A Self-tuning Fuzzy PID Control Method of Grate Cooler Pressure Based on Kalman Filter

Transcription

1 A Slf-tuning Fuzzy PID Control Mthod of Grat Coolr Prssur Basd on Kalman Filtr Zhuo Wang, Mingzh Yuan Shnyang Institut of Automation of Chins Acadmy of Scincs, Shnyang, China zwang@sia.cn Abstract. A slf-tuning fuzzy PID control mthod of grat coolr prssur basd on Kalman filtr was dvlopd to ovrcom th frquntly varying working condition and wors signal-to-nois radio of prssur signals. Basd on dynamic simulation and charactristics analysis on clinkr cooling systm, th systm variabls wr dtrmind, thn th control modl of grat coolr was obtaind by systm idntification. It was shown that this mthod could inhibit th influnc of nois of prssur signals, could nhancd adaptiv capability of controllr and could improvd hat nrgy rovry fficincy of grat coolr. Kywords: slf-tuning fuzzy PID, Kalman filtr, grat coolr 1. Introduction Clinkr cooling procss is th ky procss in cmnt production which cool hot clinkr and rycl hat nrgy. hrfor, th stabl control of clinkr cooling procss plays a ky rol to kp production quantity and rduc nrgy rsum. As th important paramtr, grat coolr prssur rprsnts th balanc rlationship btwn hot matrial and cool air, and influncs th fft of clinkr cooling and hat rovry[1]. h dsir to control grat coolr prssur has motivatd xtnsiv rsarch on clinkr cooling procss. Wu dvlopd gray modl of grat coolr, thn prdictiv control was usd to cooling procss[2]. A fuzzy prdictiv mthod was introducd to rsolv th coordination of grat coolr, which adaptd to th systm with mor output variabls than input variabls[3]. Wardana proposd a PID-fuzzy controllr for grat coolr. h proportional, intgral and drivativ constant adjustd by nw rul of fuzzy to adapt with th xtrm condition of procss[4]. Howvr, actually w cannot obtain th tru signal of grat coolr prssur du to frquntly varying working condition and wors nois. Motivatd by th abov, in this papr, w focus on procss mhanical and dynamic charactr analysis, thn provid th slf-tuning fuzzy PID control schm of grat prssur basd on kalman filtr. Our study xtnds prvious work in svral rspts. Firstly, a slf-tuning fuzzy PID approach basd on Kalman filtr is advancd in ordr to adjust th prssur undr th grat coolr. Sondly, basd on dynamic simulation and charactristics analysis on clinkr cooling systm, th systm variabls wr dtrmind, thn th control modl of grat coolr was obtaind by systm idntification. Finaly,it was found that this mthod could inhibit th influnc of nois of prssur signals, could nhancd adaptiv capability of controllr and could improvd hat nrgy rovry fficincy of grat coolr. h structur of th papr is as follows. Stion 2 dscribs th procss and analyzs th dynamic charactrs. Stion 3 introducs th control schm dsign. Stion 4 prsnts th industrial xprmnt in cmnt plant. Stion 5 is a brif conclusion of th papr. 2. Procss Dscription and Analysis Cmnt clinkr cooling procss taks plac in grat coolr, as can b sn from Fig. 1. h hot clinkr laving th kiln falls into grat coolr whr thy ncountr th cold air and transfr hat to th air. h hatd air acts as th sond air and third air to kiln and calcinr rsptivly. his procss not only improvs ful fficincy but also savs hat nrgy. Finally, th qualifid clinkr is crushd and snt to storag. Fig. 1 Structur of cmnt grat coolr h cooling fft of clinkr is afftd dirtly by th clinkr thicknss in grat coolr. Usually w adjust th clinkr thicknss by grat spd. But th clinkr thicknss has not dirt dttion in practic. h prssur undr th grat of th coolr is monitord and is takn to b dirtly proportional to th thicknss of th bd of clinkr on th grat. According to opration rquirmnts, th sond room prssur is adjustd by th first grat spd. Whn th first grat

2 spd boms slow, th load of clinkr ntring th coolr thickns th bd and th prssur undr th grat riss. Convrsly, th first grat spd boms fast, th clinkr bd thins out and th prssur undr th grat falls. Nxt, a stp chang of th first grat spd is imposd and w obtain th trnd of th prssur basd on dynamic modl of clink cooling modl [5] Grat prssur(pa) Fig. 2 Stp rspons of th prssur Firstly, th grat spd is incrasd by10% from 420rpm, thn dropd 10%. Whn th grat spd incrasd, th prssur dropd soon(s Fig. 2). h rason is that th grat pushs th clinkr forward fastr, thn th thicknss of bd boms thinr and th rsistanc of cold air boms lss. As can b sn that th lag tim is not vry larg in th curv, but th transition procss has a littl long duration. hrfor, th procss has high inrtia. According to th analysis of stp rspons, th transfr function can b xprssd as ñ60s Gp s. (1) 496sı1 3. Control Schm Dsign In this papr a slf-tuning fuzzy PID control schm basd on kalman filtr is prsntd. h paramtrs of controllr can adapt to frquntly varying working condition and th filtr can liminat th influnc of wors nois. h control structur is shown in Fig.3. Figur 3 Grat coolr prssur slf-tuning fuzzy PID control structur basd on Kalman filtr In this schm th sond room prssur undr th grat is th controlld variabl and th first stag grat spd is th manipulat variabl. h stimatd valu of th prssur is fdback signal for closd-loop control. In addition, fuzzy rasoning mthod is usd to adjust th paramtrs of PID controllr in ordr to improv systm robustnss. A.Kalman Filtr. Kalman filtr is usd in various fild of applications for optimal stat stimation, nois filtring and prdiction. A brif introduction to a kalman filtr is statd as follows: Assum that th volution of th undrlying signals to b obsrvd can b modld as x( kı 1) Axk ( ) ı Bu( k) ı wk ( ). (2) y ( ) ( ) ( ) v k Cx k ı vk. (3) Whr x(k) is th stat at tim k, A is th stat transition matrix, B is th input transition matrix, u(k) is th grat spd, y v (k) is th prssur signal with nois, and additiv nois trms ar includd in th procss w(k) and masurmnt v(k), thir covariancs ar rsptivly Q w and Q v. h discrt Kalman filtr quations to stimat th stat x(k) ar givn as th following quations[6,7]. h symbols (-) and (+)usd blow rprsnt th prior and updatd valu basd on th us of th currnt masurmnt. Stat stimat xtrapolation x Ax ı Bu. (4) Error covarianc xtrapolation Kalman gain matrix Stat stimat updat im(s) k( ñ) kñ1( ı) k P AP A ı Q. (5) k( ñ) kñ1( ı) w K P C ( CP C ı Q ). (6) k k( ñ) k( ñ) r x x ık ( y ñ Cx ). (7) k( ı) k( ñ) k k k( ñ)

3 Error covarianc updat P ( Iñ KCP ). (8) k( ı) k k( ñ) Finally th stimatd valu of th prssur as y( k) Cx( k). (9) B. Slf-tuning fuzzy PID Control. h fuzzy PID can adapt to th dynamics of th procss bttr than th convntional PID controllr[8]. In this papr, w us a slf-tuning fuzzy PID mthod to adjust th prssur undr th grat. h input variabls ar th rror and which is obtaind from th diffrnc of th stting valu and stimatd valu of th prssur. Finally, th rquirmnt of th dynamic and static prformanc ar both satisfid by onlin adjusting th paramtrs of PID controllr. h slf-tuning of PID paramtrs must considr two factors,on is th intraction and rlationship among th thr paramtrs at diffrnt tims, and th othr is th adjustmnt of paramtrs,such as polarity and magnitud. According to practical xprinc th adjustmnt fuzzy ruls sht ar stablishd (s ab.1, ab.2 and ab.3). ab.1 Fuzzy ruls sht of k p k p NB PB PB PM PS PS ZO NS NM PB PB PM PS PS ZO NS NS PM PM PM PM ZO NS NS ZO PM PM PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB k i ab.2 Fuzzy ruls sht of k i NB NB NB NM NM NS ZO ZO NM NB NB NM NS NS ZO ZO NS NB NM NS NS ZO PS PS ZO NM NM NS ZO PS PM PB PS NM NS ZO PS PS PM PB PM ZO ZO PS PS PM PB PB PB ZO ZO PS PM PM PB PB k d ab.3 Fuzzy ruls sht of k d NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS ZO NS ZO NS NM NM NS NS ZO ZO ZO NS NS NS NS NS ZO PS ZO ZO ZO ZO ZO ZO ZO PM PB NS PS PS PS PS PB PB PB PM PM PM PS PS PB According to th ruls sht, thpid paramtrs k p,k i,k d can adjust onlin as following. h rang of th input variabls and is dfinit in th domain of fuzzy st., ñ5, ñ4, ñ3, ñ2, ñ 1,0,1,2,3,4,5. (10) h corrsponding fuzzy st is, NB,NM,NS,ZO,PS,PM,PB. Whr, th lmnts ar rsptivly ngativ big, ngativ middl, ngativ small, zro, positiv small, positiv middl and positiv big. Assum that, and k p, k i, k d ar all gauss mmbrship function.

4 According to th mmbr function of fuzzy st and fuzzy control modl, w obtain th accurat paramtrs k p, k i, k d of PID controllr. hn w gt th corrtion valu of k p, k i, k d with th diffrnt combination of and,,,. hs. hs corrtion valu prsnts with fuzzy matrix tabl which ar i i p, i i i and i i d corrtd paramtrs of PID controllr calculat as follows. k k ı p p i i p k k ı i i i i i k k ı d d i i d. (11) Whr, k p, k i and k d ar th initial valus of PID paramtrs. Finally, th calculation squnc of th slf-tuning fuzzy PID mthod basd on Kalman filtr can b xprssd as: Stp1: Giv th initial paramtrs of Kalman filtr and control algorithm; Stp2: Calculat th prssur undr th grat by (4)~(9) and input-output data; Stp3: Updat k tims control valu by slf-tun fuzzy PID control algorithm; Stp4: Lt k=k+1, and rturn Stp2. 4. Industrial Exprimnt in Cmnt Plant h control schm in this papr was usd at a nw dry cmnt production lin of Shanshui Cmnt Group Ltd. h spification of th production lin as: Prhatr two string 5 stag with pralcinr Rotary kiln about 74 mtrs long Clinkr coolr with grat hydraulic driv otal capacity 5000t/d clinkr h algorithm which is discribd in this papr is packagd in th slf-dfinition function block and downloadd to DCS controllr. h convntional PID and th algorithm discribd in this papr hav bn in opration succssivly at 320t/h working condition, and th control curv is shown as Fig.4. whr, th paramtrs of th two algrithms ar th sam, k p =0.8,k i =0.05,k d =2.5. It can b sn that th fluctuation magnitud dropd down obviously aftr th algorithm proposd in this papr, and th rror rducd by 51.5%. Fig.4 rnd of th prssur in sond room undr th grat According to th xprimnt w can gt th statistic data shown in ab.4. During slf-tuning fuzzy PID basd ong Kalman filtr was applid in opration with th grat coolr, w can obsrv th rsult that: h prssur undr th grat was much mor stabl h tmpratur of clinkr in outlt was furthr rducd h hat nrgy rovry fficincy incrasd ab.4 Statistics of opration data Opration h prssur of sond Clink tmpratur in Avrag tmpratur of tim(h) room grat (Pa) outlt( ) sond air( ) PID ± Slf-tuning fuzzy PID basd on kalman filtr ± Conclusions his papr prsnts a slf-tuning fuzzy PID approach basd on Kalman filtr to adjust th prssur undr th grat coolr. h hat rovry fficincy problm in cmnt plant has improvd. Industrial xprimnt has provd that this

5 approach not only has a good stability and robustnss, but also has bttr nrgy fficincy. Howvr, th long-trm opration of th controllr will b dvlopd ultriorly in th futur. 6. Acknowldgmnt his work was supportd by Shnyang Scinc and hnology Ky Projt (F ). h author wishs to thank th staffs of Shanshui Cmnt Group Ltd. and Jinan Univrsity for thir valuabl support and assistanc during this projt. Rfrncs [1] Q. D. Chn, h Principl and Application of Nw Dry Cmnt hniqu, Bijing: China Building Matrial Industry Publishing Hous, [2] S. Q. Wu, X. H. Wang,. Shn,Application of Advancd Control in Clinkr Cooling Systm, China Cmnt, vol. 5, 2007, pp [3] C. X. Li, J. Zhu, Application Study of Singl Input and Dual Output Fuzzy-Prdictiv Coordination Control on Grat Coolr, Journal of h Chins Cramic Socity, vol. 30, no. 6, 2002, pp [4] A. N. I. Wardana, PID-Fuzzy Controllr for Grat Coolr in Cmnt Plant, 5th Asian Control Confrnc, 2004, pp. 1563~1567. [5] Z. Wang, Rsarch on Modling and Control of Cmnt Calcination Procss, Ph.D Dissrtation, Graduat School of Chins Acadmy of Scincs, [6] A. Glb, Applid Optimal Estimation, MI Prss, [7] M. M. Mustafa, S. Rozaimah, S. Abdullah, R. A. Rahman, Robust On-Lin Control of Hxavalnt Chromium Rduction Procss Using A Kalman Filtr, Journal of Procss Control, vol. 12, 2002, pp [8] Y. H. ao, Y. X. Yin, L. S. G, Nw yp PID Control and Its Application, Bijing, China Machin Prss, 1998.