An Application of Fuzzy c-means Clustering to FLC Design for Electric Ceramics Kiln

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1 An Applcaton of cmeans Clusterng to FLC Desgn for lectrc Ceramcs Kln Watcharacha Wryasuttwong, Somphop Rodamporn lectrcal ngneerng Department, Faculty of ngneerng, Srnaharnwrot Unversty, Nahornnayo 6, Thal ABSTRACT Ths paper presents an applcaton of fuzzy cmeans clusterng to desgnng the fuzzy logc controller for the temperature control n electrc ceramcs ln. Ths research ams to controllng the temperature n frng step of burnng the ceramc products whch were coated wth blac, ntensely red green chemcal substances. The epermental results show that the fuzzy cmeans clusterng desgned FLC gves better temperature characterstcs when compared to the conventonal FLC the hard cmeans clusterng desgned FLC. KYWORDS logc controller, fuzzy cmeans clusterng, controller desgn, electrc ln. Introducton In the ceramcs producng process, both the temperature the tmng control s very crtcal to the qualty of products. The product qualtes ncludes the color, the smoothness, clear surfaces endurance of the ceramcs produced. In [4],[5] [] the controllers used are the fuzzy logc controllers n the desgn of the fuzzfcaton part of the controllers, all the fuzzy sets are appromated.e. the shape of the membershp functons, the startng ponts ranges for each fuzzy set, the slopes for all the set the overlappng areas. The desgns were carred on usng the desgner s eperences wthout any acceptable reasons. In ths paper, we are proposng to overcome the stated problem by usng the cmeans clusterng method to fnd approprate fuzzy sets for each worng parameter of the ceramcs ln. In ths research, the control system conssts of a fuzzy FCM controller, thermocouple, SCR power control unt, A/DD/A converter an electrc ln as shown n Fg... Conventonal FLC Desgn The three man parts of a Logc Controller are the fuzzfcaton part, fuzzy nference part the defuzzfcaton part as shown n Fg.. reference sgnal + Fuzzfcaton system response fuzzy 'statse' Rule Base Inference Plant fuzzy control Defuzzfcaton non fuzzy control sgnal Fgure. The Structure of Kln Control System FCM Controller Mcrocomputer A/D D/A Transmtter SCR Power Control lectrc Ceramcs Kln Thermocouple Fgure. The Structure of Logc Controller Generally, n the desgn process of the fuzzy nference part [], fuzzy rules are created from the closed loop control system as shown n Fg. 3. The nput varables of the fuzzy logc controller are the error () the error rate (). The output of the

2 controller s the control voltage (CV). Let the step response of the feedbac system be as llustrated n Fg. 4. The phase plane can be constructed wth the two nputs, as llustrated n Fg. 4. Let us desgn a set of fuzzy control rules to reduce the overshoot the rse tme. Referrng to the phase plane of the system step response shown n Fg. 4., the fuzzy control rule can be formulated as table. Fgure 3. The Closed Loop Control System Fgure 4. TmeResponse of Controlled System Table. Shows Rules Generated Rule NB NS AZ PS PM PB NB NB NS NS NS AZ PM AZ NB NS AZ PS PM PB PS AZ PS AZ PM PM PB PM PB For the defuzzfcaton part, a method of defuzzfcaton s to be selected from the popular ones, center of gravty (COA), mean of mamum (MOM) etc. And then for the fuzzfcaton part, fuzzy sets are created appromately as shown n Fg SP + NB Y SP a b Logc Controller c d Membershp grade NS AZ PS PM PB Fgure 5. Typcal Sets n Conventonal Desgned Logc Controller As seen n Fg. 5. conventonal desgn of the fuzzy sets follows the followng rules : Generally used e CV A B C D F G H I J K f g lectrc K l n h Temp l Tme o C membershp functon s the trangularshaped functon, the ranges for each set are equally dvded from the unverse of dscourse of the parameter, the pea ponts are at the mdrange ponts adacent sets overlap to the mdrange ponts etc. It can easly be seen that these rules have very lttle relatonshps to the behavor of the controlled system the desgners cannot eplan clearly why to follow these rules. 3. cmeans Fuzzfcaton Desgn 3. Set Determnaton by FCM Method Frstly, controlled system or plant s to be controlled by any avalable controller to operate over ts whole range of operaton then the nput output varables of the plant are recorded. The operatng data of the controlled system s analyzed by the fuzzy cmeans clusterng method to separate nto groups or clusters of data each cluster of data s then nterpreted nto a fuzzy set of the varable. 3. Hard cmeans Clusterng Method The hard cmeans algorthm [3, 8] parttons a collecton of n vector, =,.n, nto c groups G,I=,,c, fnds a cluster center n each group such that an obectve functon of dstance measure s mnmzed. When the ucldean dstance s chosen as the dstance measure between a vector n group the correspondng cluster center c, the obectve functon can be defned by The parttoned groups are defned by an c n bnary membershp matr U, the element u s f the th data pont belongs to group, otherwse. Once the cluster centers c are fed, the mnmzng u can be derved as follows: u otherwse. Snce a gven data pont can only be n a group, the membershp matr has the followng propertes: c c J = J = = =, G = f c u = c () If u s fed, then the optmal center c that mnmze equaton() s the mean of all vectors n group : c c =, =,,3,..., n c n u = = = n, for each, () (3) (4)

3 c = G, G (5). F c ( c < n) select a value for parameter m. Intalze the partton matr, U (). ach step n ths algorthm wll be labeled r =,,,.... Calculate the c centers {v ( r ) } for each step. 3. Update the partton matr for the rth step, U ( r) as follows: 3.3 cmeans Clusterng Method The Hard cmean could be mproved wth use of fuzzy set method. To develop these method n classfcaton, we classfy the varous data ponts as a fuzzy cpartton [3, 8] on a unverse of data ponts assgn membershp value to t that determne from the data of each pont the data of a cluster center n each group. Hence, a sngle pont can have partal membershp n more than one class the membershp value that the th data pont has n the th class wth the followng notaton: In the determnaton of the fuzzy cpartton matr U for groupng a collecton of n data sets nto c classes, we defne an obectve functon J m for a fuzzy cpartton, n G = u = µ = µ ( ) [,] A n c m Jm( U, v) = (µ ) (d ) = µ s the membershp of the th data pont n the th class, d s dstance measure or ucldean dstance between the th cluster center the th data pont n mspace, m s a weghtng parameter whch has a range m [, ) v s th cluster center, whch s descrbed by m coordnates can be arranged n vector form, v = {v, v,,v m }. ach of the cluster coordnates for each class can be calculated as µ = v = () n m µ = s a varable on the coordnate space,.e., =,,,m. The optmum fuzzy cpartton wll be the smallest of the parttons descrbed n quaton (8 ) ; The effectve algorthm for fuzzy classfcaton s called teratve optmzaton as follows (6) m / d = d( v ) = [ ( v ) ] = n m * * * J m( U, v ) = mn J( u, v) M fc () (9) (7) (8) or /( m ) c (r) (r ) + d µ = for (r) I = φ = d (r+ ) ~ µ = for all classes I (r) I = { c < n; d = } ~ I = {,,..., c} I (r+ ) µ = I () (3) (4) (5) (6) 4. If U (r+) U ( r ) ε L, stop; otherwse set r = r+ return to step. 4. Research Methodologes In the desgn process of the FLC, fuzzy rules are defned for two nput varables, the error () the error rate (), sngle output varable, the control voltage (CV) whch are used as the nput output varables of the plant respectvely. The desgn were carred on usng the plant of electrc ceramcs ln wth the procedures: 4.) Wth the autotunng PID controller operate the plant n steps over ts full range of operaton at each step, record the values of the nput output varables of the plant whch can be shown n Fg. 6., for setpont at 5 C Fgure. 6. The Recorded Values of

4 Fgure. 7. The Recorded Values of (c) The Set of CV Fgure. The Sets from FCM Method voltage (volts) Fgure. 8. The Recorded Values of CV 4.) The fuzzy cpartton from 4. are then analyzed by fuzzy cmeans clusterng algorthms for 7 clusters of data for the nput varables the output varable as shown n Fg. 9. The obtaned clusters were then normalzed to get the fuzzy sets as shown n Fg.. 4.3) Implement the fuzzy logc controller wth fuzzy sets obtaned n 4. operate the controller. 5. permental Results The fuzzy cmeans clusterng desgned FLC was tested on the setpont of 5 C for the electrc ln of 45 cm. n hgh, 35 cm. n nternal dameter, 45 cm. n eternal dameter. The results were compared to the results by conventonal desgned FLC hard cmeans clusterng desgned FLC on the same setpont, the proposed controller were able to gve the output response as followng : 5.) Operatng characterstcs temperature ( C) vs tme (mn.) of the ceramcs ln control by conventonal desgned fuzzy logc controller s shown n Fg Fgure 9. The Converged Partton for Temperature n lectrc Ceramcs Kln Fgure. Temperature Characterstcs of The Conventonal FLC 5.) Operatng characterstcs temperature ( C) vs tme (mn.) of the ceramcs ln control by hard c means clusterng desgned fuzzy logc controller s shown n Fg.. (a) The Set of Fgure. Temperature Characterstcs of The Hard cmeans Desgned FLC (b) The Set of

5 5.3) Operatng characterstcs temperature ( C) vs tme (mn.) of the ceramcs ln control by fuzzy c means clusterng desgned fuzzy logc controller s shown n Fg Fgure 3. Temperature Characterstcs of The cmeans Desgned FLC 6. Concluson Ths paper has nvestgated the applcaton of fuzzy cmeans clusterng algorthms n the desgn of the fuzzy sets for the fuzzy logc controller of the electrc ceramcs ln temperature control. Ths method of the desgn s epected to solve the problem of the classcal or conventonal desgn method. The results from the eperments show that the fuzzy cmeans clusterng desgned FLC gves better output response when compared to the conventonal FLC the hard cmeans clusterng desgned FLC. Moreover t gves products wth a hgh qualty of color, very close to the stard ceramcs products. Development of Adaptve Logc Control System for Temperature Control n lectrc Kln. Proc. of The 999 Natonal Computer Scence ngneerng Conference. Bango, 999, pp 8. [6] Karat Ceramc Ltd. Report of Ceramcs Producton Operaton. 995, pp 4,8. [7] KeowKamnerd, Kanchana. nergy ffcent Kln Constructon Operaton Manual. Bango:ThaGerman nergy ffcency Promoton Proect (NP), 997. [8] Ross, Tmothy J. Logc wth ngneerng Applcatons, McGrawHll, Sngapore., 995. [9] Wang, Hua O. ; Tanaa, Kazuo Grffn, Mchael F. An Approach to Control of Nonlnear Systems: Stablty Desgn Issues. I Transactons on Systems, vol, 996, pp 43. [] Xangang, Zhang.; Jng, Zhang Hua, Chen. The applcaton of data fuson based on fuzzy theory n temperature udgement of rotary ln. Proceedngs of the 3 rd World Congress on Intellgent Control Automaton., vol l3,, pp [] Yan, Jun.; Ryan, Mchael. Power, James. Usng Logc. PrentceHall, London, 994. Acnowledgements The authors apprecate the nd suggestons of Prof.Kaornsa Kantapant, Mr.Hn Chanasuta. than for help n programmng of Mr.Vasutan Tunbunheng. References [] Bezde, J. Pattern Recognton wth Obectve Functon Algorthms, Plenum, New Yor, 98. [] Bezde, J.C. Pal, N.R. On Cluster Valdty for the cmeans Model, I Transactons on Systems., 995, pp [3] Jang, JyhShng Roger.; Sun, ChuenTsa. Mzutan,. Neuro Soft Computng : A Computatonal Approach to Learnng Machne Intellgence, Prentce Hall, New Yor., 997. [4] Ja, Y ; Ln, Wang. And Shuangye, Chen. The applcaton of fuzzy neural networs to the temperature control system of olburnng tunnel ln. Proc. ICIPS 97 I Internatonal Conference on Intellgent Processng Systems. Vol., 997, pp 556. [5] Kantapant, Kaornsa. Chanasuta, Hn.