EFFECTIVE DECENTRALIZED TITO PROCESS IDENTIFICATION FROM CLOSED-LOOP STEP RESPONSES

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1 54 Aian Journal of Conrol, Vol. 7, No., pp. 54-6, Jun 5 EFFECIVE DECENRALIZED IO PROCESS IDENIFICAION FROM CLOSED-LOOP SEP RESPONSES Shao-Yuan Li, Wn-Jian Cai, Hua Mi, and Qiang Xiong ABSRAC In hi papr, a nw idnificaion mhod prformd in h im domain bad on h dcnralizd p- i propod for wo inpu and wo oupu (IO) proc wih ignifican inracion. In rm of paramr idnificaion, h coupld clod-loop IO ym i dcoupld o obain four individual ingl opn-loop ym wih h am inpu ignal. A in h SISO ca, nw linar rgrion quaion ar drivd, from which h paramr of a fir- or cond-ordr plu dad-im modl can b obaind dircly. h propod mhod ouprform h xiing imaion mhod for mulivariabl conrol ym ha u p- rpon. Furhrmor, h mhod i robu in h prnc of high lvl of maurmn noi. Simulaion xampl ar givn o how boh ffcivn and pracicaliy of h idnificaion mhod for a wid rang of mulivariabl proc. h ufuln of h idnifid mhod in mulivariabl proc modling and conrollr dign i dmonrad. KyWord: Idnificaion, wo inpu and wo oupu (IO) proc, p, la quar. I. INRODUCION Sym idnificaion ha bn an aciv ara of rarch on auomaic conrol for a fw dcad, and i ha rong link wih ohr ara of nginring, including advancd conrol ragy, opimizaion, and ignal procing [-4]. A conidrabl numbr of idnificaion mhod hav bn rpord in h liraur. ranfr funcion migh b h wlcom paramric modl. In indurial proc, conrol paramr ar ofn o nominal valu or manually und in an ad hoc mannr [5]. h raon i ha ool for ymaically uning indurial conrollr ar lacking. Poorly und conrol loop rprn a gra conomic co for indury; hu, runing of unaifacory conrollr i ofn ncary. For mulivariabl proc, Manucrip rcivd July 3, 3; rvid Novmbr 7, 3; accpd July, 4. Shao-Yuan Li and Hua Mi ar wih Iniu of Auomaion, Shanghai Jiao ong Univriy, Shanghai 3 (mail: yli@ju.du.cn). Wn-Jian Cai and Qiang Xiong ar wih School of Elcrical and Elcronic Enginring, Nanyang chnological Univriy, Singapor mo conrol chm, uch a h invr Nyqui array or characriic locu mhod [6-8], rquir a full modl of h proc in h form of a ranfr-funcion marix or a frquncy-rpon marix ovr h nir working frquncy rang. In many ca, uch a modl i no availabl, and phyical modling may rquir a prohibiiv nginring ffor. hrfor, pracical and ffciv on-lin imaion of h full proc modl i appaling. hr ar wo way o idnify a mulivariabl proc for conrol applicaion: opn-loop and clod-loop approach. Opn-loop mhod can b viwd a xnion of ho applid in SISO ym. hrfor, om imdomain mhod can b adopd for mulivariabl proc idnificaion [9-]. Compard wih h opn-loop, h clod-loop cau l prurbaion o h proc. A majoriy of h xiing chniqu for clod-loop proc idnificaion ar prformd in h frquncy domain, whil h frquncy rang of inr for uch applicaion uually rang from zro up o h proc criical frquncy [3,4]. In pracical proc conrol, h clod- loop rlay fdback provid vral inring advanag [5-8], uch a robun, ffcivn in daling wih rong nonlinar ym, and h a of combining i wih auo-uning conrol mhod [9,]. Dpi h advan-

2 Shao-Yuan Li al.: Effciv Dcnralizd IO Proc Idnificaion from Clod-Loop Sp Rpon 55 ag, howvr, i i im conuming for h clod-loop rlay fdback o achiv abl ocillaion, which i ncary o obain corrc rul. h p i anohr commonly ud mhod. I main advanag i ha h ing procdur i impl and rquir lil prior knowldg, which mak i popular for proc conrol applicaion. During h pa dcad, hr ha bn rong inr in u of h p chniqu o drmin h dynamic of unknown proc. For an opn-loop conrol ym, a impl y robu idnificaion mhod for a linar monoonic proc bad on h p wa propod by Bi and Cai al. in []. A fir-ordr plu dad-im modl wa adopd and applid o a haing, vnilaion, and air-condiioning (HVAC) ym in [], whr h obaind ym modl wr ud for conrollr auo-uning. Exprimnal rul dmonrad h ffcivn of h idnificaion mhod. Wang and Clu [3] prnd an idnificaion algorihm for proc opraing in clod-loop mod, whr wo Lagurr modl ar adopd for fiing dircly o h conrol ignal and h proc oupu ignal gnrad by man of a p chang in h poin. Wang al. propod om robu idnificaion mhod for linar im-dlay proc bad on p rpon in h im domain [4] and in h frquncy domain [5], rpcivly. In [4], Wang al. conidrd an idnificaion mhod bad on p for SISO opn-loop proc and hn qunially applid i o om wo-inpu and wo-oupu (IO) proc. h ruling fir-ordr plu dad-im modl wa ud for dcouplr dign and PID qunial uning. In [5], Wang al. xplaind h rlaionhip bwn h rgrion paramr and ho in h proc, and analyzd h robun of h idnificaion mhod in dail. Finally PID conrollr auo-uning mhod bad on h obaind modl wr conidrd. o our knowldg, h abov nir idnificaion algorihm ha only bn conidrd for SISO ym; MIMO ym idnificaion uing h p i an opn problm. In hi papr, an nginring orind on-lin idnificaion chniqu for IO proc i propod. I xnd h SISO idnificaion mhod in [] o IO ym. h propod mhod only rquir p rpon daa of h clod-loop proc, and no prior knowldg of h proc dynamic or conrollr dynamic i rquird. hi papr i organizd a follow: Scion prn h formulaion of dcnralizd IO idnificaion ym. Scion 3 inroduc an idnificaion algorihm, which i imilar o ha propod in [4] and [6]. h procdur of h propod algorihm propod in hi papr ar givn in cion 4, and imulaion xampl ar prnd in cion 5. II. DECENRALIZED IO IDENIFICAION SYSEMS Conidr a IO proc undr dcnralizd conrol a hown in Fig., whr r, r ar poin,, ar rror, u and u ar oupu of conrollr K, K, and G ; i, j =, ar ranfr funcion, and y, y ar proc oupu, rpcivly. For IO clod-loop conrol ym, h fundamnal rlaionhip bwn h conrollr oupu ignal and ranfr funcion oupu for h proc i xprd a y = Gu, whr y y =, y u u =, u G G G =. G G Aum ha h proc i iniially a r a a ady a wih iniial poin, r, r, y, y, u and u o idnify h proc paramr; h p involv h following wo p:. A p chang of r i mad from r o r whil r i kp unchangd. h conrollr oupu and proc oupu ignal for h wo loop ar rcordd unil h nw ady a i rachd a = > ( Fig. ). i h maximum ling im for all h ranfr funcion, which can b obrvd from h ym rpon. h incrmnal quaion from h iniial a o h nw a bcom Δ y = G Δ u G Δ u, (a) Δ y = G Δ u G Δ u, (b) whr, Δ u = u u and Δ u = u u.. A p chang of r i mad from r o r, whil r i kp unchangd,.g., r = r. h conrollr oupu and r r K Conrollr Conrollr K u u G G G G Fig.. Clod-loop IO conrol ym y y

3 56 Aian Journal of Conrol, Vol. 7, No., Jun 5 G G G G Δ Δ Δ Δ () Δ u Δ u Δ u Δ u Δ Δ Δ Δ () Δ u Δ u Δ u Δ u Δ Δ Δ Δ () Δ u Δ u Δ u Δ u ΔyΔu ΔyΔu Y () Δ u Δ u Δ u Δ u y u y u Y () y u y u Y (). y u y u Y () () (3) For paramr idnificaion, h coupld clod-loop IO ym i xplicily dcoupld o obain four individual opn-loop ym wih h am inpu ignal acing on h four ranfr funcion a hown in Fig. 3. G Y( ) G Y( ) Fig.. Sling im for paramr idnificaion. G Y( ) proc oupu for h wo loop ar rcordd unil h nw ady a i rachd a = >. Again, h incrmnal quaion from a () o h nw a can b wrin a Δ y = G Δ u G Δ u, (a) Δ y = G Δ u G Δ u. (b) whr Δ u = u u( ) and Δ u = u u( ). u( ) and u( ) ar conrollr ady oupu of h fir p a wll a h iniial valu of h cond p. hn, w can combin (a), (b), (a), and (b) o obain h marix form Y = AX, whr G Δy Δu Δu Δy, Δu Δu G, and Δy Δu Δu G Δy Δu Δu G Y A X. A hr i alway a -poin chang for ach, i.., A i noningular, h marix G() ar drmind by X = A Y, which rul in G Fig. 3. Dcnralizd idnificaion proc Conqunly, h problm of idnificaion for h coupld clod-loop IO ym i ranformd ino idnificaion for four opn-loop SISO ym. h rlaionhip bwn h original ym inpu/oupu and h dcnralizd idnificaion ym i a follow: h ym inpu u for all four loop i u()* u() u ()* u() u() = L [ Δu () Δu ( ) Δu () Δ u ()] =Δ Δ Δ Δ. (4) For all of h ranfr funcion inpu givn in (4), h oupu ignal for h quivaln idnificaion ym ar = Δ Δ Δ Δ y()* u() y()* u() y () L [ y () u ( ) y ( ) u ( )] =Δ Δ Δ Δ, (5a) = Δ Δ Δ Δ y()* u() y()* u() y () L [ y ( ) u () y () u ()] =Δ Δ Δ Δ, (5b) = Δ Δ Δ Δ y () L [ y ( ) u ( ) y ( ) u ( )] =Δy ()* Δu () Δy ()* Δ u (), (5c) Y( )

4 Shao-Yuan Li al.: Effciv Dcnralizd IO Proc Idnificaion from Clod-Loop Sp Rpon 57 = Δ Δ Δ Δ y()* u() y()* u() y () L [ y () u () y ( ) u ()] =Δ Δ Δ Δ, (5d) whr * i an opraor of a convoluion ingral. Rmark. During ing, a p chang for ach poin i prformd qunially a hown in Fig., whr i dfind a h maximum im rquird for all oupu o l a ady a undr h wo. Rmark. If incrmnal ignal ar ud, hn zro iniial condiion for h quivaln dcnralizd idnificaion ym will b guarand; ha i, u = y =,, for i, j =,, rgardl of h valu of h iniial ady a rror. Rmark 3. According o h dfiniion of convoluion, h convolving ignal dnod a u and u mu b aboluly ingrabl or priodic. hu, whn compuing Eq. (4)-(5), w nd o fir dcompo Δu j i and Δy j i ino hir ady a par and ranin par, and hn convolv hm paraly. Hr, w will how wih Eq. (4) blow ha h compuaion i imilar o ha for Eq. (5). L h ady a j j j par of Δ u i b Δ u SSi, and l h ranin par b δ u i ; hn, Eq. (4) bcom uss u uss u SS SS SS SS SS () uss u() u()* u() [ uss uss uss u ( ) uss u u u u () =Δu()* Δu() Δu()* Δ u() = ( Δ δ ( ))*( Δ δ ( )) ( Δ u δu ( ))*( Δ u δ u ( )) =Δu Δ u Δu δ u Δ δ δ δ Δ Δ Δ δ Δ δ () δ ()* δ ()]. III. PROCESS IDENIFICAION ALGORIHM IN HE IME DOMAIN Aum ha h proc i abl undr clod-loop proporional conrol; h forward ranfr funcion can b rprnd by n n b b bn n n n a a an L G (), i, j =,. (6) For zro iniial condiion, Eq. (6) can b wrin quivalnly in h im domain a ( n) ( n ) n y () a y () a y () ( n ) ( n ) n = b u ( L ) b u ( L ) b u( L ). Dfin (7) ( m) τm τ f () f( τ) dτ dτ [, ] m m max(, ) (8) for an ingr m ; Eq. (7) can b olvd by ingraing n im: () () () () () [, ] [, ] ( n ) ( n) a ( n ) y () an y () [, ] [, ] () () = b u( L ) b u( L ) [, ] [, ] ( n ) ( n) b ( n ) u L bn u L [, ] [, ] y a y a y ( ) ( ). (9) Uing fir-ordr aylor xpanion for h im dlay, i.., L L, Eq. (9) bcom () () () () () [, ] [, ] ( n ) ( n) ( n ) n [, ] [, ] () () = b u() b u() [, ] [, ] ( n ) ( n) b( n ) u() bn u() [, ] [, ] y a y a y a y () a y () () () () [, ] ( n ) ( n ) ( n ) n [,] [,] Lb u Lb u L b u() L b u(). () I i wll known in proc conrol ha - or nd-ordr plu im dlay modl ar nough o approxima mo proc. hu, h formulaion for n = and n = ar a follow.. Whn n =, Eq. () bcom y () = a y () τ dτ b u( τ) dτ L b u(), () which can b wrin in h compac form γ () = [ φ ()] θ, () whr γ () = y () φ () = y () τ dτ u() τ dτ u(). (3) θ = a b Lb

5 58 Aian Journal of Conrol, Vol. 7, No., Jun 5. Whn n =, Eq. () bcom τ y () = a y ( τ) dτ a y ( τ) dτ dτ τ ( ) ( ) b u τ dτ b u τ dτ dτ L b u() L b u( τ) dτ which can b alo xprd a whr () [ ()], (4) γ = φ θ, (5) IV. IDENIFICAION PROCEDURES AND ALGORIHM h propod idnificaion algorihm and om implmnaion iu ar ummarizd a follow: Iniializaion: Bfor h ar conducd, h proc hould b und o obain ady a. Sp : Prform h qunial -poin changing xprimn a xplaind in cion and rcord h conrollr oupu u j i and proc j oupu y i (i, j =, ) during ach xprimn. Sp : Form h quivaln inpu u wih Eq. (4) and h oupu y wih Eq. (5). γ () = y () τ τ φ () = y () τ d τ y( τ ) d τ d τ u() τ d τ u( τ ) d τ d τ u() u() τ d τ (6) θ = [ a a b b Lb Lb )] Equaion () and (5) can b olvd uing h La Squar mhod for i, j =, and k =,, o obain h rgrion form Γ = ΨΘ, (7) k k whr Γ = [ γ ( ), γ ( ), γ ( ) ], Ψ = [ φ ( ), φ ( ), φ ( )]. h LS ima for Θ i N Θ Ψ Ψ Ψ Γ. (8) = ( ) Onc Θ ar found from Eq. (8), a, b, and L can b rcovrd from a θ b = θ3 L θ / θ 3 k N (9) for n =, and a, a, b, b, and L can b rcovrd from a θ a θ b = θ 3 b θ 4 L θ5 / θ3 for n =. () Sp 3: U h La Squar formula (8) o calcula Θ i, j =,. Sp 4: Eima ach modl paramr uing (9) for n = or () for n =. Rmark 4. From Eq. (), i can b n ha h fir ampl u ( ) [ u( ) u( )] and u ( ) [ u( ) u( )] hould no b akn unil max (L ), whn h oupu dvia from h prviou ady a, o h low limid max (L ) hould b imad o achiv br modling accuracy. h lining priod mhod can b adopd a in [7]. h iniial par of h p rpon conain mor xniv high frquncy informaion, whil h par of h rpon following h ady a par conain only zro frquncy informaion, i.., a ω =. Exniv imulaion rul ugg ha N can b o. ~.5max ( ) for i, j =,, whr i h ling im, which i dfind a h im rquird for h proc o l wihin ±% of i ady a. h compuaional ffor bcom havy if oo many ampl ar akn ino conidraion, inc hi will lad o a larg Ψ. Morovr, Ψ Ψ may bcom illcondiiond for a vry larg N, and hi may cau h compuaional difficuly of imaing Θ o incra. hrfor, h iz of N ha o b limid. h dfaul valu of N i rcommndd o b, and i may b a i i = ( N ), i =,,, N. N Rmark 5. In gnral, h ordr of h proc i unknown. For mo idnificaion chm, a mhod wih a known ordr i aumd [7]. Hr, w alo adop uch a ragy, and h -ordr plu dad-im modl (FOPD) or nd-

6 Shao-Yuan Li al.: Effciv Dcnralizd IO Proc Idnificaion from Clod-Loop Sp Rpon 59 ordr plu dad-im (SOPD) modl i pr-pcifid a in many prviou udi [3,-6,8,9]. Whhr h FOPD or SOPD modl i ud i drmind by h man quar rror (MSE) bwn h acual oupu and ha bwn h imad on. W rcommnd uing low-ordr modl fir. If MSE i oo larg, h modl ordr will incra, and a highr-ordr modl will b imad wih h gnral idnificaion mhod [9]. Rmark 6. A h inpu u() in our idnificaion chm i no h p, ( m ) m u ( L) = ( L) do no hold a in h [, ] m! SISO ca udid in [4]. hu, w u h fir-ordr aylor xpandr for h dad-im im, i.., L, o L rduc h compuaional burdn, which may rul in dcrad accuracy for paramr L. o obain br idnificaion accuracy, on can u h highr-ordr aylor xpandr or apply h frquncy domain idnificaion approach o Eq. (8). V. SIMULAION EXAMPLES In hi cion, w will how h ffcivn of h propod approach by man of imulaion. In ordr o illura i ffcivn clarly, a cririon in frquncy domain i givn, which i dfind a: Gˆ ( jω ) G ( jω ) E = max %, (3) ω [, ωc ] G( jω) whr G(jω) and Ĝ(jω) ar h acual and imad proc frquncy rpon, rpcivly, and G ( jω c ) = π. h noi lvl i maurd wih h noi-o-ignal raio, dfind a man(ab( noi)) NSR =. (4) man(ab( ignal)) Exampl. Conidr h wll-known Wood and Brry [4] binary diillaion column plan: G () = 7 3 I i a ypical IO plan wih rong inracion and ignifican im dlay. According o h propod ing mhod, w und h dcnralizd PID conrollr and obaind h p- ignal hown in Fig. 4. In abl, boh FOPD and SOPD imad mod- abl. Idnificaion rul obaind undr diffrn noi lvl for Exampl. Noi Ĝ() E (%) Lvl Fir ordr Scond ordr Fir ordr Scond ordr % % %.799 G() G ( ) = G( ) = G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G() G()

7 6 Aian Journal of Conrol, Vol. 7, No., Jun 5 abl. Idnificaion rul for Exampl u r u u r u Noi Lvl G ˆ () E (%) %.5 G() G() G() G() y y y y Fig. 4. Squnial p prformd on h dcnralizd IO ym G 5 5 G Fig. 5. Eimad frquncy rpon for Exampl a % NSR. l undr diffrn noi lvl ar givn. Figur 5 how Nyqui plo a % NSR, whr h olid curv i a plo of h acual proc, h dahd curv i a plo of h imad FOPD modl, and h curv i a plo of h imad SOPD modl. Exampl. hi xampl i adopd from Palmor al. [6]:.5 (. ) (. ) (. )(. ) G () =..4 (. )(. ) (. )(. ) (.5 ) Larg inracion xi in hi fourh-ordr proc. h idnificaion modl obaind wih h wo mhod a % NSR ar givn in abl, and hir Nyqui plo ar 5 5 G G G G Fig. 6. Eimad frquncy rpon for Exampl a % NSR. hown in Fig. 6. In ordr o dmonra h advanag of h mhod propod in hi papr, w compar rul obaind wih h propod mhod wih ho obaind wih anohr mhod bad on a rlay fdback [3] in Fig. 6 (olid curv: acual proc; dahd curv: imad frquncy rpon obaind wih h propod mhod; : imad frquncy rpon bad on h rlay fdback ). h imulaion rul how ha h propod idnificaion mhod i pracical and can achiv good accuracy, vn in a noiy nvironmn. h idnifid modl can b ud o run an xiing IO conrol ym on dign advancd conrollr for IO proc. VI. CONCLUSIONS In hi papr, an on-lin idnificaion mhod for IO proc ha bn prnd. h propod mhod rquir no prior knowldg of h proc and can b prformd coninuouly hroughou a, vn if i i diurbd omwha from h nominal poin. h ranfr funcion marix wih cond-ordr plu dlay modl lmn can alo b obaind dircly by man of p-. h compuaion ar impl and can b aily implmnd. h ignificanc of h work i ha i rlax mo of h rricion of xiing mulivariabl proc idnificaion mhod: () i i valid for clod-loop ; () G G

8 Shao-Yuan Li al.: Effciv Dcnralizd IO Proc Idnificaion from Clod-Loop Sp Rpon 6 mulivariabl ym can b dcoupld o obain ingl opn-loop ym wih h am inpu ignal acing on h mulipl ranfr funcion; (3) i can idnify boh clo-coupld and wak-coupld proc. Variou proc hav bn mployd o dmonra h ffcivn and pracicabiliy of h mhod. ACKNOWLEDGEMENS hi work wa uppord by h Naional Naur Scinc Foundaion of China (Gran: 64745), h Spcializd Rarch Fund for h Docoral Program of Highr Educaion of China (Gran: 488) and h an Chin uan Exchang Foundaion of NU. h auhor ar graful o h anonymou rviwr for hir valuabl rcommndaion. REFERENCES. Friman, M. and V.W. Kur, A wo-channl Rlay for Auouning, Ind. Eng. Chm. R., Vol. 36, No. 7. pp (997).. Haykin, S., An Inroducion o Analog & Digial Communicaion, John Wily & Son, NY, U.S.A. (989). 3. Palmor, Z.J., Y. Halvi, and N. Krany, Auomaic uning of Dcnralizd PID Conrollr for IO Proc, Proc. h IFAC World Congr., Sydny, pp (993). 4. Poulin, E., A. Pomrlau, A. Dbin, and D. Hodouin, Dvlopmn and Evaluaion of an Auo-uning and Adapiv PID Conrollr, Auomaica, Vol. 3, No., pp. 7-8 (996). 5. Wang L., and W.R. Clu, Sym Idnificaion Bad on Clod-Loop Sp Rpon Daa, IEE Proc.-D, Vol. 4, No., pp. 7- (994). 6. Arom, K.J. and. Hagglund, Auomaic uning of Simpl Rgulaor wih Spcificaion on Pha and Ampliud Margin, Auomaica, Vol., No. 5, pp (984). 7. Arom, K.J. and. Hagglund, Auomaic uning of PID Conrollr, Inrumn Sociy of Amrica, Rarch riangl Park, NC, U.S.A. (988). 8. Arom, K.J. and. Hagglund, PID Conrollr: hory, Dign, and uning, nd Ed., Inrumn Sociy of Amrica, Rarch riangl Park, NC, U.S.A. (995). 9. Choi, J.Y., J. L, J.H. Jung, M. L, al., Squnial Loop Cloing Idnificaion of Mulivariabl Proc Modl, Comp. Chm. Eng., Vol. 4, pp ().. Johanon, L. and H., Koivo, Invr Nyqui Array chniqu in h Dign of a Mulivariabl Conrollr for a Solid-Ful Boilr, In. J. Conr., Vol. 4, pp (984).. Macowki, J.M., Mulivariabl Fdback Dign, Addion-Wly, Workingham, U.K. (989).. Zhu, Y.C., and F. Buoyi, Ca Sudi on Clod- Loop Idnificaion for MPC, Conr. Eng. Prac., Vol., pp (). 3. Wang, Q.G. and Y. Zhang, A Fa Algorihm for Rducd-Ordr Modling, ISA ran., Vol. 38, pp. 5-3 (999). 4. Wang, Y.G., W.J. Cai, and M. G, Dcnralizd Rlay-Bad Mulivariabl Proc Idnificaion in h Frquncy Domain, IEEE ran. Auoma. Con., Vol. 48, No. 5, pp (3). 5. Hang, C.C., K.J. Arom, and W.K. Ho, Rlay Auo-uning in h Prnc of Saic Load Diurbanc, Auomaica, Vol. 9, pp (993). 6. Lva, A., PID Auouning Algorihm Bad on Rlay Fdback, IEE Proc.-D, Vol. 4, No. 5, pp (993). 7. Loh, A.P., C.C. Hang, C.K. Quk, and V.U. Vanani, Auouning of Muliloop Proporional-Ingral Conrollr uing Rlay Fdback, Ind. Eng. Chm. R., Vol. 3, pp. -7 (993). 8. Loh, A.P. and V.U. Vanani, Ncary Condiion for Limi Cycl in Muliloop Rlay Sym, IEE Proc.-D, Vol. 4, No. 3, pp (994). 9. Huang, H.P., Auo-uning for Modl-Bad PID Conrollr, AIChE J., Vol. 4, No., pp (996).. Wang, Q.G., C.C. Hang, and Q. Bi, Proc Frquncy Rpon Eimaion from Rlay Fdback, Conr. Eng. Prac., Vol. 5, No. 9, pp (997b).. Bi, Q., W.J. Cai, E.L. L, Q.G. Wang, al., Robu Idnificaion for Fir-Ordr Plu Dad-im Modl from Sp Rpon, Conr. Eng. Prac., Vol. 7, pp (999).. Bi, Q., W.J. Cai, Q.G. Wang, C.C. Hang, al., Advancd Conrollr Auo-uning and I Applicaion in HVAC Sym, Conr. Eng. Prac., Vol. 8, No. 6, pp (). 3. Wang, Q.G., B. Zao,.H. L, and Q. Bi, Auo-uning of Mulivariabl PID Conrollr from Dcnralizd Rlay Fdback, Auomaica, Vol. 33, No. 3, pp (997a). 4. Wang, Q.G., and Y. Zhang, Robu Idnificaion of Coninuou Sym wih Dad-im from Sp Rpon, Auomaica, Vol. 37, pp (a). 5. Wang, Q.G., Y. Zhang, and X. Guo Robu Clod-Loop Idnificaion wih Applicaion o Auo- uning, J. Proc. Conr., Vol., pp (b). 6. Wang, Q.G., X. Guo, and Y. Zhang, Dirc Idnifi- Caion of Coninuou im Dlay Sym from Sp Rpon, J. Proc. Conr., Vol., pp (c). 7. Luybn, W.L., Proc Modling, Simulaion and

9 6 Aian Journal of Conrol, Vol. 7, No., Jun 5 Conrol for Chmical Enginr, McGraw-Hill, NY, U.S.A. (99). 8. Wang, Q.G., B. Huang, and X. Guo, Auo-uning of IO Dcoupling Conrollr from Sp, ISA ran., Vol. 39, pp (). 9. Wang, Y.G., and H.H. Shao, PID Auounr Bad on Gain and Pha Margin Spcificaion, Ind. Eng. Chm. R., Vol. 38, No. 8, pp (999). 3. Young, P.C., An Inrumnal Variabl Mhod for Ral im Idnificaion of a Noiy Proc, Auomaica, Vol. 6, pp (97). 3. an, K.K.,.H. L, and Q.G. Wang, Enhancd Auomaic uning Procdur for Proc Conrol of PI/PID Conrollr, AIChE J., Vol. 4, No. 9, pp (996). Shaoyuan Li wa born in 965. H rcivd hi B.S. and M.S. dgr from Hbi Univriy of chnology in 987 and 99, rpcivly. H rcivd hi Ph.D. dgr from h Dparmn of Compur and Sym Scinc of Nankai Univriy in 997. Now, h i a profor a h Iniu of Auomaion, Shanghai Jiao ong Univriy. Hi rarch inr includ fuzzy ym and nonlinar ym conrol. Wnjian Cai wa born in 957. H rcivd hi B.S. and M.S. dgr from Harbin Iniu of chnology in 98 and 983, rpcivly. H rcivd hi Ph.D. dgr in Sym Enginring from Oakland Univriy, USA, in 99. Now, h i an aocia profor in h School of Elcrical & Elcrical Enginring, Nanyang chnological Univriy, Singapor. Hi rarch inr includ advancd proc conrol, fuzzy logic conrol, robu conrol, and imaion chniqu. Hua Mi wa born in 977. H rcivd hi B.S. and M.S. dgr from Norh China Elcric Powr Univriy in 999 and, rpcivly. H i now a Ph.D. candida a Shanghai Jiao ong Univriy. Hi rarch inr ar ym idnificaion and fuzzy ym. Qiang Xiong rcivd hi B.Eng. dgr in Indurial Auomaion in 986 from Huazhong Univriy of Scinc and chnology and hi M.Eng. dgr in Auomaic Conrol hory and Applicaion in 99 from h Univriy of Scinc and chnology, Bing, h Popl Rpublic of China. H i currnly working oward a Ph.D. dgr in h School of Elcrical and Elcronic Enginring, Nanyang chnological Univriy, Singapor. Hi prn rarch inr ar proc idnificaion and conrol dign for mulivariabl ym.