Auto-tuning and Fuzzy PID Temperature controllers for Hollow Metal Block

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1 Ato-tnng an Fzzy PID emeratre controllers for Hollow Metal Block Shh-Jer Hang an Y-Ho Lo Deartment of Mechancal Engneerng Natonal awan Unversty of Scence an echnology No. 43, Keelng Roa, Secton 4, ae, 106, AIWAN htt:// Abstract: - emeratre s an mortant rocton control arameter n chemcal an semconctor nstry. Generally, the temeratre control system has nonlnear tme-elay, slow resonse see an one-way control nt characterstcs. It s ffclt to accrately estmate the ynamc moel an esgn a general rose temeratre controller for achevng goo control erformance. Here moel-free ato-tnng an fzzy PID control strateges are emloye to esgn a general temeratre controller for fferent lants. he exermental reslts show that these control schemes can obtan reasonable control erformance. he steay state error of the ste nt resonse s less than 0.2 C wth small overshoot. he tme resonse behavor s better than that of the moel-base IMC-PID e to the moelng error. Key-Wors: - ato-tnng PID, fzzy PID, temeratre control an one-way control nt 1 Introcton emeratre s an mortant control arameter n chemcal, materal an semconctor manfactrng rocesses. For examle, materal annealng, thn flm eoston, lamnator oeraton an V glass meltng frnace all nee arorate temeratre control system. Some of the temeratre control systems have heatng an coolng control hases an others only have heatng nt control hase. her ynamc behavors have sgnfcant fference. he temeratre control system wth heater nt only s more ffclt to montor than two hases control systems for obtanng goo control erformance. How to esgn a general rose temeratre controller wth goo resonse see, smaller steay state error an overshoot for nstral mlementaton s stll a challenge work n control research fel. Crrently, the on-off control an PID control schemes are emloye n the commercal rocts. PID controller was roose n It has been wely se n nstral atomatc control systems. However, how to ajst the control gans s the key factor of mlementng a PID controller. If the accrate ynamc moel of a control system s avalable, the Zegler an Nchols rle [1] an IMC control strategy [2,3] can be se to calclate the arorate gans. However, the heatng lant has tme-elay an temeratre eenence nonlnear behavors. It s har to establsh an accrate ynamc moel for a PID controller esgn. Generally, t nees a tral-an-error rocess for obtanng a goo control resonse. When the system has external strbance or set-ont change, ts transent resonse may eterorate. It nees an onlne oerator to reajst t or swtch t to the manal control. hs s not a convenent alcaton an the rocton arameters may not mantan n a goo level rng manfactrng rocess. Hence the moel-free ntellgent control schemes have gane the researcher attenton. Ato-tnng PID control strategy was roose by Astrom an Haggln[4]. Hang et al. [5-7] roose some ajstng rles for the ato-tnng PID controller by emloyng the aatve control technqe an worke ot the erformance comarson for those methos [8,9]. he arorate gans searchng of ths aroach s base on the system ott resonse of an on-off oen loo relay control. he crtcal ero an crtcal gan are fon frst, an then the arorate PID gans can be calclate by sng the Zegler an Nchols rle. Fzzy control has been sccessfl emloye n a lot of nstral rocess. It has moel-free ntellgent characterstc. Recently, the fzzy control theory s se to mrove the aatvty an robstness of a PID controller. here has a lot of fzzy PI, fzzy PD an fzzy PID control schemes were roose n lteratre [10-12]. he PID gans are nonlnear fnctons of trackng control erformance. hey can be ajste atomatcally base on the ott error. It can acheve better robstness, qck resonse an smaller overshoot than that of a tratonal PID controller. Usally, the heater nt only one-way ISSN: ISBN:

2 temeratre control roblem has nonlnear tme-elay an n-symmetrc control behavor. It s ffclt to estmate an arorate ynamc moel for moelbase controller esgn for achevng recse temeratre control accracy wth goo transent resonse. Hence the moel-free PID control scheme wth ato-tnng or gan ajstment mechansm s the stable aroach to evelo the heater nt only temeratre controller. Here ato-tnng an fzzy PID control strateges are emloye to esgn general rose temeratre controller for montorng the temeratre of one hollow metal cylner an one hollow metal block wth heater nt only. 2 Hollow Metal Block emeratre Control System Strctre he control system strctre of ths temeratre montorng system s shown n Fg. 1. It s a PC base strctre. PC sens the control crrent nto a SCR rver throgh the D/A car. hs SCR can montor the ower ott of a sngle hase 220 V an 20A alternatve crrent ower sorce. It reglates the crrent nt of the heatng ro for rasng the temeratre of the hollow metal cylner or hollow almnm rectanglar block. he mem nse the hollow cylner hole s ar. he temeratre of the hollow metal cylner s measre by sng a RD resstance temeratre sensor an fe back nto the PC throgh A/D car. he control algorthm s mlemente wth C++ rogram. In orer to evelo a general rose temeratre controller, two fferent control lants are reare for evalatng the control erformance. he menson of the hollow ron cylner s 250 mm heght an 51 mm ameter wth 10 mm ameter hollow hole for nstallng the heatng ro an RD P100 temeratre sensor. he menson of the hollow almnm rectanglar block s mm wth 10 mm ameter hollow hole for nstallng the heatng ro an RD P100 temeratre sensor. he accracy of the selecte P100 RS sensor s abot 0.2 C for the measrng temeratre ner120 C. he senstvty of ths RD sensor s er C. he sensng elay s abot 0.1 secon whch s accetable wth resect to the 4Hz samlng freqency. 3 Ato-tnng PID Control he key role whch nflences the system control erformance of a PID controller s how to fn the otmal roortonal gan, ntegral tme constant an ervatve tme constant. For ractcal mlementaton, these gans ajstment s acheve by exertse exerence an tral-an-error mofcaton. It s a tme consmng work an the ynamc resonse behavor can not be garantee. Hence, Astrom an Haggln [4] roose a relay feeback evalatng metho to fn the gan arameters for a PID controller. Frstly, On-Off swtchng control s emloye for the begnnng two cycles. When the system temeratre s below the settng comman, the control ower s flly oene to rve the temeratre. When the temeratre reaches the settng vale, the control nt s swtche off mmeately. hen the crtcal gan, K, an crtcal ero, P, can be fon from these nt-ott resonse crves as Fg. 2. Where 4 K a (1) Hence, the gan arameters can be calclate by sng the exerence formla of Zegler-Nchols. K 0. 6K, P, an P 2 8 (2) hat means K 0. 6K, K K / an K K (3) 4 Fzzy PID Controller Snce the temeratre control system has tme varyng behavor an the ynamc resonse may een on the temeratre settng vale, t s not easy to establsh the arorate PID gans. Fzzy self-tnng PID controller [13] was roose to solve ths roblem an obtanng the controller aatablty. he man ea of ther aroach s emloye a arameter to arameterze the Zegler-Nchols tnng formla for gettng faster set ont ynamc resonse. hs arameter s ajste by sng a fzzy strategy base on the system ott error an the error change. he system control block agram s shown n Fg. 3. he control law formla for a stanar PID controller s 1 t e ( t ) (4) ( t ) K [ e( t ) e( t ) t ] 0 t Where e(t) s the system ott error, an are the resettng an ervatve tmes, resectvely. hen the relatonash between Fzzy PID control gans an the arameter can be reresente as K 1. 2 K P Where K an P arameters are obtane from the ato-tnng rocess. hs Fzzy-PID controller wll become a basc Zegler-Nchols formla, P (5) ISSN: ISBN:

3 when he ott error e (t), error change e(t) an the arameter atng vale h (t) are classfe nto seven membersh fnctons {-3, -2, -1, 0, 1, 2, 3}. hree arorate gan factors ge, gce an g are selecte to ma these varables, e (t), e(t) an, nto the secfe range of the fzzy nverse of sclose [-3, -2, -1, 0, 1, 2, 3]. he tranglar membersh fncton s emloye for those fzzy varables. 1 ( x ) ( x a W ) (6) W Where a s the t ont vale of each membersh fncton an W s one-half of the wth of the membersh fncton. he fzzy rle table for ajstng the Fzzy PID controller arameter s shown n able 1. hs rle table s esgne base on fzzy control knowlege an a mnor tral-an-error checkng rocess. he weght metho s se to e-fzzlze the atng vale. x ( x ) x (7) h ( t ) ( x ) x hen the arameter can be ate by the followng recrsve formla ( t 1) ( t ) h ( t )[1 ( t )] for ( t) 0. 5 ( t 1) ( t) h( t) ( t) for ( t) 0. 5 (8) Where s a ostve learnng rate constant. It can be chosen between [0.2, 0.6] for most ynamc system. he ntal vale of s set to 0.5 for matchng the staton of ato-tnng PID controller statement. 5 Exermental Reslts In orer to evalate the control erformance of the ato-tnng an Fzzy-PID control schemes, two small temeratre control lants are blt for the exermental rose. One s a hollow ron cylner an the other s a hollow almnm rectanglar block. he mensons of these two metal lants are escrbe n revos secton. Both have a heatng col to nt energy an a RD temeratre sensor to measre the temeratre. he tme-elay of these control lants s abot 20 secon measre from the transent resonse of ato-tnng rocess. he 4 Hz slow samlng freqency s chosen for the followng exerments. wo fferent temeratre changes are secfe for each control lant n the followng exerments to nvestgate the erformance an robstness of the roose controllers. he control gans of the ato-tnng PID control scheme are calclate from the Zegler-Nchols formla base on the crtcal gan, K, an crtcal ero, P, obtane from the ato-tnng rocess. hese arameters an the ato-tnng PID control gans of followng for exermental cases are lste n able Hollow ron roller wth Ato-tnng PID control:: he arameters K an P are estmate from the ato-tnng rocess wth the secfe temeratre change between 50 C an 80 C. hen the PID control gans can be calclate base on the Zegler-Nchols formla. hey are lste n able 2. he temeratre resonse an the heatng crrent for an 80 C settng ont are shown n Fg. 4(a) an (b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 3.5 mnte an the steay state error s less than 0.1 C wthot overshoot. For the secfe temeratre change between 90 C an 120 C, K 5. 8 an P 162 are obtane. he temeratre resonse an the heatng crrent for a 120 C settng ont are shown n Fg. 5(a) an (b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 4.5 mnte an the steay state error s less than 0.1 C wth 0.5 C overshoot. 5.2 Hollow almnm rectanglar block wth ato-tnng PID control: he arameters K an P are estmate from the ato-tnng rocess wth the secfe temeratre change between 45 C an 80 C. hen the PID control gans can be calclate base on the Zegler-Nchols formla an lste n able 2. he temeratre resonse an the heatng crrent for an 80 C settng ont are shown n Fg. 6(a) an (b), resectvely. In ths case, the heater nt crrent s swtche from the satraton (20A) to the PID control law at 20 C ahea the settng ont. he roortonal gan K s chosen as one-half of the vale calclate from the Zegler-Nchols formla to evalate the system erformance an transent resonse varaton. It can be observe that the system temeratre has slow rsng resonse. he temeratre resonse reaches steay state wthn 13 mnte an the steay state error s less than 0.1 C wthot overshoot. It stll can obtan goo control erformance. For the secfe temeratre change between 25 C an 100 C, K an P 266 are obtane. ISSN: ISBN:

4 he temeratre resonse an the heatng crrent for a 120 C ste settng are shown n Fg. 7(a) an (b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 18 mnte an the steay state error s less than 0.2 C wthot overshoot. 5.3 Hollow ron roller wth Fzzy PID control: he arameters K an P are estmate from the ato-tnng rocess. K an P 448 are obtane from the ato-tnng test wth the secfe temeratre change between 24 C an 80 C. he gan factors of the fzzy varables are selecte as: ge gec 0. 01, an g he learnng rate constant s chosen as 0.1. he temeratre resonse an the heatng crrent for an 80 C settng ont are shown n Fg. 8(a) an 8(b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 12 mnte an the steay state error s less than 0.2 C wth 0.45 C overshoot. he steay state error wll converge nto 0.1 C wthn 14 mntes. he varaton hstory of the fzzy control arameter s shown n Fg. 8(c). K 5.8 an P 162 are obtane from the ato-tnng test wth the secfe temeratre change between 70 C an 120 C. he gan factors of the fzzy varables are: ge gec 0. 01, an g he learnng rate constant s chosen as 0.1. he temeratre resonse an the heatng crrent for a 120 C settng ont are shown n Fg. 9(a) an 9(b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 8 mnte an the steay state error s less than 0.2 C wth 0.7 C overshoot. he varaton hstory of the fzzy control arameter s shown n Fg. 9(c). 5.4 Hollow almnm rectanglar block wth Fzzy-PID control: In orer to evelo a general-rose fzzy PID controller, the same fzzy varables gan factors an learnng rate constant as the ron cylner case are selecte for ths control lant. K 3.38 an P 424 are obtane from the ato-tnng test wth the secfe temeratre change between 45 C an 80 C. he temeratre resonse an the heatng crrent for a 80 C ste settng are shown n Fg. 10(a) an 10(b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 15 mnte an the steay state error s less than 0.1 C wth 0.4 C overshoot. he varaton hstory of the fzzy control arameter s shown n Fg. 10(c). K 3.83 an P 266 are obtane from the ato-tnng test wth the secfe temeratre change between 25 C an 100 C. he temeratre resonse an the heatng crrent for a 100 C settng ont are shown n Fg. 11(a) an 11(b), resectvely. It can be observe that the temeratre resonse reaches steay state wthn 12 mnte an the steay state error s less than 0.2 C wth 1.0 C overshoot. he varaton hstory of the fzzy control arameter s shown n Fg. 11(c). It can be concle from these exerments that the temeratre ste resonse has fnal steay-state error wthn 0.2 C wth small even no overshoot for both ato-tnng PID an Fzzy-PID control algorthms. It has satsfe the reqrement of nstral alcaton. Snce, the Fzzy-PID control scheme has varyng PID gans, t has better transent resonse erformance for hollow almnm rectanglar block wth qckly resonse see. However, the ato-tnng PID controller has smaller overshoot. 6 Conclson he heater nt only temeratre control system has tme-elay an n-symmetrc control behavor. It s ffclt to establsh reasonable ynamc moel for moel-base control esgn. wo PID gans ato-tnng control algorthms are roose for the heater nt only temeratre control system. hey can ato-search or ato-ajst the PID control gans base on the ato-tnng rocess or a fzzy strategy nstea of the tral-an-error rocess of esgnng a tratonal PID controller. It has effectvely elmnate the tme-consmng work an obtane a goo ynamc resonse. he steay-state error always converges nto 0.2 C wth very smaller overshoot even wthot overshoot. hey have satsfe the nstral alcaton reqrements. able 1 Fzzy rle bank for the ajstng arameter. ISSN: ISBN:

5 Acknowlegement hs research s sorte by the Natonal Scence Concl ner the contract NSC E MY3 an NSC E CC2. Athors wol lke to thank the fnancal sort of Natonal Scence Concl. References: [1] Zegler, J. G. an N. B. Nchols, Otmm Settngs for Atomatc Controllers, ransacton of the ASME, vol.64,.759~768, [2] Rvera, D. E., Skogesta, S., an Morar, M., Internal Moel Control. 4. PID Controller esgn, In. Eng. Chemcal Process Desgn Dev., 25,. 252~265, [3] Chen, I. L., an Frehaf, P. S., Conser IMC nng to Imrove Controller Performance, Chemcal Engneerng Process,. 33~41, [4] Astrom, K.J. an. Haggln, Atomatc nng of Smle Reglators wth Secfcatons on Phase an Amlte Margns, Atomatca, vol.20,.645~651, [5]Hang C.C., K.J. Astrom an W.K. Ho, Refnements of the Zegle-Nchols tnng formla, IEE roceengs Pt. D, Control theory & Alcatons, vol.138, no. 2, 111~118, [6] Ho, W, K.,C. C. Hang L. S. Cao, nng of PID Controllers Base on Gan an Phase Margn Secfcatons, Atomatca, vol.31, no. 3,. 497~502, [7] Astrom, K. J., C. C. Hang, P. Persson an W. K. Ho, owar Intellgent PID Control, Atomatca, vol.28., no. 1,.1~9, [8] Ho, W. K., O. P. Gan, E. B. ay an E. L. Ang, Performance an Gan an Phase Margns of Well-Known PID nng Formlas,IEEE rans. On Control Systems echnology, vol.4,.473~477, [9] Ho, W. K., C. C. Hang an J. H. Zho, Performance an Gan an Phase Margns of Well-Known PI nng Formla, IEEE rans. On Control Systems echnology, vol.3, no. 2,.245~248, [10] Malk, H. A., Msr, D., Fegensan, D., Chen, G., Fzzy PID Control of a Flexble-Jont Robot Arm wth Uncertantes from me-varyng Loas, IEEE ransactons on Control Systems echnology, vol. 5,.371~378, [11] A. Vsol, nng of PID controllers wth fzzy logc, IEE Proc. Pt. D.-Control heory Alcatons, Vol. 148, No. 1,. 1-8, [12] A. Vsol, Fzzy logc base set-ont weghtng for PID controllers, IEEE rans. System, Man, Cybernetcs, Pt. A, Vol. 29, , [13] Sh-Zhong He, Shaoha an, Feng-Lan X,an Pe-Zhang Wang, Fzzy self-tnng of PID controllers, Fzzy Sets an systems, vol.56,.37~46, able 2 Ato-tnng PID control arameters Fg. 1 he exermental system set-. Fg. 2 he estmatng of crtcal ero an crtcal gan from on-off control. ISSN: ISBN:

6 e yr Fg. 3 Fzzy-PID control system block agram. Fg. 6 (a) emeratre 80 C ste resonse an (b) the heater nt crrent of a almnm rectanglar block wth ato-tnng PID control. Fg. 4 (a) emeratre 80 C ste resonse an (b) the heater nt crrent of an ron cylner wth ato- tnng PID control. Fg. 5 (a) emeratre 120 C ste resonse an (b) the heater nt crrent of an ron cylner wth ato-tnng PID control. Fg. 7 (a) emeratre 120 C ste resonse an (b) the heater nt crrent of a almnm rectanglar block wth ato-tnng PID control. ISSN: ISBN:

7 Fg. 8 (a) emeratre 80 C ste resonse, (b) the heater nt crrent an (c) the ajstng arameter of an ron cylner wth Fzzy-PID control. Fg. 10 (a) emeratre 80 C ste resonse, (b) the heater nt crrent an (c) the ajstng arameter of an almnm rectanglar block wth Fzzy-PID control. Fg. 9 (a) emeratre 120 C ste resonse, (b) the heater nt crrent an (c) the ajstng arameter of an ron cylner wth Fzzy-PID control. Fg. 11 (a) emeratre 120 C ste resonse, (b) the heater nt crrent an (c) the ajstng arameter of an almnm rectanglar block wth Fzzy-PID control. ISSN: ISBN: