J4 A [s] TD ( < T T T ) TD s A [s] ()l sl ()l q sl ql B [s] sl q sl ql (l i)! qi (T )i l (l i)!i! P ) J5 33G T s B[s] T s A[s] B[s]B [s] (A [s]b[s]ts B[s]B [s]) J6 in_jbgo!nh&?(il. B[s]B [s] P (s) N (s) P (s) P (s) J7 sf93shm<io Fig. (9 Youla-ucra Qia Hj<<7gshCF?(il. R(s) (Y (s) Q(s)N (s)) (s) J8 U (s) X(s) Q(s)D(s) J9 V (s) Y (s) Q(s)N (s) J 33G Q(s) RH OBjJU<IPC3sHm<i N_WQia<? Gj I>- (s) O3~V GPC! hcf_w5l. X $Y $N $D$ Q N_WO! ( 3) )
W)fXq:H@8 h 7 h 7 f 5 NH*j?(il. Gi X(s) RH H Y (s) RH r!n Bzout yr~-9h&aa. X(s)N (s) Y (s)d(s) J D. ~O)sr}?J$D<WONBjJC-?` T [s] rja7 RN{srrJ<Nh&ja. 3) ) g F [s] (s) g Y (s) X(s) G (s) J 8 inpoo69lgbj ~O)sP~7?s Ao$sICW3sHm<iWG. \@8GO$ ~O)srTNJs~AWGV-9(F$3Ns~AW GmP9HJ3sHm<iraa. 9JoA$D.N L rq$3hhcfmp9hroraa3hg -. Fig. G(7?s~AOO Fig.3 G(7?OH_J9 3HG-. 33G φ OD.NX8r~-9. 7) 3) 8) 3) 7) 8) 33G g F [s] G [s] L [s]!n E [s] F [s] G [s] H [s] L [s] O8% hcfja. ^? s F [s] E [s] J3 G [s] B[s]B [s]e [s] H [s] J4 3) ) J5 G Q(s) O Q(s) r^`$(9) () N U (s) V (s) * hs$s(s) V (s) U (s) rq$f$!ntyr~-9 h&*v. s B[s]B [s] L [s] H [s] Fig. 3 Th quivalnt diagram of th proposd control systm S(s) (D N S) N < J6 3NroOTBjJD<WOBjHJ.$sj} H7FNilF$. 9JoA$3Nror~?9H-B jj3shm<i S(s) hcf~o)sr}?j$wm; 9OBjHJ. 33G N O (7) GjA5l$D.N r~7 $NjxQ93HG-. ) u φ(u ) u u V U P Y QN (X QD)( A [jω]b[jω] { P o (jω) T (ω) A[jω] P (jω) T (ω)} ω [ ) T (ω) T (ω) ( jωt J Fig.3 G (w u ) i (u y) XN~POVX8 G O if ω if ω > jωt G (s) G (s) G (s) G (s) u w J G (s) (I V U P ) V R < if T π T if ω > π T G (s) (I V U P ) P V R π T ND<WOO (9) Nror~99YFN φ P 7 D.Nror~?93sHm<i S(s) hjmp9hb jhj.. S(s) V (s) U (s) Bj. Fig. π T T ω Tπ π T. G (s) RHg 5B HJ. q q O (5) G?(ilF$. (6) r~9 h& Q r*vh G u u H7 (9) () i $N`@~VmP9HBjJ3sHm<i S(s) V U r_w93hg-. l ~O)sr<&TNJOP9mP9H_W ~O)sNWm;9P7FO$TBjJ3sHm< 3. y G (s) (I V U P ) (V U P I) J7 ql ql s P (s) l s q sl ql ql s ql3 s3 Po (s) l s q sl ql u G (s) (I V U P ) P jωt if ω N (s) N (s) ) D(s) D ( U N ) N (jω) J8 J9 J (z φ(z)) φ(z) z σ(z) 3. M D(s)M U (jω) N (jω) < ω [ ) 4. D(jω) 3)8) M. 33G O5jMPQTsG hcf$anr o (6) C(F$RN 4 DNror~93sHm<i raalph$. 33G$ro O (6) hcf~?5l F$.
W)fXq:H@8 h 7 h 7 f 4. ~AoN9Y)fn3L \8M )f!t )fhv:n )fe_:λ. G.hV:T GghV:T 9 _WQia<?:u. u u n d g.96 s 3 F [s] 7.557s.63 G [s].589 L [s] 7.6356s.979 Q(s).5 Tabl. Strongly stabl controllr dsign paramtrs : T 58.83s 7.49s.63 D<WONC-}x Bj D<WON 3) 88.6885.4746.358 D.N3AESE79F`*~AoNbGrQ$ F \sfj!nb!qrtc?. B[s] J3 33GO`@~V;$?a!Naw (l )$9JoA T T 3.7 TD 3.5 A [s] 3.7s B [s] 3.7s rq$?. n3go n H7 \YJ_WQia<?O Tabl. Tabl. (9LjG. )f'rsf!pe-aa$ C G s.49 @?. D.$() rq$. 7.86s.574 s3 (7?)fo C \sfj!rq7?h-n n3lr Fig.4 *hs Fig.5 (9. Fig.4 O~Ao9Y JFig. * T NW9YQr(7F*j B~OB SMr$@~O\8Mr(7F$. Fig.5 O Fig. * C NPOG3A!Lr(9. \n3*$fob Q!*$FHQ5lF$j!$9JoA$a\89Y ~5;?a$^:$g-5 8[gmin] N9FCW~Or?($\89Yr6(b$M 74 n~5;$n$ 9sc \89Yr 7 nh7fj)fro7?. l}$>h)f!h7f Fig.6 (93Y)f! h8i ronbhgn)flr Fig.7 *hs Fig.8 (9. )foomn`nrtc?. 3NH-N Fig.6 fn)fqia<?o$\8mu? α.4 β.33 fc$s. Q~V T 5[sc] y~v T [sc] η.8. Fig.7 O Fig.4 HM~Ao9Yr (7$Fig.8 O Fig.5 HM3A!Lr(9. >B3*$F )foo8rogb3rtc? Fig.4 GO 745.7 ni)fo^j Fig.7 GO 743. n igj.7 nn9 3N9O\n3B!n3G j btn(^nuvnc$hbng \89 7 np7f.4%gj )flnfsofa7j$. Fig.4$Fig.7 Hb*<P<7<Hr7F$$N} 3O )fo~@go~aobn~ai9yo\89yr 6(F$$~A(^O.FLr-7F:95lF $J$?a x$~a?~j[.?~tolf*i:9 Y:3?aG. 77 Fig.4 GO Fig.7 fs7 F*<P<7<H.5$s 7sc Gj7F$N P7F$Fig.7 GOs 3sc Gj7F$3Hi$\ sfj!hji>-~7f*j$\sfj!-zg 3H(5l. 3) I 5. gc F 7.83s.574 X(s) 5 D.988.78j.988.78j A[s] 5.9s Fig. Tabl. CGPC dsign paramtrs : w : Ny 6 CGPC 8 Y (s) s.49 s3 58.83s 35.5s 58.83s 7.49s.63 3.7s N (s) 58.83s 7.49s.63 D(s) hcf$)f'o (9) () hj!hj. g F [s] Q(s)D(s) U (s) X(s) Q(s)D(s) 7.86s.574 s3 58.83s 35.5s.5 58.83s 7.49s.63 G [s] Q(s)N (s) V (s)y (s) Q(s)N (s) s.49 3.7s.5 s3 58.83s 7.49s.63 @ `@~VTN5*hS~O)BNDNC-r-9 3AESE79F`*~AoN9Yj)fBj CAGPC 79F`NQrTC?. ~O)s*hSTNJ `@~VNro<G {srh Youla-ucra Qia Hj<<7gshCF3sHm<ir_W7?. NL sfj!n-z-rb!n3rl8fn'g-?. M 8 % H. Dmircioglu Constraind continuous-tim gnralizd prdictiv control IEE Proc. Control Thory and Appl. 46-5 47475 999. M. Cannon and B. ouvaritais Infinit horizon prdictiv control of constraind continuous-tim linar systms Automatica 36-7 943955. 3 M. Dng A. Inou A. Yanou and Y. Hirashima Continuous-tim anti-windup gnralizd prdictiv control of non-minimum phas procsss with input constraints Proc. of IEEE CDC 3 4457446 3. 4 Dng 35-7 8586 df \ TN5rbDWm;9OP9c ~)fo_w W)fXq@88
5 W)fXq:H@8 h 7 h 7 f 8 999. 5 B. ouvaritais J. A. Rossitr and A. O. T. Chang Stabl gnralizd prdictiv control: an algorithm with guarantd stability IEE Proc. Control Thory and Appl. 39-4 34936 99. 6 M. V. othar P. J. Campo M. Morari and C. N. Ntt A unifid framwor for th study of anti-windup dsigns Automatica 3-869883 994. 7 P. J. Campo M. Morari and C. N. Ntt Multivariabl anti-windup and bumplss transfr: A gnral thory Proc. of ACC 989 767 989. 8 Youla 3-9 3954. 9 4-4 33333 3. Youla Paramtrization GPC 8 SICE 45 999. M. Dng A. Inou. Tata and Y. Hirashima Continuous-tim anti-windup gnralizd prdictiv control of uncrtain procsss with input constraints and tim dlays Proc. of th 43rd IEEE Confrnc on Dcision and Control (CDC) 553558 4 H. Dmircioglu and P. J. Gawthrop Continuous-tim gnralizd prdictiv control(cgpc) Automatica 7 5574 99. 3. Fig. 4 Tmpratur chang at T by CAGPC YD ) QiaHj<$7gspEbGI>?sAo$sICW)fON>\_W 79F`)fp sxq@8o 3\$gh Wm;9)fN_$an$$h WH)f p< Y f }D?h {srrq$? h3~v NH% h s fqytxqviq@88 Fig. 5 Control input by CAGPC -f G8?Wu)f79F`NpCH~Q )H;Q R Nx T R po P 6 > 'J5qw 989 gx)xt4h. 99 gx )X&fJX!)Xl6$N]x$;. )E)H ;Q\t~R$_j. 5 i3gxgx!3jx&fjnn]x_ Xf. gh7f)f79f`n$wm;9) fn&f>v. Fig. 6 Control Systm of Two-dgr frdom Control H Fig. 7 Tmpratur chang at T by Two dgr frdom control f Fig. 8 Control input by Two dgr frdom control @ oj5qw 997 '\gxgx!nn]x$;. '\ gxuj$ $.j9 Extr gx Rsarch Associat$ n NTT 3_<7g sjxpc&fjj5<a7($h$ n3gx)xt\. _gx!3j X&fJZ5x. 79F`)f$NcGGJIN &f>v. nnjxq. <J5qw 968 ~TgXgX!$N]x$;. ~TgX uj$j@ Albrta gx Rsarch Fllow$' \gxu5x$5x$987 5xH7F3gX )Xt\. _gx!3jx&fj5x. )f${sr$ncggjin&f>v. SICE Fllow. )XnN.