Nonlinear identification for diffusion/cvd furnaces
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1 José-Job Flors-Godo aramno d Físca amácas Unvrsdad Ibroamrcana éxco C. F. EXICO job.lors@a.mx ars Gas Inl Nonlnar dncaon or dson/cv rnacs rol C Z Z Z Z Z5 rol rol rol r o l rol 5 5 Kosas. saals armn o Elc. En. Ira A. Flon cool o Ennrn Arzona a Unvrs m AZ UA saals@as.d Kvn oddard G EE Conrol sms Broos Aomaon Inc. onx AZ UA vn.soddard@broos.com Qarz or lcon Carbd b an Rsl: Nonlnar Idncaon mods can rovd lobal modls smoo ranson bn oran ons and smlar modln rrors as local lnar modls sabl or conrollr dsn. Exrmnal vrcaon: Vrcal or orzonal rnacs oran a amosrc rssr or a lo rssr. a rovdd b lcrcal rmal lmns mrars masrd b o ss o rmocols C nar an lmn rol C nsd racon cambr mlaon s-bd: aral rnal Eqaon modl basd on rs rncls odl nclds a ransr d o radaon and convcon Florssaalsoddard AEC/AC rsdn
2 Florssaalsoddard AEC/AC rsdn odl srcr and aramrzaon d n n n x Fx x & [ ] [ ] ; F si c F si x C - q q q K Nonlnar modl srcr: Lnar n aramrs ARX nralzaon... Lonars 85 L acorzaon o lan cal o Exrmns: ll Oran ons 5- dc saraon Random bnar sqnc xcaon o rovd md- rqnc normaon ss o rovd lo rqnc normaon cal Exrmn: or s rol
3 Florssaalsoddard AEC/AC rsdn { } [ ] s I I N N.. mn > < l l l { } L L E s E ρ.:. ˆ ˆ mn mn mn mn Idncaon srcr Las-sqars roblm or ndn nnon aramrs Uncran smaon Uncran smas: ncrmnal ans ranslad o snsv and co-snsv bonds or loo-san conrollr dsn. cdld Conrollr dsn: andard -nn dsn n ALAB : mn γ γ < I I Rlarzd aramr smas : lan modl x : or scrm o x : nsv : Co-snsv
4 or- NL modl Fx -rol NL modl Fx odl srcr or smlaon s-bd aa rom 5 ss o xrmns From 5 o 9 C Nonlnar odl 65 o aramrs 55 rol aramrs Lnar scdld modl 5 oran ons 65 aramrs rol aramrs Addv Error rol Addv Error Florssaalsoddard AEC/AC rsdn
5 mlaon s-bd modl or- odl Comarson bn closd-loo drncs : E modl and lnar scdld lan rd; E modl and nonlnar lan bl -rol odl Rrnc snal: ram rom 5 o 8 d/mn. nlar vals Uncran Esmas Closd-loo a an-scdld -nn conrollr Lnarzd modl as ns./co-ns. bonds dals: [Flors-Godo ] > asbl o conrollr dsn Florssaalsoddard AEC/AC rsdn 5
6 odln Examl: rmco nbr 5n orzonal zons Fx or- NL modl Fx -rol NL modl or- odl Idncaon Exrmns: Exrmns RB snal a oran ons rom 55 o 5 C [saals 99] Conrollr sn Fasbl: mlar o local lnar modls rad/mn s loo bandd - rad/mn rol loo bandd [saals 99] nlar vals o Lnarzd modl -rol odl Uncran Esmas Addv rrors Florssaalsoddard AEC/AC rsdn 6
7 Examl: Vrcal Frnac 5 zons Fx or- NL modl -rol NL modl Fx Closd-loo comarson bn G vs NL nlar vals o Lnarzd modl Uncran Esmas Addv rrors Florssaalsoddard AEC/AC rsdn 7
8 Conclsons Gnralzaon o lnar modln and ncran smaon cnqs. Ecn aramr smaon va las-sqars alorms. namc ncran smas ncrmnal an nrraon sabl or robs conrollr dsn Conrollr dsn: lnarzaon-and-scdln mods ll-sablsd [saals 99] lnar-aramr-varn mods nx as [acard 9 R Gan 95] Rrncs J.J. Flors-Godo Nonlnar Idncaon or son/cmcal Vaor oson Frnacs. ssraon Arzona a Unvrs c.. K. saals J.-J. Flors-Godo and K. oddard. mrar Conrol o son/cv Frnacs Usn Robs lvarabl Loo-an cnqs roc. 8 Con. cson and Conr onx AZ c I. J. Lonars and. A. Bllns. In-o aramrc modls or non-lnar ssms. ar I: drmnsc nonlnar ssms. Inrnaonal Jornal o Conrol : Gan A. Nmrovs A. Lab. Clal. LI Conrol oolbox For Us ALAB. aors Inc A. acard. Gan cdln va lnar raconal ransormaon. sms & conrol Lrs : J. R and J.. amma. Rsarc o an scdln. Aomaca 6:-5. Florssaalsoddard AEC/AC rsdn 8
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