ACE Journal, Volume (6), Iue (), June, 6 Direct Torque Control for Induction Motor Uing Fuzzy Logic R.Toufouti.Meziane,H. Benalla Laboratory of Electrical Engineering Univerity Contantine Algeria [toufoutidz,meziane_elc,benalladz]@yahoo.fr Abtract In thi paper we propoe an approach to improve the direct torque control (DTC) of an induction motor (IM). The propoed DTC i baed on fuzzy logic technique witching table, i decribed compared with conventional direct torque control (DTC). To tet the fuzzy control trategy a imulation platform uing MATLAB/IMULINK wa built which include induction motor d-q model, inverter model, fuzzy logic witching table and the tator flux and torque etimator. The imulation reult verified the new control trategy. Keyword: DTC, Fuzzy logic, induction motor, witching table.. Introduction Advanced control of electrical machine require an independent control of magnetic flux and torque. For that reaon it wa not urpriing, that the DC-machine played an important role in the early day of high performance electrical drive ytem, ince the magnetic flux and torque are eaily controlled by the tator and rotor current, repectively. The introduction of Field Oriented Control [] meant a huge turn in the field of electrical drive, ince with thi type of control the robut induction machine can be controlled with a high performance. Later in the eightie a new control method for induction machine wa introduced: The Direct Torque Control (DTC) method i characteried by it imple implementation and a fat dynamic repone. Furthermore, the inverter i directly controlled by the algorithm, i.e. a modulation technique for the inverter i not needed. However if the control i implemented on a digital ytem (which can be conidered a a tandard nowaday); the actual value of flux and torque could cro their boundarie too far [] [], which i baed on an independent hyterei control of flux and torque. The main advantage of DTC are abence of coordinate tranformation and current regulator abence of eparate voltage modulation block. Common diadvantage of conventional DTC are high torque ripple and low tranient repone to the tep change in torque during tart-up. Thee are diadvantage that we want to remove by uing and implementing modern reource of artificial intelligence like neural network, fuzzy logic and genetic algorithm. In the following, we will decribe the application of fuzzy logic in DTFC control [9]. Fuzzy control i a way for controlling a ytem without the need of knowing the plant mathematic model. It ue the experience of people' knowledge to form it control rule bae. There ha appeared many application of fuzzy control on power electronic and motion control in the pat few year. A fuzzy logic controller wa reported being ued with DTC [7]. However there arie the problem that the rule number it ued i too many which would affect the peed of the fuzzy reaoning. Thi paper we propoe an approach to improve the direct torque control (DTC) of an induction motor (IM). The propoed DTC i baed on fuzzy logic technique witching table and the platform to perform the imulation by uing IMULINK.. Direct Torque Control with Three-Level Inverter The baic functional block ued to implement the DTC cheme are repreented in Figure. The intantaneou value of the tator flux and torque are calculated from tator variable by uing a cloed loop etimator []. tator flux and torque can be controlled directly and independently by properly electing the inverter witching configuration Figure. Baic direct torque control cheme for ac motor drive 9
ACE Journal, Volume (6), Iue (), June, 6 Vector model of inverter output voltage: In a voltage fed three phae, the witching command of each inverter leg are complementary. o for each leg a logic tate C i (i=a,b,c) can be defined. C i i if the upper witch i commanded to be cloed and if the lower one in commanded to be cloe (firt). Figure. Three phae voltage inverter ince three are independent leg there will be eight different tate, o 8 different voltage. Applying the vector tranformation decribed a: = π 4π j j V U C + C e + Ce, () A it can be een in econd, there are ix non-zero voltage vector and two zero voltage vector which correpond to (C, C, C )= ()/ () a hown by Figure. [] []. The tator reitance can be aumed contant during a large number of converter witching period Te. The voltage vector applied to the induction motor remain alo contant during one period Te. The tator flux i etimated by integrating the difference between the input voltage and the voltage drop acro the tator reitance a given by equation (4): t ϕ = ( V R I ) dt, (4) During the witching interval, each voltage vector i contant and (4) i then rewritten a in (5): ϕ ( t ) ϕ +VT e, (5) In equation; φ tand for the initial tator flux condition. In fact, we have d ϕ V.The following Figure 4 i dt etablihed for the cae V =V. q q d Figure 4. An example for flux deviation d Figure. Partition of the d, q plane into 6 angular ector tator flux control: tator voltage component (V d,v q ) on perpendicular (d,q) axi are determined from meaured value (U o and I abc ). Boolean witching control (C,C,C,) by, [][]: V d = U C ( C + C ) V d = U ( C C ) and tator current component (I d,i q ) : I I d d = = Ia ( Ib Ic ) () () Neglecting the tator reitance, (5) implie that the end of the tator flux vector will move in the direction of the applied voltage vector, a hown in Figure.4. I the initial tator flux linkage at the intant of witching. To elect the voltage vector for controlling the amplitude of the tator flux linkage, the voltage vector plane i divided into ix region, a hown in Figure.. In each region, two adjacent voltage vector, which give the minimum witching frequency, are elected to increae or decreae the amplitude of, repectively. For intance, vector and are elected to increae and decreae the amplitude of when i in region one and i rotating in a counter-clockwie direction. In thi way, can be controlled at the required value by electing the proper voltage vector. Figure how how the voltage vector are elected for keeping within a hyterei band when i rotating in the counter-clockwie direction. [] [7]. tator flux and torque etimation: The magnitude of tator flux, which can be etimated a following [] [6].
ACE Journal, Volume (6), Iue (), June, 6 t ϕ d = ( V d R I d ) dt (6) t ϕ = q ( V d R I d ) dt The tator flux linkage phaor i given by ϕ + = ϕ ϕ (7) d q By comparing the ign of the component tator flux (ϕ d, ϕ q ), the relationhip between thee component and the amplitude of flux, the number (N) of the zone in which flux i can be obtained, [] [5]. Electromagnetic torque calculation ue flux component (6), current component () and P, pair-pole number of the induction machine: Γ = p ϕ I ϕ I (8) em ( ) d q q d. tator Flux and Electromagnetic Torque The calculated magnitude of tator flux and electric torque are compared with their reference value in their correponding hyterei comparator a are hown in Figure.5 and 6, repectively. Finally, the output of the comparator with the number of ector at which the tator flux pace vector i located are fed to a witching table to elect an appropriate inverter voltage vector. The elected voltage vector will be applied to the induction motor at the end of the ample time []. 4. Principal of Fuzzy Direct Torque Control The principal of direct torque control uing fuzzy logic (FDTC). The fuzzy controller i deigned to have three fuzzy tate Variable and one control variable for achieving direct torque Control of the induction machine[], there are three variable input fuzzy logic controller, the tator flux error, electromagnetic torque error, and angle of flux tator repectively the output it i the voltage pace vector hown Figure 7. Figure 7. witching table in fuzzy logic Flux linkage error: The error of flux linkage i related value of tator flux ϕ ref and real value of tator ϕ, they are ubject to equation ϕ = ϕ ϕ (9) ref voltage vector hall caue different affection to tator flux in different flux poition; how figure given that tator flux θ locate in domain θ.then V 4 will make flux increae rapidly, V will make flux decreae rapidly, V 5 and V 6 will make flux increae lowly; and V and V will make flux decreae lowly, we ue the three following linguitic term: negative value, zero value and poitive value denoted repectively N, Z and P. Three fuzzy et are then defined by the delta and trapezoidal memberhip function a given by Figure.8, []. Figure 5. tator flux hyterei comparator Figure 6. Torque hyterei comparator A hown in Figure, eight witching combination can be elected in a voltage ource inverter, two of which determine zero voltage vector and the other generate ix equally paced voltage vector having the ame amplitude. According to the principle of operation of DTC, the election of a voltage vector i made to maintain the torque and tator flux within the limit of two hyterei band. The witching election table for tator flux vector lying in the firt ector of the d-q plane i given in Table. I [][]. Figure 8. Memberhip function for flux error Electromagnetic torque error: Error of torque Γ i related to deired torque value Γ ref and real torque value Γ ; they are ubject to equation () Γ = Γref Γ, () Table I: the witching table for DTC bai In domain θ, V and V 6 will make torque increae rapidly, V and V 5 will make torque increae rapidly, V 4 will make torque increae lowly, V, V and V 7 will make torque increae lowly []. Therefore, thee rule may be decribed by language variable, i, e. Poitive Large (LP), Poitive mall (P), Negative mall (N), and Negative
ACE Journal, Volume (6), Iue (), June, 6 Large (NL), their memberhip function ditribution i hown a Figure 9. [], repectively. The weighting factor α i for i th rule can be written a []: α min( µ ( ε ), µ ( ε Γ ), µ ( ε )), () i = Ai ϕ Bi Ci θ By fuzzy reaoning, Mamdani' minimum procedure [] give :, µ n) = min( α, ( n)), () Ni ( i µ NI Figure 9. Memberhip function for Torque error Angle of flux linkage θ : The angle of flux linkage θi an angle between tator flux ϕ and a reference axi i defined by equation: θ ϕ d = arctan, () ϕ q In (6), (ϕ d,ϕ q ) are the component of flux linkage ϕ in the plan (d,q) on the bai of voltage vector hown a Figure., fuzzy variable may be decribed by language value (θ θ ),it the memberhip function ditribution i hown Figure.8 []. The memberhip function µ N of the output n i point given by: i= 8, µ N ( n) = max( α, µ i= i NI ( n)), (4) In thi cae, the output are crip; the maximum criterion i ued for defuzzifizcation []. By thi method, the fuzzy of output which ha the maximum poibility ditribution, i ued a control output. 7 µ Nout ( n) = max( µ ( n)), (5) i= Nout According to the all rule and Mamdani organ, and all the variable memberhip function, a fuzzy control have 8 table can gain, a hown table I [], the fuzzy control table be queried in real time, depoited the table into memory of microcomputer. Figure. Memberhip function for flux poition The control variable: The control variable i the inverter witching tate (n). In a ix tep inverter, even ditinct witching tate are poible [], [8]. The witching tate are crip thu do not need a fuzzy memberhip ditribution. Each control rule can be decribed uing the tate variable ϕ, Γ and θ and the control variable n (characteriing the inverter witching tate). The i th rule R i can be written a: R i : if ϕ, i Ai, Γ i B i and θ i C i then n i N i Thoe rule are etablihed uing literature and our experience with the help of an intenive imulation tage computing the enitivity factor defined in []. The inference method ued in thi paper i Mamdani' procedure baed on min-max deciion []. The memberhip function of variable A, B, C and N are given by µ A, µ B, µ C and µ N
ACE Journal, Volume (6), Iue (), June, 6 Figure b, however, the peed i low and the peed ha big ripple in conventional DTC hown Figure a, for an abrupt change in command torque. It can be een Figure 4.b that the tator flux trajectory of the FLDTC i more approximately circle than it of the conventional DTC Figure 4a. Figure 5.(a)-(b) how that the magnitude of tator flux of the FLDTC i etablihed more quickly than that of the conventional DTC, the teady tate current reult are preented in Figure 6.(a)-(b) in the two control method. compared with large ditorted by the conventional DC, the teady tate current can be approximately be ine wave including low high frequency component. Table II: fuzzy logic rule 5. Interpretation Reult To verify the technique propoed in thi paper, digital imulation baed on Matlab/imulink. have been implemented. The induction machine ued for the imulation ha the following parameter: P N =KW, U N =V,f N =6Hz,R =.89Ω,R r =.9Ω,P=, L =L r =.5H,L m =.4H,J=.5kgm. The ampling period of the ytem i 5µ. To compare with conventional DTC and FLDTC for IM are imulated. In two cae, the dynamic repone of torque, peed, flux, and tator current for the tarting proce with [5 7 ] Nm load torque applied at. are hown in Figure from 9 to repectively. The imulation reult how that flux and torque repone are very good dynamic torque repone for two DTC method, but the repone of the torque conventional DTC preented of the ripple, what how that there i a tatic error between the couple and the couple of reference what how by the Figure a. By FLDTC technique hown Figure b, the ripple of torque in teady tate i reduced remarkably compared with conventional DTC, the torque change through big ocillation and the torque ripple i bigger in conventional DTC hown Figure a, Figure b how it FFT. Both the waveform, in the time and frequency domain, how that the harmonic content of the torque repone i highly reduced by employing the fuzzy logic technique. I the peed tranient waveform when the command peed tep change from to 68 [rad/]. The hort repone time i achieved from to table value baed on the FDTC hown 6. Concluion In thi paper, author preent a kind of fuzzy torque control ytem for induction motor baed on fuzzy control technique. On the bai of analying diagram of voltage vector, author acquired whole fuzzy control rule et. The imulation reult ugget that FLDTC of induction machine can achieve precie control of the tator flux and torque. Compared to conventional DTC, preented method i eaily implemented, and the teady performance of ripple of both torque and flux are coniderably improved. The main improvement hown are: Reduction of torque and current ripple. No flux dropping caued by ector change circular trajectory. Fat torque repone. Zero-teady-tate torque and flux. 7. Reference [] I. Takahahi and T. Noguchi, A New Quick-Repone and High-Efficiency Control trategy of Induction Motor, IEEE Tran. On IA, Vol., N.5, ept/oct 986, PP.8-87. [] M. Depenbrock, Direct elf Control (DC) of Inverter Fed Induction Machine, IEEE Tran. Power Electronic, Vol., N.4, Oct 988, PP.4-89. [] D.Caadei, F.Profumo, G.erra and A.Tani, FOC and DTC:Tox Viable cheme for Induction Motor Torque Control, IEEE Tran. Power Electronic. On PE, Vol.7, N.5, ept, [4] D.Caadei and G.erra, Implementation of Direct Torque Control Algorithme for Induction Motor Baed on Dicrete pace Vector Modulation, IEEE Tran. Power Electronic, Vol.5, N.4, JULY. [5] A.A.Pujol, Improuvment in Direct Torque Control of Induction Motor, Thèe de doctorat de L UPC, Novembre [6] Y.A. Chapui, Contrôle Direct du Couple d une Machine Aynchrone par L orientation de on Flux tatorique, Thèe Doctorat INP, Grenoble 996. [7] Y.Xia W.Oghanna " tudy on Fuzzy Control of Induction Machine With Direct Torque Control Approach ",IEEE Catalog Number: 97TH88- IIE'97 - GuimarBe, Portugal [8] R.Toufouti,H.Benalla and.meziane, "Three-Level Inverter With Direct Torque Control For Induction
ACE Journal, Volume (6), Iue (), June, 6 Motor", World Conference on Energy for utainable Development: Technology Advance and Environmental Iue, Pyramia Hotel Cairo - Egypt, 6-9 December 4 [9] Grabowki.P "Direct Flux and Torque Neuro-Fuzzy Control of Inverter Fed Induction Motor Drive", PhD Thei, Warzawa 999. [] C.C. Lee, "Fuzzy Logic in Conud Wtemr: Funy Logic Contmlpattl," IEEE Trmtoction on ytem, Mon mtd cybemctic, vol., NO., MarchiApd, l99, pp. 4448 [] Jia-Qiang Yang, Jin Huang "A New Full-peed Range Direct Torque Control trategy for Induction Machine" Proceeding of the Third International Conference on Machine Learning and Cybernetic, Guangzhou, 6-9 Augut 4. [] Jia-Qiang Yang, Jin Huang "Direct Torque Control ytem for Induction Motor With Fuzzy peed Pi Regulator" Proceeding of the Fourth International Conference on Machine Learning and Cybernetic, Guangzhou, 8- Augut 5. [] Hui-Hui Xia, han Li, Pei-Lin Wan, Ming-Fu Zhao, "tudy on Fuzzy Direct Torque Control ytem" Proceeding of the Fourth International Conference on Machine Learning and Cybernetic, Beijing, 4-5 Augut. 8. Biographie Toufouti Riad : wa born in Algeria in 974, in 999 received the Engineer degree from the univerity of Montouri Contantine. Algeria. In received the M.. degree in electrical engineering, Option electrical machine. Aociate teacher in Contantine Univerity from October 999 to. In incription in doctor' degree, permanent teacher from January 4 in ouk ahra Univerity, member for laboratory Of Electrical engineering univerity of Montouri Contantine. Algeria Hocine Benalla : wa born in Algeria in 957. He received the D.E.A. and Doctor engineer degree in power electronic from the National Polytechnic Intitute of Touloue, France, in 98, and. 984, repectively. In 995, he received the Ph.D. degree in electrical engineering from Univerity of Juieu -Pari 6, France. He i currently an Aitant Profeor at Univerity of Contantine Algeria. Hi current reearch interet include electric machine, ac drive and active filter. Meziane alima : in received the Engineer degree from the univerity of Montouri Contantine. Algeria. In received the M.. degree in electrical engineering, Option electrical machine. Aociate teacher in Oum El Bouaghi Univerity from October to. In 4 incription in doctor' degree, permanent teacher from October 4 in ouk ahra Univerity, member for laboratory Of Electrical engineering univerity of Montouri Contantine. Algeria. 4
ACE Journal, Volume (6), Iue (), June, 6 9. imulation Reult 8 7 ELECTRPMAGNETIC TORQUE Celm Cref ELECTRPMAGNETIC TORQUE Celm Cref 6 TORQUE[N.m] 5 4 Ripple Torque TORQUE[N.m] 8 6 4....4.5.6.7.8.9 Figure a. Electromagnetic Torque Repone....4.5.6.7.8.9 Figure b. Electromagnetic Torque Repone 7 6 pectrum Torque 5 5 Harmonic pectrum Torque 5 4 Harmonic 5 5 5 5 4 45 5 Number of harmonic Fig.a. Frequency pectrum of the torque repone 5 5 5 5 4 45 5 Number of harmonic Fig.b. Frequency pectrum of the torque repone 7 PEED PEED 6 5 4 Wr[Rad/] Wr[Rad/] 5 -....4.5.6.7.8.9....4.5.6.7.8.9 Figure a. peed repone Figure b. peed repone 5
ACE Journal, Volume (6), Iue (), June, 6.8 TATORIC DIRECT and OPPOITE FLUX.8 TATORIC DIRECT and OPPOITE FLUX.6.6.4.4.. Fq [Wb] -. Fq [Wb] -. -.4 -.4 -.6 -.6 -.8 -.8 -.6 -.4 -...4.6.8 Fd[Wb] Figure 4a. The tator flux circle -.8 -.8 -.6 -.4 -...4.6.8 Fd[Wb] Figure 4b. The tator flux circle.7.6 TATOR FLUX MAGNITUDE F Fref.7.6 TATOR FLUX MAGNITUDE F Fref.5.5.4.4 F[Wb]. F[Wb].........4.5.6.7.8.9 Figure 5a. The tator flux magnitude....4.5.6.7.8.9 Figure 5a. The tator flux magnitude 5 TATOR CURRENT TATOR CURRENT 5 5 Ia[A] Ia[A] -5-5 - - -5-5....4.5.6.7.8.9 -....4.5.6.7.8.9 Figure 6a. The tator current Figure 6b. The tator current Conventional DTC Fuzzy Logic DTC 6