Fuzzy Speed Regulator for Induction Motor Direct Torque Control Scheme

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This paper presents a novel design of a control
scheme for induction motor as a fuzzy logic application,
incorporating fuzzy control technique with direct torque
control method for induction motor drives. The direct torque
control method has been optimized by using fuzzy logic
controller instead of a conventional PI controller in the speed
regulation loop of induction motor drive system. The
presented fuzzy based control scheme combines the benefits of
fuzzy logic control technique along with direct torque control
technique. Compared to the conventional PI regulator, the
high quality speed regulation of induction motor can be
achieved by implementing a fuzzy logic controller as a PI-type
fuzzy speed regulator which is designed based on the
knowledge of experts without using the mathematical model.
The stability of the induction motor drive during transient
and steady operations is assured through the application of
fuzzy speed regulator along with the direct torque control.
The proposed fuzzy speed regulated direct torque control of
induction motor drive system has been validated by using
MATLAB simulink.

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Fuzzy Speed Regulator for Induction Motor Direct Torque Control Scheme

  1. 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 Fuzzy Speed Regulator for Induction Motor Direct Torque Control Scheme Jagadish H. Pujar 1, S. F. Kodad 2 1 Research Scholar JNTU, Anantapur & Faculty Department of EEE, B V B College of Engg. & Tech., Hubli, India Email: jhpujar@bvb.edu 2 Professor, Department of EEE, Aurora’s Engineering College, Hyderabad, India Email: kodadsf@rediffmail.comAbstract—This paper presents a novel design of a control the performance of conventional DTC a fuzzy logicscheme for induction motor as a fuzzy logic application, controller is used along with conventional DTC [7].incorporating fuzzy control technique with direct torque The main objective of this paper is to simulate the fuzzycontrol method for induction motor drives. The direct torque speed regulator for induction motor direct torque controlcontrol method has been optimized by using fuzzy logiccontroller instead of a conventional PI controller in the speed scheme to improve the speed regulation performanceregulation loop of induction motor drive system. The under transient and steady state uncertainties caused bypresented fuzzy based control scheme combines the benefits of variation in load torque which in term replacing PIfuzzy logic control technique along with direct torque control regulator of DTC by FLC.technique. Compared to the conventional PI regulator, thehigh quality speed regulation of induction motor can be II. INDUCTON MOTOR STATE MODELachieved by implementing a fuzzy logic controller as a PI-typefuzzy speed regulator which is designed based on the The dynamic input and out put equations of inductionknowledge of experts without using the mathematical model. motor are formulated as a state model in the statorThe stability of the induction motor drive during transient reference frame under the assumptions of linear magneticand steady operations is assured through the application of circuits, equal mutual inductances and neglecting ironfuzzy speed regulator along with the direct torque control. losses as follows;The proposed fuzzy speed regulated direct torque control of & (1) X (t ) = A X (t ) + B U (t )induction motor drive system has been validated by usingMATLAB simulink. Y (t ) = C X (t ) (2) Where A is the system, B is the control and C is theIndex Terms—Fuzzy Logic Control (FLC), Direct TorqueControl (DTC), Induction Motor (IM), Space Vector observation matrices. And X(t) is the state, U(t) is inputModulation (SVM), switching table. and Y(t) is out put vectors with elements as follows; X (t ) T = [i sd i sq φ sd φ sq ] (3) I. INTRODUCTION ⎡ V sd ⎤ & ⎡ i sd ⎤ (4) Fuzzy logic is recently getting increasing emphasis in U (t ) = ⎢ ⎥ Y (t ) = ⎢ ⎥drive control applications. Recent years, fuzzy logic control ⎣ V sq ⎦ ⎣ i sq ⎦has found many applications in the past two decades. This ⎡ 1−σ ω (1 − σ )⎤ ⎢− δ 0 σM τ σM ⎥is so largely increasing because fuzzy logic control has the ⎢ r ⎥capability to control nonlinear uncertain systems even in ⎢ ω (1 − σ ) ω (1 − σ ) ⎥ ⎢ 0 −δ −the case where no mathematical model is available for the σM σM τ ⎥ A=⎢ ⎥ (5) rcontrol system [1]. So, the development of high- ⎢M 1 ⎥performance control strategies for AC servo system drives ⎢τ 0 − −ω ⎥ τresulted in a rapid evolution. To overcome the ⎢ r r ⎥ ⎢ M 1 ⎥disadvantages of vector control technique, in the middle of ⎢ 0 ω − ⎥ ⎣ τ τ ⎦1980’s, a new quick response technique for the torque r rcontrol of induction motors was proposed by Takahashi as ⎡ 1 ⎤ ⎢σL 0 0 0⎥direct torque control (DTC) [2]. DTC provides very quick B =⎢ T s ⎥ (6)response with simple control structure and hence, this ⎢ 1 ⎥technique is gaining popularity in industries [2]. Though, ⎢ 0 σL 0 0⎥ ⎣ s ⎦DTC has high dynamic performance, it has few drawbacks ⎡1 0 0 0 ⎤ (7)such as high ripple in torque, flux, current and variation in C = ⎢ ⎣0 1 0 0 ⎥ ⎦switching frequency of the inverter. The effects of flux andtorque hysteresis band amplitudes in the induction motor Lr ; L ⎛ 1 1−σ ⎞ ; τs = s ; σ = 1− M ; δ =⎜ 2drive performance have been analyzed in [3]. To improve τr = Rr Rs ⎜ στ + στ ⎟⎟ Lr Ls ⎝ s r ⎠ 1© 2010 ACEEEDOI: 01.IJEPE.01.03.30
  2. 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 Where ω represents rotor speed. Rs and Rr are the stator ⎛ 2π ⎞and rotor resistances respectively. Ls, Lr are the stator and V BN = V m cos ⎜ ω t − ⎟ (11) ⎝ 3 ⎠rotor self-inductances and M is the mutual inductancerespectively. ⎛ 2π ⎞ The electromagnetic torque developed by the induction V CN = V m cos ⎜ ω t + ⎟ (12) ⎝ 3 ⎠motor is expressed as, T em = 3 P (i sq φ sd − i sd φ sq ) (8) Vi = 2 3 ( V AN + aV BN + a 2VCN ) (13) 4 Where φ sd, and φ sq, are respectively, the stator fluxes where i = 0 to 7projections on the (d, q) axis reference frame. These three phase voltages are applied to the three phase The induction motor electromagnetic torque and load induction motor employing the equation (13). The threetorque balancing under equilibrium can be expressed as, phase bridge inverter of Fig.1 has eight permissible dω switching states. The switching states and the T em = J + Bω + TL (9) dt corresponding phase to neutral voltage of isolated neutral Where J is the moment of inertia of the rotor, B damping induction motor are summarized in Table.I in which “0” iscoefficient and TL is the load torque. off state and “1” is on state indication for the switches S1 to From the above mathematical representation, we can see S3. Table 1that the dynamic model of an induction motor is a strongly SVM Iverter Switching Statescoupled nonlinear multivariable system. The controlproblem is to choose (Vsd , Vsq) in such a way as to force the V S1 S2 S3 VAN VBN VCNmotor electrical angular speed ω and the rotor flux V0 0 0 0 0 0 0magnitude φ s=[ φ 2sd + φ 2sq]1/2 to track given reference V1 1 0 0 2VDC /3 -VDC /3 -VDC /3values by denoted ωref and φ ref respectively. Note that thechoice of a reference frame rotating at the same angle and V2 1 1 0 VDC /3 VDC /3 -2VDC /3is more suitable for the control problems since in this frame V3 0 1 0 -VDC /3 2VDC /3 -VDC /3the steady state signals are seems to be constant. V4 0 1 1 -2VDC /3 VDC /3 VDC /3 III. DTC SCHEME FOR INDUCTON MOTOR DRIVE V5 0 0 1 -VDC /3 -VDC /3 2VDC /3 V6 1 0 1 VDC /3 -2VDC /3 VDC /3A. Working Strategy of Conventional DTC V7 1 1 1 0 0 0 The SVM technique is used to approximate the voltagereference vector by employing the combination of two outof eight possible vectors generated by the three phase Consider, for example state V5 space vector voltage is,voltage source inverter for IM drive is as shown in Fig.1. 2 ⎛ − V DC − V DC 2V ⎞ V5 = ⎜ +a + a 2 DC ⎟ (14) 3⎝ 3 3 3 ⎠ S1 S2 S3 As there are three independent limbs, there will be eight different logic states, provides eight different voltages obtained applying the vector transformation described as: A 2π 4π 2 ⎡ j j ⎤ B Vi = VDC ⎢ S1 + S 2e 3 + S3e 3 ⎥ (15) VDC 3 N ⎢ ⎣ ⎥ ⎦ C Eight switching combinations can be taken according to Inducton the above expression (15). So, the partitions of d-q plane in S1 S2 S3 Motor to two zero voltage vectors and six non-zero voltage vectors are as shown in Fig.2. Figure 1. SVM Inverter for Induction Motor Drive The three phase sinusoidal instantaneous voltageequations of three phase inverter of Fig.1 are as follows. V AN = V m cos ω t (10) 2© 2010 ACEEEDOI: 01.IJEPE.01.03.30
  3. 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 we can write, the expression for change in stator flux over the sampling time period TS as, φ S (k + 1) ≈ φ S (k ) + V S TS (24) Δφ S ≈ φ S (k + 1) − φ S (k ) ≈ V STS (25) Equation (25) implies that by applying a vector of tension which is co-linear in its direction, we can increase the stator flux. Therefore, by selecting adequate voltage vector one can increase or decrease the stator flux amplitude and phase to obtain the required performances [3] [5]. C. Switching Table Formation Figure 2. Partition of the d-q planes in to six angular sectors The vectors Vi+1 or Vi-1 are selected to increase theB. Stator Flux and Torque Estimation amplitude of flux, and Vi+2 or Vi-2 to decrease it when flux is in sector I. If V0 or V7 is selected, then the rotation of The components of the current (Isd, Isq) and stator voltage flux is stopped and the torque decreases whereas the(Vsd, Vsq) are obtained by the application of the module of flux remains unchanged. Which shows that thetransformation [5] given by (1) and (2). The components of choice of the vector tension depends on the sign of thethe stator flux (ϕsd, ϕsq) are given by (18). The stator flux error of flux is independent of its amplitude [5].linkage per phase and the electromagnetic torque estimatedare given by (19) and (21) respectively. Table II Switching table for DTC basis 1 I sd = 2 I A & I sq = (I B − I C ) (16) 3 2 Sector I II III IV V VI 1 Flux Torque 2 ⎛ 1 ⎞ Vsd = VDC ⎜ S1 − (S 2 + S3 )⎟ & Vsq = VDC(S2 − S3 ) (17) 3 ⎝ 2 ⎠ 2 T=1 V2 V3 V4 V5 V6 V1 F=1 T=0 V7 V0 V7 V0 V7 V0 ∫ (V ) ∫ (V ) t t φ sd = sd − R S I sd dt & φ sq = sq − R S I sq dt (18) T=-1 V6 V1 V2 V3 V4 V5 0 0 T=1 V3 V4 V5 V6 V1 V2 φs = φ sd + φ sq 2 2 (19) F=0 T=0 V0 V7 V0 V7 V0 V7 T=-1 V5 V6 V1 V2 V3 V4 The angle between referential and stator flux is given by ⎛φ ⎞ (20) Obviously, the exit of the corrector of flux must be a θ = tan − 1 ⎜ sd ⎟ ⎜φ ⎟ Boolean variable. One adds a band of hysteresis around ⎝ sq ⎠ zero to avoid unwanted commutations when the error of Tem = P (φsd I sq − φsq I sd ) (21) flux is very small [2] [5]. Indeed, with this type of corrector in spite of its simplicity, one can easily control and The stator resistance RS can be assumed constant during maintain the end of the vector flux in a circular ring form.a large number of converter switching periods TS. The The switching table proposed by Takahashi [2] is as givenvoltage vector applied to the induction motor also remains in Table.II. The voltage vector switching table receives theconstant over the time period TS. Therefore, resolving first input signals from change in flux hysteresis controller,equation of system leads to; change in torque hysteresis controller and another signal ( ) φS (t) =φS (0) +VSTS t from space vector modulation block, hence develops the φ S = ∫ V S − RS I S dt → (22) appropriate control voltage vector switching states for 0 PWM inverter according to the Table II. In equation (22), φS(0) stands for the initial stator fluxcondition. This equation shows that when the term RSIS D. Hysteresis controllerscan be neglected in high speed operating condition of the The change in flux and change in torque areextremity of stator flux vector VS. Also, the instantaneous compensated by using two hysteresis controllers asflux speed is only governed by voltage vector amplitude [3] represented in below Fig.3 respectively.given in (23). dφ S (23) 1 1 ≈V S dt 0 ∆φ S 0 ∆Tem The vector tension applied to the induction motor -1remains constant during the sampling time period TS. Thus Figure 3. Flux and Torque Hystereses controllers respectively 3© 2010 ACEEEDOI: 01.IJEPE.01.03.30
  4. 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 The change in flux is compensated using one level C. PI-type Fuzzy Logic Controller as a Fuzzy Speedhysteresis band as shown Fig.3. But, as the dynamic torque Regulatoris generally faster than the flux, the use of a compensatorwith two level hysteresis band is used in order to adjust the e(k) K1 FLCchange in torque and minimize the frequency switching du(k) u(k)average as shown in Fig.3 [7]. K3 z-1 K2 z-1IV. STRATEGY OF PROPOSED FUZZY SPEED REGULATOR ce(k) FOR IM DTC SCHEME The proposed DTC employs an induction motor model Figure 5. Basic Structure PI-type Fuzzy Logic Controllerto predict the voltage required to achieve a desired output In the DTC scheme of SVM voltage source inverter-fedtorque [5]. By using only current and voltage induction motor drive system, simultaneous control of themeasurements, it is possible to estimate the instantaneous torque and the flux linkage was required. So, the referencestator flux and output torque. An induction motor model is torque to DTC is fed from speed loop of the IM drive asthen used to predict the voltage required to drive the flux shown in Fig.5 which is regulated using PI-type FLCand torque to the demanded values within a fixed time shown inFig.6. In which K1, K2 and K3 are normalizationperiod. This calculated voltage is then synthesized using factors. The input linguistic variables speed error e(k),SVM. change in speed error ce(k) and output linguistic variableA. The structure of Fuzzy Speed Regulator for Induction du(k) membership functions will be divided into seven Motor DTC Scheme fuzzy sets with the linguistic values NL (negative large), NM (negative medium), NS (negative small), ZE (zero), PS The DTC scheme of Induction Motor drive system (positive small), PM (positive medium), PL (positive large)includes flux and torque estimators, flux and torque respectively.hysteresis controllers, fuzzy logic controller as a fuzzyspeed regulator and a switching table and a three phase The fuzzy logic controller is basically an input outputPWM inverter as shown in Fig.4. In addition, we need a static non-linear mapping technique. The PI-type FLCDC bus voltage sensor and two output current sensors for control action can be expressed as [6],flux and torque estimation [7]. VDC du(t ) = K e(t ) + K ce(t ) I (26) P Ф ref Hysteresis Controlle r Where KP and KI are proportional and integral gains. On Фr Switching PWM integrating above equation, we getωre f Te m Hysteresis Table Inverter FLC Controlle r u (t ) = K e(t ) + K ∫ e(t )dt P (27) I ω VDC S TL The discrete form of equation (21) can be expressed as, Flu x and V Torque M id du(k ) = K e(k ) + K ce(k ) I (28) P Estimator iq Equation (28) is a PI-type FLC with non-linear gain Encoder factors. The fuzzy associative memory (FAM) of Mamdani Z -1 IM rule base model to develop the PI-type FLC as a fuzzy speed regulator which in term replace the PI speed regulator of conventional DTC [8] is given in Figure 4. The Structure of Fuzzy speed regulator for IM Direct Torque Table. III. Control scheme Table IIIB. Fuzzy Logic Controller Concepts FAM of FLC as a Fuzzy Speed Regulator of IM In the research work considered in this paper, fuzzy CHANGE IN ERRO R (ce) dulogic controller is used to coordinate between the various NB NM NS ZE PS PM PBparameters induction motor drive system as shown in the NB NVB NVB NVB NB NM NS ZEblock diagram of the Fig.5. These fuzzy controllers have NM NVB NVB NB NM NS ZE PSgot a lot of advantages compared to the the conventional PI ERRO R (e)controllers, such as the simplicity of control, low cost, high NS NVB NB NM NS ZE PS PMreliability, compactness of the hardware as fuzzy logic ZE NB NM NS ZE PS PM PBcontroller just makes use of fuzzy rules and the possibility PS NM NS ZE PS PM PB PVBto design without knowing the exact mathematical model PM NS ZE PS PM PB PVB PVBof the process [1]. PB ZE PS PM PB PVB PVB PVB 4© 2010 ACEEEDOI: 01.IJEPE.01.03.30
  5. 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 V. SIMULATION AND RESULTS Vector locations are shown in order to validate the control strategies as discussed above. The digital To verify the proposed scheme, a numerical simulation simulation studies were made by using MATLABhas been carried out by using MATLAB SIMULINK. In environment for the system described in Fig.4. The speedthe performed simulation, certain stator flux and torque regulation loop of the induction motor drive is designedreferences are compared to the values calculated in the and simulated with fuzzy logic controller. The feedbackdriver and errors are sending to the hysteresis comparators. control algorithms were iterated until best simulationThe outputs of the flux and torque comparators are used in results were obtained. The system dynamic responsesorder to determine the appropriate voltage vector and stator obtained by simulation were shown in Fig.5 and Fig.6 forflux space vector. stator current, torque and speed to conclude the comparative results of conventional DTC with PI speed regulator and proposed DTC with FLC as a fuzzy speed regulator. The DTC with FLC as a fuzzy speed regulator of IM presents the high quality performances compare to the conventional DTC with PI speed regulator shown in Fig.6 and Fig.7. CONCLUSIONS The paper presents a new approach for speed control of three phase induction motor using fuzzy logic technique. The paper develops a DTC with FLC methodology for AC drive systems is intended for an efficient control of the torque and flux without changing the motor parameters. Also the flux and torque can be directly controlled with the inverter voltage vector using SVM technique. Two independent hysteresis controllers are used in order to satisfy the limits of the flux and torque. The proposed system was analyzed, designed and performances were studied extensively by simulation to validate the theoretical concept. The simulation results shows that the proposed DTC with FLC as a fuzzy speed regulator is superior to Figure 6. Conventional DTC simulated responses with PI speed conventional DTC with PI speed regulator in robustness, in regulator tracking precision and in presence of load disturbances because FLC is inherently adaptive in nature. REFERENCES [1] Jagadish H. Pujar, S. F. Kodad “Simulation of Fuzzy Logic Based Direct Torque Controlled Permanent Magnet Synchronous Motor Drive”, Proceedings of the International Conference on Artificial Intelligence- ICAI09, Vol. I, pp. 254-257, July 13-16, 2009, Las Vegas Nevada, USA. [2] Takahashi I, Naguchi T. “A new quick-response and high- efficiency control strategy of an induction motor”. IEEE Transactions on Industry Application [ISSN 0093-9994], 1986, IA-22(5): 820-827. [3] D. Casadei, G. Grandi, G. Serra, A. Tani ”Effectes of flux and torque hysteresis band amplitude in direct torque control of induction machines”, IEEE-IECON-94, 1994, 299–304. [4] Jia-Qiang Yang, Jin Huang, ″Direct Torque Control System for Induction Motors With Fuzzy Speed Pi Regulator″ Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005. [5] R.Toufouti S .Meziane ,H. Benalla, “Direct Torque Control for Induction Motor Using Fuzzy Logic” CGST Trans. on ACSE, Vol.6, Issue 2, pp. 17-24, June, 2006. [6] Lee, C. C. “Fuzzy Logic in Control System: Fuzzy Logic Controller”, Part I/II, IEEE Trans. Systems Man. Cybernet 20 (1990), 404-435. [7] Hui-Hui Xia0, Shan Li, Pei-Lin Wan, Ming-Fu Zhao, ″StudyFigure 7. Proposed DTC simulated responses with Fuzzy speed regulator on Fuzzy Direct Torque Control System″, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Beijing, 4-5 August 2002. 5© 2010 ACEEEDOI: 01.IJEPE.01.03.30
  6. 6. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010[8] Jagadish H. Pujar, S. F. Kodad “Digital Simulation of Direct Dr. S. F. Kodad received the M.Tech. degree in Energy Torque Fuzzy Control of PMSM Servo System”, Systems Engg. from JNTU, Hyderabad, International Journal of Recent Trends in Engineering- IJRTE, Vol. 2, Nov. 2009 Issue, pp. 89-93, Academy India in the year 1992. He received his Publishers, Finland. Ph.D. degree in Electrical Engg. from JNTU, Hyderabad, India in the year Mr. Jagadish. H. Pujar received the M. 2004. Currently, he is working as Tech in Power and Energy Systems from Professor and Head in Aurora College of NITK Surthkal, Mangalore University in Engg., Hyderabad, Andhra Pradesh, the year 1999. Currently, he is working as India in the Dept. of Electrical & Electronics Engg. He has an Asst. Professor in B V B College of published a number of papers in various national & Engineering & Technology, Hubli, international journals & conferences & done a number of Karnataka, India in the Dept. of Electrical in-house & industry projects. He is also guiding a number& Electronics Engg. & simultaneously pursuing his Ph.D. of PhD. His area of interests is neuro-fuzzy systems,in Electrical & Electronics Engg. from the prestigious Renewable energy systems, etc.Jawaharlal Nehru Technological University, Anatapur,Andhra Pradesh, India. His area of interests is SoftComputing techniques based systems. 6© 2010 ACEEEDOI: 01.IJEPE.01.03.30

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