Aluminum Electrolysis 1

Transcription

1 3rd Internatonal Conference on Mechatroncs, Robotcs and Automaton (ICMRA 2015 Dynamc Decson Model for Amount of AlF 3 Addton n Industral Alumnum Electrolyss 1 Zeng Shupng 1,a*,Cu Fuwe 1,b 1 College of Electrcal And Control Engneerng of North Chna Unversty of echnology, Bejng, Chna a zshp@ncut.edu.cn, b @qq.com Keywords: decson model; alumnum electrolyss; AlF 3 addton Abstract: Addng alumnum fluorde to electrolyte, s the most mportant to regulate electrolyte molecule rato and the electrolyss temperature n alumnum electrolyss, whch drectly nfluences the current effcency and energy consumpton. hs paper presents a decson model to decde the amount of AlF 3 addton by use of the hstorcal data ncludng electrolyss temperature, cell workng voltage, the amount of alumnum tappng and the amount of AlF 3 addton. We establshed dynamc regresson equatons and got the regresson correlaton coeffcent by transformaton of orthogonal matrces. Selectng two electrolyss cells to check the model, the standard devaton of predcted value and the actual value wthn two months was ,1.7768, whch can meet the requrements of practcal producton. Introducton: In the process of alumnum electrolyss, the approprate electrolyte molecular rato and electrolyss temperature can keep a regular cell ledge [1], and reduce the horzontal current, mprove the current effcency and help to prolong the lfe of cell. Research has shown that, under normal producton condtons, the decrease of the electrolyte temperature can mprove the current effcency. But f the electrolyss temperature s too low, the sedment would be n bottom. herefore, how to determne the AlF 3 addton reasonably to control of alumnum electrolyss temperature and electrolyte molecule rato s a very mportant n alumnum electrolyss. At present, the techncans manly rely on ther experence to decde the amount of AlF 3 addton. Some techncans control the AlF 3 addton through the expert system, but because electrolytc cells have gradually changed, the expert system cannot make adjustment accordng to these changes, as well as the expert s advce produces certan conflct sometmes, whch wll affect the decson of the AlF 3 addton [2]. Because of the complcty of the alumnum electrolyss, t s more dffcult to establsh the mechansm model [3]. AlF 3 related manly to electrolyss temperature, work voltage, alumnum content and prevous the AlF 3 addton, so the model to make the decson of AlF 3 addton can be bult accordng to the exstng data and the requred electrolyss temperature. he establshment of the model for AlF3 addton he model structure Alumnum electrolyss s very complex, the establshment of a mechansm model to descrbe the amount of AlF 3 addton s very dffcult. We selected the man factors that nfluence the amount of 1 Project supported by the Natonal Natural Scence Foundaton( ; he authors - Publshed by Atlants Press 787

2 AlF 3 addton, whch s electrolyss temperature, work voltage and the alumnum tappng content. he followng s the structure of the model, F(K - F(K -2 = a(v(k-v(k-2+b(l(k-l(k -2+ c((k-(k +d (1 Here: F (K, F (K-2 were the amount of addng fluorde of K moment and K-2 moment respectvely. V(K, V(K-2 were the the average workng voltage of K moment and K-2 moment respectvely. L(K, L(K-2 were the the the alumnum content of K moment and K-2 moment respectvely. (K, (K were electrolyss temperature of K moment and K moment respectvely. a, b, c, d were the correlaton coeffcent,whch should be updated n tme. he correlaton coeffcent got by transformaton of orthogonal matrces. he data, whch ncludng electrolyss temperature, the workng voltage, the amount of alumnum tappng the amount of fluorde addton were sampled from the cell 216# and 217# lasted for three months. By selectng 40 group of nput data,.e: the workng voltage of frst days to forteth days, the amount of alumnum tappng, the amount of fluorde addton and electrolyss temperature from the of second day to forty-frst day, and obtanng the daly varaton, and gettng a set of data of 39 elements, denoted as ΔV(39, ΔL(39, ΔF(39,Δ(39 respectvely. he 39 sets of data were dvded nto 10 groups accordng to the tme sequence, and each of whch has 30 elements,.e: 1-30, 2-31, , respectvely, as a group, the seral number was 1, 2,..., 10. Each vector were recorded as Vorg(, Lorg(, Forg(,org(. he establshment of the ndependent varable matrx: Xorg( =( I,Vorg(,Lorg(,org( he I of 30x1 elements are column vectors whch all s 1;, he dependent varable vector: yorg( =Forg( ; A new matrx was formed: ÊXorg( ˆ Xorg( Xorg( yorg( Aorg( = Ë yorg( Xorg( yorg( yorg( ; he nput data are treated by addng the weght coeffcents, the Vn, An, Fn, n, for the vector Vorg, Lorg, Forg, org respectvely. Constructng a new matrx Anew by makng: Vnew=Vn Vorg Lnew=An Lorg Fnew=Fn Forg new=n org; Xnew = ( I,Vnew,Lnew,new ynew =Fnew ; Ê Xnew Xnew Xnew ynew ˆ Anew= Ë ynew Xnew ynew ynew ; hs matrx can be decomposed nto: Êλ 1( ˆ 0 λ 2( Anew( ( = u( 1 ( 2 3( 4( 5( 0 0 λ 3( λ 4( 0 Ë λ 5( ( u( ( ( ( ( Where λ 1 (,λ 2 (,λ 3 (,λ 4 (,λ 5 ( s egenvalue of the matrx Anew (, u 1 ( 2 ( 3 ( 4 ( 5 ( were standard orthogonal egenvectors corresponded to the egenvalue. Each egenvalue n +l moments can be calculated by prevous one usng the model 788

3 l( t = g ( t + d. he egenvectors at the moment of +l calculated as folloeng. For a standard orthogonal matrx =(u 1,u 2, L,u 5, where u j s the j column of, can be decomposed nto the followng form: =(1213L 15 ( L ( 45 ; (2 Where (1 < j 5 have the followng specal form: j Ê ˆ 0 cosθj 0 -snθj 0 j =(θ j j = snθj 0 cosθj 0 Ë (- qj hs decomposton s unque [4], and each θ j s ndependent. herefore, as long as we can calculate each θ j, we can get matrx. he followng method to solve the θ j : Makng 1 =, then 1 =(V 11,V 12,,V 15 =(u 1,u 2,,u 5, Due to the specal structure of j, we can get the frst column of 1 : And q Êcosθ cosθ Lcosθ snθ cosθ Lcosθ V =u = snθ Lcosθ snθ14 cosθ15 Ë snθ = arcsn V (5, ÏÔ V ( k Ô q1 k = Ì = ÔÓ cosq15l cosq1k+ 1Ô (- q1j, j = 2,3,4,5 By the formula (2 we can get: 11 arcsn, k 2,3,4 ( L =( L ( Makng: 2 =(1213L 15 1 =(V21, V22L V 25 he frst and second column of 2 can be obtaned as: 15 ˆ 789

4 And : q Ê1 0 0 cosθ cosθ cosθ (V,V = 0 snθ cosθ cosθ 0 snθ cosθ Ë0 snθ = arcsn V (5, ÏÔ V ( k Ô q2k = Ì = ÔÓcosq25L cosq2k + 1Ô (- q2 j, j = 3,4,5 22 arcsn, k 3,4 25 ˆ Smlarly we can get each of the remanng θ j, untl fnally we can get q 45 = arcsn V45(5 Wth the angle at the moment of +l by the model, we can calculate the standard orthogonal matrx (+l at the moment of +l, namely standard orthogonal vector group of Anew matrx at the moment of +l, thus we can determne the matrx Anew at the moment of +l. ÊA4 4 B41 ˆ Makng: Anew = hen the least squares estmate value of the correlaton Ë C D coeffcent β =( a,b,c,d s ˆ β =A B. Decson of AlF3 addton Calculaton of the AlF3 addton on the same day he formula (1 was changed to F(K=a(V(K-V(K-2+b(L(K-L-L(K-2+c((K-(K-L+d+F(K-2 (3 he formula (3 can be used to decde the amount of AlF 3 addton. In the producton, the amount of AlF 3 addton F(K ths day was calculated by usng the settng temperature (K next day, the set voltage V(K ths day, the alumnum tappng amount L(K ths day, the temperature (K ths day and some hstorcal data (workng voltage, the amount of alumnum tappng, the amount of AlF 3 addton, Feedback correcton In the producton, the envronment changes constantly, he set temperature and actual temperature have devaton. When the devaton s larger than a gven value, whch s determned by techncan (50 degrees, or for greater than 5 degrees contnuously, we must recalculate the model coeffcents of a, b, c, d. he mplementaton of the decson Makng a forecast to the two electrolytc cell temperature respectvely. Smulaton calculaton was carred out by Malab programmng. Weght coeffcent, Vn, An,Fn,n s obtaned by Matlab optmzaton functon, and experments show that, the reasonable selecton of Vn, An, Fn, ncan mprove the accuracy of the model. 790

5 he nspecton of decson model Usng the followng formula to calculate the standard devaton,to test the fttng degree of themodel and the actual value: S = N Â pred =1 (F - F N 2 real (4 Here, F pred, F real are the predcton and the actual amount of AlF3 addton; N to test the number of days. N=51. Fg.1 s the comparson of the mode decson value wth the actual value of the amount of AlF 3 addton for cell 216#. In the calculaton process, makng Vn=2.0610, An=1.1658,Fn=0.8333, n=0.5810, By calculatng, we can know that the standard devaton of the model output value and actual output value s Fg.2 s the comparson of the mode decson value wth the actual value of the amount of AlF 3 addton for cell 217#, and makng Vn=1.9402, An=1.2597, Fn=0.4913,n= By calculatng, we can know that the standard devaton of the model output value and actual output value s Fg.1 the comparson of the output value Fg.2 s the comparson of the output value wth the actual value of the amount of wth the actual value of the amount of groove AlF3 addton model(216# groove AlF3 addton model(217# Concluson hs paper establshed the decson model for AlF3 addton n the alumnum electrolyss by use of the electrolyss temperature, the workng voltage, the alumnum tappng amount and the amount of AlF3 addton as the parameters. hrough the nspecton of producton data, the decson model can be used as a decson makng reference of the amount of AlF3 addton n the ndustral alumnum electrolyss. References [1] Zeng Shupng. Model Predctve Control of Superheat for Prebake Alumnum Producton Cells. MS Lght Metals 2008: [2] Lu Yexang,L Je. Modern alumnum electrolyss.be Jng: Metallurgcal Industry Press [3] Shupng Zeng, Ln Cu and Jnhong L. Dagnoss System for Alumna Reducton Based on BP Neural Network, JOURNAL OF COMPUERS, 2012,7(4: [4]. Anderson,.W., Olkn, I., UnderHll, L.. eneraton of random orthogonal matrces, SIAM Sc. Statst. Comput. 8, ,