Robust Temperature Control of a Reformer by Using Stable Continuous-Time Generalized Predictive Control

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1 Vol.7 No.7 485J8 3~VlL)fh~AoNmP9H9Y)f P 6 > ' 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 c 8 SICE

2 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) )

3 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$.

4 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] s.979 Q(s).5 Tabl. Strongly stabl controllr dsign paramtrs : T 58.83s 7.49s.63 D<WONC-}x Bj D<WON 3) 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 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*$F )foo8rogb3rtc? Fig.4 GO ni)fo^j Fig.7 GO 743. n igj.7 nn9 3N9O\n3B!n3G j btn(^nuvnc$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$\sfj!-zg 3H(5l. 3) I 5. gc F 7.83s.574 X(s) 5 D j j A[s] 5.9s Fig. Tabl. CGPC dsign paramtrs : w : Ny 6 CGPC 8 Y (s) s.49 s s 35.5s 58.83s 7.49s s N (s) 58.83s 7.49s.63 D(s) hcf$)f'o (9) () hj!hj. g F [s] Q(s)D(s) U (s) X(s) Q(s)D(s) 7.86s.574 s s 35.5s s 7.49s.63 G [s] Q(s)N (s) V (s)y (s) Q(s)N (s) s s.5 s s `@~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 M. Cannon and B. ouvaritais Infinit horizon prdictiv control of constraind continuous-tim linar systms Automatica 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 Dng 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.

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.

$sAo$sICW)fON>\_W 79F`)fp sxq@8o 3\$gh Wm;9)fN_$an$$h WH)f p< Y f }D?h {srrq$? h3~v NH% h s fqytxqviq@88 Fig. 5 Control input by CAGPC -f G8?Wu)f79F`NpCH~Q )H;Q R Nx T R po P 6 > 'J5qw 989 gx)xt4h.$

5 5 h 7 h 7 f 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 M. V. othar P. J. Campo M. Morari and C. N. Ntt A unifid framwor for th study of anti-windup dsigns Automatica P. J. Campo M. Morari and C. N. Ntt Multivariabl anti-windup and bumplss transfr: A gnral thory Proc. of ACC Youla Youla Paramtrization GPC 8 SICE 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) H. Dmircioglu and P. J. Gawthrop Continuous-tim gnralizd prdictiv control(cgpc) Automatica 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$wm;9) fn&f>v. Fig. 6 Control Systm of Two-dgr frdom Control H Fig. 7 Tmpratur chang at T by Two dgr frdom control f Fig. 8 Control input by Two dgr frdom oj5qw 997 '\gxgx!nn]x$;. '\ 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.

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[1, 2, 3, 4, 5, 6, 7, 8] 208 5 [, 2, 3, 4, 5, 6, 7, 8] 2 () ϕ = λ θ () ϕ [W/m 2 ] θ [K] λ [W/(m K)] Schmatic rprsantation of Fourir s law (2) ρc θ = ϕ + f (2) ρ [kg/m 3 ] c [J/(kg K)] θ = t f [W/m3 ] () (2) (3) ρc θ = (λ θ) +