Fuzzy controller tunng of a boost rectfer unty power factor correcton by expermental desgns Jérôme Faucher, Stéphane Caux, Pascal Mausson To cte ths verson: Jérôme Faucher, Stéphane Caux, Pascal Mausson. Fuzzy controller tunng of a boost rectfer unty power factor correcton by expermental desgns. Electrcal Engneerng, Sprnger Verlag, 2009, vol. 9, pp. 67-76. <0.007/s00202-009-03-0>. <hal-0094807> HAL Id: hal-0094807 https://hal.archves-ouvertes.fr/hal-0094807 Submtted on 7 Feb 204 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.
Open Archve TOULOUSE Archve Ouverte (OATAO) OATAO s an open access repostory that collects the work of Toulouse researchers and makes t freely avalable over the web where possble. Ths s an author-deposted verson publshed n : http://oatao.unv-toulouse.fr/ Eprnts ID : 097 To lnk to ths artcle : DOI: 0.007/s00202-009-03-0 http://dx.do.org/0.007/s00202-009-03-0 To cte ths verson Faucher, Jérôme and Caux, Stéphane and Mausson, Pascal Fuzzy controller tunng of a boost rectfer unty power factor correcton by expermental desgns. (2009) Electrcal Engneerng (Archv fur Elektrotechnk), vol. 9 (n 3). pp. 67-76. ISSN 0948-792 Any correspondance concernng ths servce should be sent to the repostory admnstrator: staff-oatao@lstes-dff.np-toulouse.fr
FUZZY CONTROLLER TUNING OF A BOOST RECTIFIER UNITY POWER FACTOR CORRECTION BY EXPERIMENTAL DESIGNS J.D. Faucher 2, S. Caux 2 and P. Mausson 2 Unversté de Toulouse ; INPT, UPS ; LAPLACE (Laboratore Plasma et Converson d Energe) ; ENSEEIHT, 2 rue Charles Camchel, BP 722, F-307 Toulouse cedex 7, France. 2 CNRS ; LAPLACE ; F-307 Toulouse, France. pascal.mausson@laplace.unv-tlse.fr Abstract: Ths paper shows the valdty of expermental desgns as an effcent on-ste tunng tool for fuzzy controllers, dedcated to electrcal engneerng applcatons wth mult-objectve crtera. Our purpose s to mprove the nput and output system characterstcs that s to say the global qualty of the electrcal power n a boost rectfer wth unty power factor correcton. The desrablty noton combnes here tme dynamc and harmonc crtera, t llustrates the trade-off that has to be satsfed between the dfferent propertes. Keywords: fuzzy control, expermental desgns, tunng methodology, mult-objectve crteron, boost rectfer, power factor correcton, desrablty.. INTRODUCTION Our work deals wth the tunng of fuzzy controller n order to mprove the control of electrc systems. Fuzzy-logcbased controllers are used n varous applcatons, manly because of advantages such as the dynamc performance, the robustness or the possblty to take nto account an expermental knowledge of the process. Nevertheless, some drawbacks have to be underlned: frst, the huge number of parameters that have to be tuned even for a very smple fuzzy structure and the lack of an effcent on-ste tunng strategy for all these parameters. The fuzzy controller parameters could of course be tuned trough tral-and-error procedure, but t could be qute long and rather delcate. On the other hand, some methods have already been proposed, for the tunng of fuzzy controllers, usng adaptve algorthms (Barrero, 995) and (Kang et al, 992), addtonal fuzzy rules (Takag, 992), neural networks (Perneel et al, 995), H and LMI methods (Lu et al, 200) and (Park, 2004) or genetc algorthms (Hoffmann, 200). These tunng methods are successful but are generally far from smple. Besdes, a smple tunng methodology based upon expermental on-lne desgns for all the parameters of a PID-lkefuzzy-logc controller have already been proposed (Hssel et al., 999) few years ago. Ths method, based on tme crteron only, for fuzzy controller tunng gave expermental and smple pre-establshed settngs just lke the wellknown Zegler-Nchols methods for the classcal PID controllers. Our am s now to show that expermental desgns methodology could be an effcent tool n order to tune fuzzy controllers for applcatons that requre mult-objectve crtera. In ths paper, the methodology wll be appled to a sngle phase boost rectfer wth unty power factor correcton. Ths knd of converter s strongly nonlnear, t means that lnear controllers are not truly effcent, especally when sudden and hard parameter varatons due to hgh load varatons occur. Then a fuzzy controller should be an effcent soluton for the control of such a converter. Two crtera have to be regarded: a tme-response-based crteron on the output voltage and an harmonc crteron based on the nput current dstorton on the grd. Fuzzy controllers have already been used for ths system control (Yu et al. 996), (Henry et al., 999), (Pres et al., 999) and (Mattavell et al., 995), and the harmonc reducton by fuzzy control has been shown n (Palandöken, 2003) but there s stll a lack of effcent tunng methodology. Ths paper wll show how the expermental desgns could be an effcent tool, n smulaton or on the expermental process, for the on-ste tunng of a nonlnear controller under those specfcs constrants. Ths s the man contrbuton of our work. Secton 2 descrbes the system and ts classcal lnear control s presented n secton 3. The structure of the fuzzy controller s gven by secton 4 whle secton 5 descrbes the expermental desgn methodology, appled n secton 6 for the tunng of the fuzzy controller. Smulaton results are presented n secton 7, expermental results n secton 8 and ther comparson n secton 9. Fnally, secton 0 concludes the paper and gves some trends for future works. 2. System descrpton 2. SYSTEM DESCRIPTION The system s a sngle phase boost rectfer wth unty power factor correcton and kw nomnal power. In a classcal soluton wth a dode brdge rectfer, an addtonal capactor reduces the voltage rpple. However, ths capactor also reduces the dode conducton angles and generates harmonc dstorton on the electrcal network descrbed by V n (network voltage) and L n (network nductance). In order to solve theses problems, a boost converter s added to the
system. The capactor C out s the output flter for the load that needs a constant voltage. The values of these dfferent components are gven n table. I rec L boost D I load K vmeas L n V rec V DC T C out R V n C f K vn ABS I ref + - Current control PWM Reference V DC + - Voltage Control Low pass flter Fg.. System structure V n 325V R load 00 L n 0. mh R 0 2000 Cf 25 F K vmeas /00 L boost 4 mh K vn /325 C out 500 F Ref V DC 4 V Tab.. System parameters values Hard and sudden load varatons are appled to the system n order to evaluate the performance of the control strategy. The benchmark test s the followng: from steady-state operaton under no load condtons (R = R 0 ) to sudden maxmum load connecton (R=R load ), and sudden dsconnecton. In addton, t s mportant to notce that capactor C f prevents hgh frequency harmoncs from gong back to the network. A cut-off frequency F c chosen above the hgher frequency (the 00 Hz frequency of the rectfed voltage V rec ) and around one decade below the swtchng frequency (20 khz) s sutable. We fx C f = 25 F, that means F c = 500 Hz (). Fc () 2 L. C f A complementary study shows that ths C f value also reduces the current dstorton under no load condtons. 2.2 Behavour requrement The boost rectfer has some characterstcs that mpose a constrant on the output voltage. When transstor T s ON, the dode D s OFF (V D = - V DC ) and : f di dt rec V L rec boost 0 (2) When transstor T s OFF, the dode D s ON (I D = I rec ) and : di dt rec Vrec V L boost DC 0 (3) di rec Thus, whatever the state of the transstor, whlevdc Vrec, 0. In such a confguraton, the system s not dt controllable untlvdc Vrec. In concluson, ths system requres thatvdc Vrec, that s why t s called boost.
3. LINEAR CONTROL The control of ths knd of system s usually done by lnear controllers. Performance of such controllers wll be the reference for a comparson wth the fuzzy controllers and also ther ntal parameter values. There are two control loops (fgure ), one for the dc output voltage and the other for the rectfed nput current. 3. Current loop The objectve of ths fast loop s to get a snusodal current n phase wth the electrcal grd voltage. Thus, t reduces the harmonc rejecton and mantans a unty power factor. A lnear PI controller s used n combnaton wth a PWM module. The hgh frequency harmoncs are then reduced wth ths knd of control. The shape of the current reference s generated from the network voltage (va K vn ) and ts ampltude from the DC voltage (va the voltage controller) as shown n fgure. The transfer functon of the PI current controller s: H current ( p) ( p. T ) c Gc. (4) and s 3 +.75 n s 2 + 3.25 s 2 3 n + n p. Tc (5) The PI controller s tuned accordng to (Dorf, 990), n order to make the denomnator of the current closed loop transfer functon ft a specfc equaton (5) that mnmzes the ITAE crteron. These consderatons lead to the followng coeffcents (6) : Gc = 2. and Tc = 0,28 ms (6) Fgure 2 shows the smulaton results wth the PI controller. One can check the effcency snce the rectfed current s closed to ts reference and contans very few low frequency harmoncs. V DC Load No load THD t Fg. 2. Current control: I rec and I ref IAE Fg. 3. Crteron measurement and benchmark test. 3.2 Voltage loop Ths slow loop must control the output voltage V DC wth respect to load, nput voltage and nput current varatons. A classcal PI controller tunng s based on the average model of the system. Ths method reles on the equlbrum of the nstantaneous powers between the output of the rectfer and the DC part (Yu, 996). If the current loop s fast enough compared to the voltage loop, approxmaton (7) could be done, and the transfer functon s gven by (8). V I DC rec ( p) VDC ( p) (7) ( p) I ( p) ref VDC ( p) Vrec Rload. (8) I 4. Rload. C ref V out p. 2 where V s the V DC average value. As the transfer functon of the voltage controller s gven by equaton (9), optmum symmetrcal methodology leads to the followng coeffcents (0). H voltage ( p) ( p. T ) v Gv. (9) p. Tv G T v v 7.5 0.062 (0)
3.3 Dfferent tunng crtera The control qualty for the whole system wll be evaluated trough two crtera. The frst one s the IAE (ntegral of absolute error, expresson (). Ths crteron appled to V DC wll show the robustness and the dynamc performance of the controller. In addton, a second crteron, the harmonc dstorton rate (THD) n (2), represents the harmonc rejecton qualty at the nput. I k k2 IAE e( t). dt () THD. 00 (2) The CEI 6000-3-2 nternatonal standard defnes the electromagnetc compatblty and lmts the harmonc current emssons for the 39 frst harmoncs. It gves the maxmum allowable current ampltude for each harmonc. Fgure 3 shows how and when the two dfferent crtera are calculated durng the benchmark test. The IAE crteron s taken nto account throughout the test. The harmonc dstorton s only computed durng steady-state operaton under rated load condton,.e. rated current. 4. FUZZY CONTROLLER A fuzzy controller wll be used n the rest of ths paper n order to mprove the dynamc performance. The controller s a PI-lke fuzzy controller (FLC) (see fgure 4). Ths structure was chosen because the error s second dervatve does not have to be calculated. Indeed, ts value could be mportant as t may amplfy nose. The nherent dffculty of such a knd of controller s the huge number of parameters. The fuzzy part conssts nto two nputs / one output Sugeno FLC (Hssel et al. 999) wth seven trangular membershp functons on each nput and seven sngletons at the output. There s a normalsaton factor for each nput (em for the error sgnal and dem for the error dervatve) and for the output (gm). % 39 39 k I k e de em dem gm Fuzzy controller Normalsaton Denormalsaton Fg. 4. Fuzzy controller structure. Integral acton Control acton Sp Experment Factor Factor Interacton Crteron number 2 2 - - + y 2 + - - y2 3 - + - y3 4 + + + y4 Effects E E 2 E 2 Fg 5 : Example of an expermental table A zero-symmetry s mposed for both trangular membershp functons and sngletons n order to provde a smlar response for postve and negatve nputs. A classcal ant-dagonal rule table, wth fxed parameters, s used. By fxng em to the reference value, only 8 parameters have to be tuned among the ntal 73 ones (7*7 rules, 3*7 membershp functons and 3 gans). The tunng parameters are: dem, gm, PSe and PVSe (membershp functons on error), PSde and PVSde (membershp functons on error dervatve), gven by fgure 6 and PSs and PVSs (output sngletons), gven by fgure 7. For example, PSe s the label of the Postve Small membershp functon on the error and PVSde s the label of the Postve Small membershp functon on the dervatve of the error. The postons of these membershp functons have to be tuned. Anyway, the tunng problem remans effectve as 8 control parameters are to be tuned accordng to two crtera. Symmetry Moble sngletons Symmetry Moble sngletons Unverse of dscourse Fg. 6. Membershp functons for error and dervatve of error nputs Fg. 7 : Output sngletons Unverse of dscourse
Fuzzy logc s only used for the PI lke controller on the voltage loop. Due to frequency lmtaton of our DSP, the 4 current loop must be contnuous (the samplng perod s Te.0 s ). Moreover, two fuzzy controllers for the same system would dramatcally ncrease the number of parameters that have to be tuned. 5. EXPERIMENTAL DESIGNS PRINCIPLES The hstory of expermental desgns began n the 30 s n England wth M. Fsher, (Fsher, 935) but t had an ncreasng development snce Taguch publshed predefned tables (Taguch, 987). Ths methodology realzes a schedule of the experments n order to obtan the most accurate nformaton for a specfc problem wth a mnmum number of experments (Dey et al., 999). The dea s to modfy the level of each factor for each experment accordng to a specfc procedure. It allows a drastc reducton of the number of experments, an ncrease n the number of parameters, the detecton of nteractons between factors and gves an optmzed soluton. Consderng for example only two levels for each of the 8 factors descrbed above, the classcal expermental tunng method that conssts n varyng one of the parameters when all the others are mantaned constant, leads to 2 8 =256 requred experments. Wth expermental desgns methodology, only 6 experments out of 256 are necessary to fnd the sutable combnaton for the 8 factor levels n order to mnmze the selected crteron We use centred reduced varables,.e. - for the low level and + for the hgh level of each factor. Then, an expermental table, as shown n fgure 5, could be used. Each lne represents an experment and each column s a factor, an nput MF, an output sngleton poston or a gan. For each experment, the crteron s calculated through smulaton or measured durng experments. y y2 y3 y4 y y2 y3 y4 E (3) E 4 2 (4) 4 Accordng to the expermental desgn methodology (Dey et al., 999), the effect of a factor s obtaned through equaton (3). For example, E = 0.2 means that factor at hgh level has an effect of +0.2 on the crteron. Moreover, the effect of nteractons between factors can also be nvestgated wth ths methodology. Expresson (4) leads to the effect of nteracton E 2 between factor and 2, on the desred crteron. Furthermore, the same column could also be used to study a thrd factor. From these effects, an optmal tunng could be reached, wth a last experment n order to confrm the desgn. If the results are rrelevant, then the hypotheses must be reconsdered. The experment table s bult lke an Hadamard matrx (Droesbeke, 997) that verfes equaton (5), where n s the number of experments. Such a structure gves the best accuracy on effects. Indeed, the standard devaton on the effect ( E ) s a fracton of the standard devaton on the crteron ( y ), as shown n equaton (6) : t N _ 2 y 2 X. X ni (5) E (6) s y, j y (7) n N j A major problem s the determnaton of the expermental error. The accuracy of the estmaton s, the expermental standard devaton on the crteron y, depends on the number of experments. By repeatng N tmes each experment of the desgn table, the estmaton s for each experment s mproved. y,j s the j th repetton of the th experment and y _ s the average of the N repettons of the th experment. The varance s gven by equaton (7). The classcal sovarance assumpton s consdered and equaton (8) can be wrtten. Afterwards the estmaton of the expermental standard devaton on the effect, s E, s expressed n (9). s _ 2 s n n s 2 (8) s s E N. n (9) n.( ) The confdence nterval s thus balanced by the varable of Student t N at n.(n-) degrees of freedom wth the probablty to be exceeded n absolute value. As a consequence the confdence nterval for a probablty s n.( N t ) s around the average effect value. E 6. Parameter values 6. TUNING METHODOLOGY In ths controller, 8 parameters have to be tuned. The ntal levels of parameters are always dffcult to choose, an accurate expertse on the system s requred. The values of the contnuous PI controller parameters wll be used as
ntal values. Regardng S PI as the fuzzy controller output, on fgure 4, equaton 20 can be defned. k p s the proportonal gan and k d s the dervatve one of the frst part of the fuzzy controller. S S S PI PI PI k p gm. gm. em ( e, de). e k d ( e, de). de. dt de( t) e( t). k( e, de). dt gm. k e de dt em.. 2(, ). dem dt gm. de( t) e( t). k( e, de). dt.. k2( e, de). dt dem dt Then, equaton 20 reveals two dfferent actons: ntegral and proportonal of the complete PI-lke-fuzzy controller whch can be used for ntal tunng. If the error s sampled at the samplng perod Te, expressons (2) can be wrtten, and from the transfer functon H voltage, t comes (22) : gm Gv e( t) e( k) e( k) e( k) (2) em Tv (22) de( t) Te gmte. G v dem The levels of the membershp functons are chosen on both sdes of the values of the equ-dstrbuted membershp functon postons. Smlar choces are made for gm and dem coeffcents. 6.2. Expermental table As there are 8 parameters, a 2 8-4 IV Hadamard expermental table s used, whch mples only 6 experments. Table 2 presents the expermental desgns table. exp F PS e F2 PVS e F3 PS de F 4 PVS de F5=234 and PS s F 6=34 and PVS s F7=23 and g m - - - - - - - - 2 + - - - - + + + 3 - + - - + - + + 4 + + - - + + - - 5 - - + - + + + - 6 + - + - + - - + 7 - + + - - + - + 8 + + + - - - + - 9 - - - + + + - + 0 + - - + + - + - - + - + - + + - 2 + + - + - - - + 3 - - + + - - + + 4 + - + + - + - - 5 - + + + + - - - 6 + + + + + + + + Tab. 2. Frst set of factors levels n a 2 8-4 IV expermental table (20) F 8=24 and de m The two crtera (IAE and THD) are calculated durng smulatons or measured durng the experments. It s mportant to notce that each experment s run once n smulaton but has to be repeated durng expermental tests, n order to reduce the expermental standard devaton on the effect, as seen n secton 5. 6.3 Desrablty The desrablty noton was ntroduced by E.C. Harrngton (Harrngton, 965). It combnes several dfferent propertes Y wth dfferent scales and unts (Derrnger et al. 994). Each of them s transformed n an elementary desrablty functon d, as seen n equaton (23). A desrablty functon s ranged between zero and one. A zero level corresponds to an unacceptable value for the crteron whle a desrablty of one represents the maxmum desred performance. Many dfferent transformatons could be chosen. The most classcal one was adopted due to ts smplcty, t s descrbed below. The value of Y,p s the mnmum acceptable value for Y and Y,c s the value above whom an ameloraton of Y s not very nterestng.
d 0 Y Y Y, p Y, p Y, c Y, p Y Y, c r Y, p Y Y, c w (23) D d The parameters r balance the mportance of the ncrease of the property on the elementary desrablty (Fg. 7). Then, all the elementary desrabltes are combned nto a composte desrablty such as n equaton (24) : w (24) 520 500 r < 480 460 Fuzzy PI d r = Voltage (V) 440 420 400 380 r > 360 340 320 Analogcal PI Y,p Y Y,c 300 0 0.5.5 2 2.5 3 3.5 4 4.5 Tme (s) Fg.8 Elementary desrablty Fg.9 Smulated output voltage responses 7. SIMULATION RESULTS Two successve desgns are carred out n smulaton usng desrablty n order to combne the dynamc and the harmonc crtera. The frst one s a global and rough desgn whch gves sgnfcant levels for the tunng parameters, the second one mproves the tunng. The expermental desgn, descrbed n table 2 gves then nterestng results. 500 480 Expermental results 0 460 440 Lnear PI 5 Voltage (V) 420 400 380 Current (A) 0 360 340 Fuzzy PI -5 Irec Inet 320-0 300 0 0.5.5 2 2.5 3 3.5 4 4.5 Tme (s) Fg.0 Expermental output voltage responses 2.265 2.27 2.275 2.28 2.285 2.29 2.295 Fg. Input currents wth fuzzy control Fgure 9 shows the smulaton results for the fuzzy controller and the contnuous PI. Gvng parameter levels, ths tunng, set0, s tested also on the expermental process, leadng to expermental output responses, fgure 0 and. Dynamc performance wth the fuzzy controller s mproved and the harmonc dstorton remans low, cf table 8. Only 2 sets of 6 experments are necessary durng ths optmzaton procedure based on the model of the system. But t can be seen that there are some mportant dfferences between smulaton and expermental results for a sngle set of parameters (oscllatons remans durng steady state and the overshoot wth expermental fuzzy PI controller s not neglgble). In fact, the model of the system whch was used for the smulatons tests was not a very fne model and some addtonal components should be added n order to mprove t. But there s another way to mprove performance: an
on-ste and expermental tunng of the controller on the system tself, accordng to expermental desgns methodology. The prce to pay s an ncreased number of experments n order to mprove accuracy. 8. EXPERIMENTAL RESULTS Instead of system model mprovement for a better controller tunng, we appled the expermental desgns method drectly to the system, wth all ts characterstcs. The whole methodology s detaled hereafter. 8. Sngle crteron The tunng procedure s then realzed on the expermental process. Two successve sets of experments are agan carred out. Parameters of the frst rough desgn are gven n Tab. 3 from values of the contnuous PI controller: PSe 0.6 PSs 0.6 PVSE 0.3 PVSs 0.3 PSde 0.6 Gm 486 PVSde 0.3 dem 6.5e-3 Tab. 3. Intal fuzzy parameter values The factor levels are chosen on both sdes of ntal parameter values: PSe 0.5-0.7 PSs 0.5-0.7 PVSe 0.2 0.4 PVSs 0.2 0.4 PSde 0.5-0.7 Gm 490 570 PVSde 0.2 0.4 dem 5.5e-3 7.5e-3 Tab. 4. Frst set of factor levels. Consderng both crtera n desrablty, the expermental desgn methodology leads to the followng set of roughly optmzed parameters, n Tab.5 : PSe 0.5 PSs 0.7 PVSE 0.2 PVSs 0.4 PSde 0.7 Gm 530 PVSde 0.2 dem 5.5e-3 Tab. 5. Frst set of roughly optmzed parameters The factor levels for the second and fne desgn are gven by Tab. 6 after the frst desgn results. PSe 0.4-0.6 PSs 0.6-0.8 PVSe 0. 0.3 PVSs 0.3-0.5 PSde 0.6 0.8 Gm 490 570 PVSde 0. 0.3 dem 45e-4 65e-4 Tab. 6. Second set of factors levels. The two crtera (IAE and THD) are measured for each experment. The latter s repeated three tmes for accuracy mprovement, (confdence nterval defned as 99.9%. Factor effects are gven by Table 7. Interacton effects are less nfluent than man parameter effects and are not gven here. IAE*0-2 V.s TDH*00 % IAE*0-2 V.s TDH*00 % PSe.4-3. PSs -2-3.2 PVSe 3.9-2.9 PVSs -2.5 8.6 PSde 0.7-4.3 Gm -2.2.5 PVSde 5.6-2 dem 2.9-7.2 Average 22.5 364 Confdence nterval 0.27 4.04 Tab. 7. Factor effects on both crtera It appears that the factor effects are strongly dfferent for each crteron. The factor PVSde s always the domnant one and ts nfluence s opposte for each crteron, as shown by Table 7. From the factor effects gven by the expermental desgn, a set of optmal parameters for the fuzzy controller can be defned for each crteron: the frst one, Set, for the IAE crteron only and the second, Set 2, for the harmonc crteron only. Fgure 2 presents the
output voltage V DC for the two optmal settngs and fgure 3 depcts the nput current for the second settng only. The crtera values are gven n table 8. 480 460 440 Set 2 0 5 Output Voltage (V) 420 400 380 360 340 Set Current (A) 0-5 -0 Irec Inet 320 0 0.5.5 2 2.5 3 3.5 4 4.5 Tme (s) Fg. 2. Expermental output voltage responses for set and set 2 2.265 2.27 2.275 2.28 2.285 2.29 2.295 Tme (s) Fg. 3. Expermental nput currents for Set 2 only From theses crtera, expermental desgns can not gve a composte optmal tunng. The soluton may consst n a combnaton of the crtera n a composte crteron wth the desrablty noton. 8.2 Composte crteron From the gven results, the man dfference between harmonc rejecton for Set and Set 2 s the value of the thrd harmonc (0.325 A for Set and 0.3 A for Set 2), the others remanng equvalent. Ths preponderant harmonc ampltude s then transformed nto elementary desrablty dh 3. Values Yh 3,c and Yh 3,p are equal to Set and Set 2 results wth rh 3 = 0., ncreasng the penalty for low values. IAE s also transformed nto an elementary desrablty d IAE, wth r IAE = and Y IAE,c = 0 whle Y IAE,p s chosen slghtly hgher than the worst value of the expermental desgns. Fnally, the harmonc values of the other ranks are transformed nto elementary desrabltes dh ( [ 2,39], 3) wth Yh,c = 0 as the objectve s to reject harmonc dstorton. Yh,p s equal to the CEI 6000-3-2 standard lmt value so as to respect t. We fx rh 0.0 so that the sensblty of elementary desrabltes for harmonc rejecton s mproved near the standard values. Gvng more mportance to the IAE crteron and to the thrd harmonc ampltude through w parameters, the fnal crteron Y (25) s therefore: Y d 5 IAE. d 5 h3. 39 2 3 (25) The new tunng, Set 3, gves results shown n fg 4 and n Table 8. It appears that the THD beneft s equal to a thrd of the dfference between the best and the worst tunngs whle keepng a really good dynamc behavor. dh 47 Output Voltage (V) 500 480 460 440 420 400 380 360 340 Set 3 Lnear PI 320 0 0.5.5 2 2.5 3 3.5 4 4.5 Tme (s) Fg. 4. Expermental output voltages wth set 3 and lnear PI Set Fuzzy Controller Set Set Set 2 3 0 Lnear PI IAE voltage (0.0V.s) 9.6 47. 0. 0.9 53. TDH (%) 3.7 2.8 3.4 3.8 4. Load connecton: Tr 5% (ms) V DC mn (V) Load dsconnecton: Tr 5% (ms) V DC max (V) V DC mn (V) 57 369 8 432 390 73 338 078 476 350 Tab. 8. Expermental results 56 370 34 434 388 67 367 69 439 384 93 335 236 485 344
9. COMPARISON All expermental results are summarzed n Table 8. Lnear controller performance s qute bad and the comparson llustrates the valdty of usng FLC. Expermental desgn analyss allows to explore several tunng settngs gvng more nfluence to one or two crtera. It s mportant to notce that the grd voltage THD tself s 2.6%. Then, the THD for the optmal settng s really close to ths network s value. It underlnes the really good performance of the fuzzy controller wth respect to harmonc rejecton. The dynamc mprovement under such mportant load varatons s sgnfcant n comparson wth lnear PI. FLC tunng gven trough smulaton, set 0, s here worse n term of global performance n comparson wth results gven by the expermental study but s cheaper n term of number of experments. Moreover, the dynamc performance s mproved wth respect to lnear PI controller. 0. CONCLUSION It has been shown n ths paper that the expermental desgns methodology s an effcent tool for on-lne tunng of fuzzy controller accordng to ether smple crteron or mult-objectve crtera. The controllers were frst tuned through smulatons and showed some nterestng performance but some dfferences wth expermentatons appear due to some modellng offsets. Although the system s non lnear, expermental on-ste tunng on the real process s possble through ths method and leads to a clear performance mprovement. Consequently, there are two possbltes: get a fne model of the system and run the expermental desgns n smulaton (one experment for each of the 6 tested combnatons) or run 3 tmes more experments on the real system but wthout any need of a fne model. The next step wll consst n usng the expermental response surface methodology for global performance mprovement. REFERENCES Barrero F., Galvan E., Grener D., Fuzzy self tunng system for nducton motor controllers, EPE'95, Proc. of 6th European Conference on Power Electroncs and Applcatons, Sevlla, Span, september 995. Derrnger G., Such R. A Balancng Act : Optmzng a Product s Propertes, Qualty Progress. pp 5-58, 994. Dey A., Mukerjee R. Fractonal Factoral Plans. Wley, NewYork, 999. Dorf R.C. Modern Control Systems, Addson Wesley 990 Droesbeke J.J., Fne J., Saporta G. Plans d expérences, applcatons à l entreprse. Edtons Technp, 997. Fsher, R.A. The desgn of experments. Olver and Boyd, 935. Harrngton E. C. The Desrablty Functon. Industral Qualty Control, pp 494-498, 965. Henry S.H., Chung, Eugene P.W., Tam, S.Y.R. Hu. Development of a Fuzzy Logc Controller for boost Rectfer wth Actve Power Factor Correcton. PESC 999, Vol., pp 4 54, 999. Hssel D., Mausson P., Faucher J. Robust Pre-Establshed Settngs for PID-lke Fuzzy Logc Controllers, EPE'99, 8th European Conference on Power Electroncs and Applcatons, Lausanne, 999. Hoffmann, F., Evolutonary algorthms for fuzzy control system desgn, Proceedngs of the IEEE, Volume 89, Issue 9, Sept. 200 pp 38 333. Kang, H., Vachtsevanos, G., Adaptve fuzzy logc control, IEEE Internatonal Conference on Fuzzy Systems, 992., 8-2 March 992 pp 407 44. Bn-Da Lu; Chuen-Yau Chen; Ju-Yng Tsao, Desgn of adaptve fuzzy logc controller based on lngustc-hedge concepts and genetc algorthms, IEEE Transactons on Systems, Man and Cybernetcs, Part B, Volume 3, Issue, Feb 200 pp 32 53. Mattavell P., Buso S., Spazz G., Tent P. Fuzzy control of power factor preregulators, Industry Applcatons Conference, 995, Vol.3, pp 2678 2685, 995. Palandöken M, Aksoy M and Tümay M, A fuzzy-controlled sngle-phase actve power flter operatng wth fxed swtchng frequency for reactve power and current harmoncs compensaton, Electrcal Engneerng, Sprnger, 2003, vol 86, Nr, pp 9-6 Park C.W.,Output feedback control of dscrete-tme nonlnear systems wth unknown tme-delay based on Takag- Sugeno fuzzy models, Electrcal Engneerng, Sprnger, 2004, vol 87, Nr, pp 4-45 Perneel, C., Themln, J.-M., Renders, J.M., Acheroy, M., Optmzaton of fuzzy expert systems usng genetc algorthms and neural networks, IEEE Transactons on Fuzzy Systems, Volume 3, Issue 3, pp. 300 32, 995.
Pres V.F., Amaral T.G., Slva J.F. Crsostomo M. Fuzzy logc control of a sngle phase AC/DC buck-boost converter. EPE 999, Lausanne, 999. Taguch, G. Orthogonal arrays and lnear graph. Amercan Suppler Insttute Press, 987. Takag, H., Applcaton of neural networks and fuzzy logc to consumer products, Industral Electroncs, Control, Instrumentaton, and Automaton, 992. 'Power Electroncs and Moton Control', 9-3 Nov. 992 pp 629-633 vol.3. Yu Qn, Shanshan Du. Comparson of fuzzy logc and dgtal PI control of sngle phase power factor pre-regulator for an on-lne UPS. Proceedngs of the 996 IEEE IECON 22nd Internatonal Conference, Vol. 3, pp 796 80, 996.