VSS CONTROL OF STRIP STEERING FOR HOT ROLLING MILLS. M.Okada, K.Murayama, Y.Anabuki, Y.Hayashi

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1 V ONTROL OF TRIP TEERING FOR OT ROLLING MILL M.Okd.Murym Y.Anbuki Y.yhi Wet Jpn Work (urhiki Ditrict) JFE teel orportion wkidori -chome Mizuhim urhiki 7-85 Jpn Abtrct: trip teering i one of the mot eriou problem in the finihing mill in the hot trip rolling proce. To improve teering control trip teering control ytem which i bed on liding mode control nd ue teering oberver w deigned nd uccefully pplied to n ctul plnt. opyright 5 IFA eyword: Vrible-tructure ytem liding-mode control oberver teel indutry utomtic control metl. INTRODUTION In the hot trip rolling proce in the teel indutry heted lb re rolled to the required trip thickne nd width. From the viewpoint of improved productivity nd roll conumption trip teering i one of the mot eriou problem in the finihing rolling proce it cue til pinch. Prllel mill modulu control which i one type of teering control h been employed to prevent til pinch. Thi method i bed on proportionl control to eliminte force differentil nd chieve levelling movement but neverthele h certin inherent nd prcticl didvntge. To improve teering control new teering control ytem bed on liding mode control uing teering oberver w deigned nd uccefully pplied to n ctul plnt. Thi pper firt preent the concept of prllel mill modulu control. The new teering control ytem bed on liding mode control (M) uing teering oberver i then decribed. Experimentl reult obtined with commercil mill re lo dicued.. PROBLEM OF ONVENTIONAL ONTROL teering refer to lterl movement of the trip during rolling nd i defined by the ditnce between the trip center nd roll center. Fig. how n exmple of the teering phenomenon. In thi ce difference in the reduction rtio t the two ide of the trip occur firt cuing difference in the entry trip velocity. The trip then devite towrd the ide with the mller reduction nd the roll gp incree on the ide where the trip h moved. A reult the difference in the reduction rte continue to incree nd the trip move to the ide with mller teering Roll center trip center Fig. teering phenomenon

2 P Roll center α u u P b l 6 l b F l R h k f h b 6 l P teering h trip center P : rolling rod difference u : mnipulted roll gp difference α : contr ol gin : mill modulu Fig. oncept of prllel mill modulu control - P l ζv b Fig. 4 Block digrm of teering growing model reduction t n ccelerting rte. pecificlly if teering once occur it rte of incree i pproximtely proportionl to the econd power. Prllel mill modulu control i conventionl control method propoed by imur et l.(983). Fig. how the concept. The incree in the roll gp cued by the difference in the rolling lod i cncelled preventing further incree in the difference in the reduction rtio t the two ide. owever due to the initil difference in the reduction rtio the trip continue to move to the ide with mller reduction. Moreover prcticl didvntge thi method require high repone nd lrge movement of the ctutor nd the lrge movement cn cue ter in the trip til end. An pproch bed on imple P-control uing teering enor with no dely w lo propoed by uwno et l. (986) but in order to detect teering with dely the enor mut be intlled in hrh environment mking it difficult to mintin dequte ccurcy. A tte feedbck compentor uing tte oberver w propoed by Okmur et l. (996). owever in hot rolling procee the dely in the tte oberver cnnot be ignored. 3. DEVELOPMENT OF NEW ONTROL METOD 3. oncept of liding mode control u- u yper-plne Fig. 3 oncept of liding mode control Fig.3 how the concept of liding mode control. liding mode control i type of vrible-tructure control (V) which cue ytem tte to converge on predefined hyper-plne by frequent witching of the ytem tructure. Due to the liding motion it i robut with repect to prmeter uncertinty nd externl diturbnce (Utkin 977) (Derlo et l. 988). 3. Modelling of teering A teering growing model w dicued by Nkjim et l. (98). Fig. 4 how block digrm of the teering model where i trip teering i initil trip teering ζ i contnt which depend on rolling condition v i the entry trip velocity i the Lplcin opertor P i the totl rolling lod b i the trip width l i the ditnce between bering l R i the roll fce length h i the exit trip thickne i the entry trip thickne i the mill houing modulu F i the modulu between the work roll nd the bckup roll k f i the modulu between the work roll nd the trip in the roll bite h i the exit trip wedge i the entry trip wedge P i the rolling lod difference nd i the roll gp difference. From the block digrm the following three eqution re obtined: 6l b b h h b P k f h F l l R b P P P P h y 6 l h l ζv && h b h From Eq. () nd () Qin h Q () (). (3) 6 P b (4) y b ( Q ) l Q

3 where Q in (5) Q (6) h b b (7) k f F l 3 R l b b. (8) l 3 l F R Next from Eq. (3) nd (4) Pζv ζv y& y b h Q hl Q & (9) where ζ v Qin y b & h Q. () d ere d cn be hndled diturbnce becue nd re exogenou input. The model of the hydrulic gp control device i expreed u () T where T i the time contnt of the gp control device i the input to the device nd i the initil roll gp difference. Therefore the tte pce eqution of the plnt cn be expreed follow: x & Ax Bu Ed () y x (3) where [ y & ] T x [ && & ] T d A T B E e [ ] 3 T T T d e 3 Pζv b h Q ζv hl Q ζ v Qin. (4) b h Q 3.3 Deign of teering oberver To obtin repone teering hould be clculted directly. From Eq. () nd (4) y d l Q P ( ) Q diturbnce Plnt P LPF Oberver P (5) b Q d 6l P ( ) Q b Qin (6) P ( ) Q 6 Becue i n exogenou input d i ignored to implify the oberver. In the ctul plnt becue the put of the lod enor include ome noie fctor low-p filter (LPF) i intlled hown in Fig.5. Fig.6 how the reult of imultion which w performed to confirm the ppropritene of ignoring nd intlling the LPF. The reult howed tht ignoring nd uing n LPF i reonble method of oberving teering. cl Fig. 5 Block digrm of teering oberver teering(mm) cl Time(ec) Fig. 6 imultion reult of teering oberver

4 3.4 Deign trtegy of liding ector Becue the repone of the hydrulic roll gp device i ufficiently high in generl hot rolling procee the lg of the hydrulic gp control device cn be ignored in controller deign. Therefore the tte pce eqution ued in deigning the controller were follow: & (6) x Ax B y x (7) where [ y & ] T x A B [ ] T 3 [ ] Pζ v b h Q ζ v 3 hl. (8) Q The liding ectori defined x (9) c. () [ ] A liding ector deign trtegy bed on pole ignment w propoed b. A. Woodhm et l. (993). When ytem tte re converging on the ector they tify x. () ubtituting () into (6) the pole of the ytem become p () c where p i the ytem pole. From the bove ny pole p cn be obtined by chooing prmeter c. 3.5 Deign of V controller A V controller which converge the teering tte on the ector w introduced. Thi method i bed on the eventul liding mode witching cheme (J. Y. ung 993). tte pce eqution (6)-() re conidered in the deign of the V controller. The input i umed to be u (3) ( B) Ax k where k i control gin. To converge on the ector hould converge to zero. Therefore the following Lypunov function for i conidered: V. (4) The derivtive of the Lypunov function i V. (5) Ax B u ubtituting (3) into (5) the condition of the exiting liding mode i V & (6) kb < i.e. k > (7) becue from eqution (8) nd () B >. (8) 3 The V control ytem mut frequently witch the ytem tructure follow: u liding mode controller diturbnce Plnt P LPF Oberver ( B ) Ax k >. (9) ( B) Ax k < Becue the witching frequency hould theoreticlly be infinite inherent chttering phenomen exit in V control ytem due to the ctul finite witching frequency or witching dely. To reduce thee chttering phenomen turted function/ ( ) i ubtituted for/ Therefore the input i derived follow: Fig. 7 Block digrm of teering control ytem cl

5 () diturbnce: With control onventionl control (b) diturbnce:. With control onventionl control (c) diturbnce:. With control onventionl control Fig. 8 imultion reult ( Low crbon 3.mm 3mm ) u ( B ) Ax k. (3) 3 y c 3 y& k Fig. 7 how the block digrm of the teering control ytem. 4. imultion reult 4. REULT The reult of imultion for comprion with conventionl control re hown in Fig. 8. ere it w umed tht the diturbnce were the initil trip teering ( mm) the entry trip wedge (.mm) nd the roll gp difference (.mm). The imultion w performed bed on the condition tht the mteril i low crbon teel the trip dimenion re 3.mm*3mm the gin in conventionl control re the me thoe ctully ued nd the ytem pole i. The imultion reult howed tht when the new control method i compred with conventionl control teering devition i reduced nd the control ytem i more tble. Furthermore the ytem input u i lo reduced by erly put from the controller nd chttering phenomen do not occur. 4. Prcticl reult The new teering control ytem w pplied to the til end of trip in the finihing mill t Wet Jpn Work (urhiki Ditrict). The experimentl reult obtined with thi commercil mill re hown in Fig. 9 Fig. nd Fig.. In thi ce the control gin re the me thoe in the imultion nd the mteril i low crbon teel (3.mm*mm) from the me lot. Fig. 9 nd Fig. how exmple of conventionl control reult nd reult with the new control method repectively. From thee reult teering devition nd the rolling lod difference re reduced nd the ytem input i lo reduced in the imultion reult. Fig. how the verge of the bolute vlue of teering in ech ce. The new teering control

6 method i more tble nd trip teering h been improved by more thn 5%. 5.ONLUION Thi pper decribed newly-developed V control ytem for trip teering in hot rolling mill which i bed on liding mode control uing teering oberver. The experimentl reult how tht the new control ytem i uperior to the conventionl ytem. teering onventionl control 5.mm Fig. Averge of bolute vlue of teering ( Low crbon 3.mm mm n ) REFERENE P onventionl control t t t3 Fig. 9 Exmple of experimentl reult uing the conventionl control ( Low crbon 3.mm mm).5mm.5mm.ec 5.ton t: Previou econd tnd metl off t: Previou tnd metl off t3: metl off 5.mm.5mm.5mm Decrlo R. A. Zk.. nd Mtthew G. P. (988). Vrible tructure control of nonliner multi-vrible ytem Proceeding of IEEE ung J. Y. (993). Vrible tructure control: A urvey IEEE Trn. Ind. Electron 4 -. imur T. nd Tgw. M. (983). Automtic teering control of trip rolling mill itchi Review uwno. nd Tkhhi N. (986). enor-type utomtic teering control ytem for rolling mill t report- Ihikwjim-rim Engineering Review Nkjim. jiwr T. imur T. ikum T. Mtumoto. nd Tgw M. (98). Automtic ide-wlk control in hot trip mill The 98 Jpnee pring onf. For the Technology of Plticity Okmur Y. nd ohino I. (996). tte feedbck control of the trip teering for luminum hot rolling mill 3 T World ongre of IFA 7b Utkin V. I. (977). Vrible tructure ytem with liding mode IEEE Trn. Automt. ontr Woodhm. A. nd Zinober A..I. (993) Int.J. ontrol ec P onventionl control 5.ton t t t3 t: Previou econd tnd metl off t: Previou tnd metl off t3: metl off Fig. Exmple of experimentl reult uing the new control ( Low crbon 3.mm mm)