A Simple Method of Tuning PI Controllers for Interval Plant of Cold Rolling Mill

Transcription

1 ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 A Simpl Mtho of Tuning P Controllrs for ntrval Plant of Col Rolling Mill S.Umamahswari 1, V.Palanisamy, M.Chiambaram 3, 1 Dpartmnt of Eltronis an nstrumntation Enginring, Mahnra Engg.Collg, Namaal Dpartmnt of Eltronis an Communiation Enginring, nfo nstitut of Thnology, Coimbator 3 Dpartmnt of Chmial Enginring., National nstitut of Thnology, Trihy Abstrat-Th mathmatial mol (ntrval Plant) of th wb gui in rolling mill is ontroll using P ontrollr. Th givn intrval plant is approximat to first orr plus tim lay with intgrator (FOPTD) systm. Th quating Coffiint (EC) mtho propos by Pamasr t. al. for sign P ontrollrs for FOPTD systms is xtn to FOPTD systms. Th quating offiint mtho givs simpl quations for th ontrollr sttings. This mtho is bas on mathing th offiint of orrsponing powrs of s in th numrator an that in th nominator of th los loop transfr funtion. Controllrs ar sign using singl tuning paramtr. Th prforman of th los loop systm is valuat for both th original an th approximat mo Th ontrollrs ar also tun using Ziglr Nihols thniqu (Z-N), ntrnal Mol Control (MC). an th prforman ar ompar by simulation. nx Trms -ntrval plant, Equating offiint mtho, MC, Z-N. NTRODUCTON Thr ar many intrmiat wb guis in ol rolling mills pross suh as CRM (ol rolling mill), CGL(Continuous galvanizing lin) an so on. Th main funtions of th wb gui ar to ajust th ntr lin of th strip to th ntr lin of th stl pross, so thy ar all ntr position ontrol (CPL). Rapi pross sp aus larg viation btwn th ntr position of th strip an th pross lin. So th iffrn btwn th ntr position of th strip an th pross lin shoul b ompnsat. n gnral, th CPC of th wb is obtain by hyrauli rivr an ltrial ontrollr. Th mol of th wb gui systm is obtain from Sang Min Kim t. ( 004). For th purpos of signing ontrollrs, th ynamis of many prosss an b srib by first-orr plus tim lay with an intgrator (FOPTD) mol. Mthos for tuning PD ontrollrs for suh mols ar bas on stability analysis suh as ntrnal mol ontrollr (Rivra t. (1986). Th quating Coffiint (EC) mtho propos by Pamasr t. al. fro FOPTD systms is xtn to FOPTD systms. P ontrollsr ar also sign by Ziglr- Nihols mtho an MC mtho. Th prforman of th ontrollrs is ompar by simulation.. NTERVAL PLANT Th mol of th wb gui systm by using gomtrial rlations of th gui ignoring th mass an stiffnss of th wb is givn by Sang Min Kim t. (004). 3 1 a3s + as + a1s + a Gs () = s + b4s + b3s + bs + b1s + b0 Whr th offiints ar of intrval in natur, whih is givn by, a 3 = [4.5 4] ; a = [5 9] ; a 1 = [0.9 5] ; a 0 = [ ] ; b 4 = [ 4 9 ] ; b 3 =[ 4 9] ; b = [0.7 ] ; b0 = [0 0] ACADEMY PUBLSHER

2 ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 This is rprsnt as mol1, mol an (1 α) (1 + α) = 0 mol3 by onsiring only th minimum, 0.5(1 + α) 1+ (1 α) = α maximum an avrag valus of th intrval. Th mo1, mol an mol3 of th plant By solving th abov quations giv: ar givn by, 1 = p Mol1 = Mol = Mo3= s + 5s + 4.5s 0.03s + 0.7s + 4s + 4s + s s + 9s + 4s 0.08s + s + 9s + 9s + s s + 17s s 0.055s s + 6.5s + 6.5s + s Ths mols hav bn approximat to FOPTD systm.. Th approximat systm is givn by, RMol1 = RMol = RMo3 = s(0.5584s s(1.56s s(1.0659s s 0.793s 0.673s ( ) = 1 q = s t has bn foun by simulation that α = 1.01 givs bst rsult for Mol1, Mol an Mol3. Th valu of α is hosn by simulation wor as Th SE an AE valu for th all th thr mols ar shown in th tabl. Th valus of α hosn abov 1.01, for all thr mols osn t yil bttr SE an AE valus hn th suitabl valu of α for all th thr mols ar hosn as Solving th abov quations 1 an ar obtain. Using th finitions of 1 an, P ontrollr sttings ar obtain as, p = = n th prsnt wor, th mtho propos by Pamasr t. al..(003) is xtn to sign P ontrollrs for th FOPTD systm. Th prforman of th ontrol systm is ompar with that of th MC mtho an Ziglr- Nihols mthos.. EQUATNG COEFFCENT METHOD A stabl FOPTD systm with an ntgrator is rprsnt by Kp -t s / s(ζs+. Th los loop transfr funtion rlating th output (y) to th st point (y r ) is givn by, q yq ( ) ( q 1 + ) = q yr( q) [ q [( ) q+ 1] + ( 1q+ ) ] Th numrator an th nominator trms using th Taylor sris xpansion for 0.5q an 0.5q ar onsir. Th offiint of q,q an q 3 of th numrator ar quat α tims that of th nominator of th los loop transfr funtion(cltr). Th following sts of linar algbrai quations ar obtain for P ontrollr. V. MC METHOD Th MC bas P ontrollr sttings for FOPTD systm is givn by, (Dal, t. al. (004) an Rivra t.(1986) :. = ( + + θ) ( + θ) = ( + + θ) Th hoi of sign paramtr is a y ision in both th irt synthsis (DS) an MC sign mthos. n gnral inrasing prous a mor onsrvativ ontrollr baus rass whil inrass. Svral MC guilins for hav bn publish for FOPTD with an intgrator systm. As pr Rivra t al.,(1986), θ > 0.8 an > 0.1, pxp( s) s( s+. By simulation it was foun that =6.9 as pr Rivra t. al., givs bst rsult for all thr mols. V. ZELGLER-NCHOLS METHOD 4 Though an analytial rivation for th Z-N mtho is availabl, th prour is slightly 009 ACADEMY PUBLSHER

3 ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 ompliat whn ompar to th othr mthos. Th mol is of th form, Ziglr t.(194) [5], pxp( s) s( s+ Th phas angl ritria ar givn by, 0 1 π = 90 tan ( ω) ω Hr ω is th ross-ovr frquny. Th ultimat ontrollr stting is givn by, 0.5 u, = ω( ω + p. Th sign valus for an ar alulat from, Fig. Srvo rspons of mol. Lgn as in u, = 0.45 u, fig.1 = π 1.ω Thus, alulat valus of th ontrollr sttings ar givn in tabl for ah ontrol loop of th plant. V. SMULATON RESULTS Lt us onsir th mol1 intrval plant with p =1.667, = an = Th P ontrollr sttings by th quation offiint mtho ar =0.66 = Th P sttings by MC mtho ar =0.7 an = Th P sttings by Ziglr Nihols mtho ar =0.84, = Figur 1, an 3 show th omparison of th srvo rspons of all thr mols. Th robustnss of th los loop is valuat by using th sam ontrollr sttings on th othr two mols of th systm. Figurs 4, 5 an 6 show th rgulatory rspons of th systms. Comparison of SE an AE valus of th mol1, mo an mol3 for both th srvo problm an th rgulatoyr problms using th ontrollr sttings for th MC, Z-N an th quating offiint mthos ar shown in tabl. Fig.3 Srvo rspons of mol3.lgn as in fig.1 Fig.4 Rgulatory rspons of mol1. Lgn as in fig.1 Fig.1 Srvo rspons of mol1 soli Equating offiint mtho; ash-ot MC; hain-- Z-N ACADEMY PUBLSHER

4 ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 Fig.5 Rgulatory rspons of mo.lgn as in fig.1 Fig.6 Rgulatory rspons of mo3.lgn as in fig.1 Th srvo an rgulatory rspons of th EC mtho givs a bttr rspons than that of MC an ZN mtho. Tabl givs th omparison of SE an AE valus for both srvo an rgulatory rspons. Th prforman of th ontrollr sign by th EC mtho givs th bst both in trms of SE an AE. Mols for simulation. Tabl SE, AE VALUE COMPARSON FOR ALL THE THREE MODELS Mtho Controllr Sttings Srvo Rspons Rgulatory Rspons K Ki SE AE SE AE Mol 1 EQ MC ZN Mol EQ MC ZN Mol 3 EQ MC ZN V. CONCLUSON Th ntrval plant of th wb gui systm is tun using Ziglr- Nihols, MC an 44 Equating o ffiint mtho. Th ontrollr sign for FOPTD +ntgrator systm wors wll for vn th orrsponing atual mol. Also th robustnss of th systm is vrifi by 009 ACADEMY PUBLSHER

5 simulation. Th ontrollr has bn sign using Equating offiint mtho, MC an Ziglr-Nihols mtho. Among this, robustnss of th quating offiint mtho is sms to b bttr whn ompar to MC an Ziglr- Nihols mtho. Rfrring to th Tabl, th SE an AE valus ar omparativly lss for quation offiint mtho than that of th MC & th Ziglr-Nihols whih shows that th quating o ffiint mtho sms to wor bttr for ntrval plant of th original an approximat mol. ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 REFERENCES [1] Sang Min Kim, Byoung joon Ahn, t.al., Th moling an ontrol of wb gui pross in ol rolling mill, EEE nustrial Eltronis Soity, Kora, Nov-6,(004) [] E.Dal, Sborg, Jhomas F.Egar, Dunan A.Mllihamp, PD ssontrollr sign, tuning an troublshooting, n., pp , John Wily & sons(asia) Pt.Lt., (004) [3] Pama Sr, R., M.N. Srinivas an Chiambaram. M. A simpl mtho of tuning PD ontrollrs for intgrator / a-tim prosss, Computr& Chmial Enginring, Vol.7, pp.11-15, (003) [4] D.E.Rivra., M.Morari, & S.Sogsta, MC-PD ontrollr sign, nustrial Enginring an Chmial Pross, Dsign an Dvlopmnt, vol.5, 5, (1986). [5] J.G.Zilglr., & N.B.Nihols Optimum sttings for automati ontrollrs, ASME Transations, vol.64, 759, (194) ACADEMY PUBLSHER