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Au26297302

  1. 1. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302 Direct Torque Control Based on Space Vector Modulation with Adaptive Stator Flux Observer for Induction Motors Srinivasa Rao jalluri*, Dr.B.V.Sanker Ram***(Assistant Professor, Department of Electrical and Electronics Engineering, VNR VJIET, Hyderabad-500070, India.) ** (Professor, Department of Electrical and Electronics Engineering, JNT University Hyderabad, India.)ABSTRACT This paper describes a combination of output voltage vector is determined by the torque-direct torque control (DTC) and space vector ripple minimum condition. These improvements canmodulation (SVM) for an adjustable speed sensor greatly reduce the torque ripple, but they increaseless induction motor (IM) drive. The motor drive the complexity of DTC algorithm. An alternativeis supplied by a two-level SVPWM inverter. method to reduce the ripples is based on spaceUsing the IM model in the stator – axes reference vector modulation (SVM) technique [5], [6].frame with stator current and flux vectors Direct torque control based on space vectorcomponents as state variables. In this paper, a modulation (DTC-SVM) preserve DTC transientconventional PI controller is designed merits, furthermore, produce better quality steady-accordingly for DTC-SVM system. Moreover, a state performance in a wide speed range. At eachrobust full-order adaptive stator flux observer is cycle period, SVM technique is used to obtain thedesigned for a speed sensor less DTC-SVM reference voltage space vector to exactly compensatesystem and a new speed adaptive law is given. By the flux and torque errors. The torque ripple of DTC-designing the observer gain matrix based on state SVM in low speed can be significantly improved.feedback control theory, the stability and In this paper, SVM-DTC technique with PIrobustness of the observer systems is ensured. controller for induction machine drives is developed.Finally, the effectiveness and validity of the Furthermore, a robust full-order speed adaptiveproposed control approach is verified by stator flux observer is designed for a speed sensorsimulation results. less DTC-SVM system and a speed-adaptive law is given. The observer gain matrix, which is obtainedKeywords- DTC, Stator Flux Observer, Torque by solving linear matrix inequality, can improve theRipple robustness of the adaptive observer gain in [7]. The stability of the speed adaptive stator flux observer isI. INTRODUCTION also guaranteed by the gain matrix in very low DIRECT TORQUE CONTROL (DTC) speed. The proposed control algorithms are verifiedabandons the stator current control philosophy, by extensive simulation results.characteristic of field oriented control (FOC) andachieves bang bang torque and flux control by II. DTC-SVM TECHNIQUEdirectly modifying the stator voltage in accordance A. Model of Induction Motorwith the torque and flux errors. So, it presents a good Under assumption of linearity of thetracking for both electromagnetic torque and stator magnetic circuit neglecting the iron loss, a three-flux [1]. DTC is characterized by fast dynamic phase IM model in a stationary axes reference withresponse, structural simplicity, and strong robustness stator currents and flux are assumed as statein the face of parameter uncertainties and variables, is expressed by Rs ∆Rr R r ψD ψQ ωr 𝒰perturbations. ϊD= - + iD -ωriQ + + + D (1) σLs σLr σLsLr σLs σLs One of the disadvantages of conventional Rs ∆Rr R r 𝜓 𝑄 ψD ωr 𝒰QDTC is high torque ripple [2]. Several techniques ϊQ = + iQ +ωriD + - + (2) σLs σLr σLsLr σLs σLshave been developed to reduce the torque ripple. 𝜓 𝐷 = 𝒰D - R s 𝑖 𝐷One of them is duty ratio control method. In duty (3)ratio control, a selected output voltage vector is 𝜓 𝑄 = 𝒰Q - R s 𝑖 𝑄applied for a portion of one sampling period, and a (4)zero voltage vector is applied for the rest of the where,ψD , ψQ , 𝒰D , 𝒰Q, iD , iQ are respectivelyperiod. The pulse duration of output voltage vector the D Q axes whereof the stator flux, stator voltagecan be determined by a fuzzy logic controller [3]. In and stator current vector component ωm is the rotor[4], torque-ripple minimum condition during one electricalangular speed,LS,Lr,LMare the stator, rotor,sampling period is obtained from instantaneous and magnetizing inductances, respectively,𝜎 = 1 −torque variation equations. The pulse duration of 297 | P a g e
  2. 2. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302(𝐿2𝑀 /LR L S ) and RS,Rr, are the stator and rotorresistances, respectively.The electromagnetic torqueTe in the induction motorcan be expressed asTe = Pn 𝜓 𝑠 ×is =Pn(𝜓 𝐷 iQ − ψQ iD ) (5)Where Pn is the number of pole pairs.B. DTC-SVM TechniqueThe DTC-SVM scheme is developed based on theIM torque and the stator flux modules as the systemoutputs is shown in fig.1. Fig. 3DTC-SVM with PI controller III. SPEED ADAPTIVE STATOR FLUX OBSERVER A. Speed Adaptive Stator Flux Observer Using the IM model of (1)–(4), the speed adaptive stator fluxobserver is introduced: 𝒙 =A𝑥+BU is= C𝒙(10) where 𝐱=(iDiQψD ψQ )T , u =( uDuQ)TFig. 1 Block Diagram of DTC-SVM system is=(iDiQ)T 1 1 0 0 −1The stator voltage components are defined as system B=[σLs II]TC =[I 0] , I= J=control inputs and stator currents as measurable state 0 1 1 0 A=A0+ΔAR + ωrAωvariables. Rso Rro Rso Let the system output be − + σLr I I = σLs σLsLr + 𝑦1 = 𝑇𝑒 = 𝜌 𝑛 ψ 𝑑𝑠 i 𝑞𝑠 − ψ 𝑞𝑠 i 𝑑𝑠 (6) −R s0 I 0 ∆Rs ∆Rr ∆Rso 1 − σLs + σLr I I J σLs J 2 σLsLr +ωr𝑦2 = ψ 𝑠 = ψ2𝑑𝑠 + ψ2𝑞𝑠 (7) −∆R s0 I 0 0 0 the uncertain parameters in matrix A are Define the controller objectives e1 and e2 as split in two parts; one corresponding to nominal or𝑒1 = 𝑇𝑒 − 𝑇 𝑒𝑟𝑒𝑓 (8) constant operation and the second unknown behavior.Rs0 and Rr0 are nominal value stator resistance and rotor resistance,ΔRs and ΔRr are stator𝑒2 = ψ 𝑠 − ψ 𝑟𝑒𝑓 (9) resistance and rotor resistance uncertainties, respectively.Where Teref,ψ 𝑟𝑒𝑓 are reference value of The state observer, which estimates theelectromagnetic torqueand stator flux, respectively. state current and the stator flux together, is given byThe flux control loop and torque control are shown the following equation:in fig.2 dx dt = (A0+ΔAR+ωrAω)x+Bu+H(is -is)(11) Where 𝑥=(iDiQ 𝜓 𝐷 𝜓 𝑄 ) 𝑇 are estimated values of the state variable and H is the observer matrix. Supposing state error is i.e., e=𝑥-𝑥, so d d d dt (e) =dt (x) -dt (x)Fig.2 Control Strategy of DTC = (A0+HC+ΔAR+ωrAω)e +ΔωrAωx(12) In order to derive the adaptive scheme, LyapunovC. DTC-SVM Technique with PI Controller theorem is utilized. Now, let us define the following PI control is one of the earlier control Lyapunov function:strategies. It is applied to the D-axis and Q-axis V = 𝑒 𝑇 e+(ω 𝑟 -ωr)2 ∕ λ (13)rotor flux of the Induction motor obtained from the The time derivative of V is as follows: dvIM model equation of (1) – (4). This improvement =eT [(A0 +HC+ΔAR+ωrAω)T dtcan greatly reduce the torque ripple. The Block (A0 + HC + ΔAR+ωrAω)]ediagram of DTC-SVM with PI controller is shown in 2 dωfig.3. +Δωr(x T AT e + eT Aωx)+λ (ωr -ωr) dtr (14) ω Let 298 | P a g e
  3. 3. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302 2 dωrΔ ωr(x T AT e+eT Aωx)+ (ωr -ωr) ω =0 (15) G(s) = A0 + ωrAω E I (21) λ dt 𝐹 0 0 𝐼 0 0If we select observer gain matrix H so that thevalidity of inequality As System(21), there will be a state feedback H∞ controller K, if and only if there are𝑒 𝑇 [(A0+HC+ΔAR+ωrAω) 𝑇 positive definite matrix X and W to make linear+(A0+ HC+ ΔAR+ ωrAω)] e< 0 (16) matrix inequality (22) is satisfied AX + 𝑊(𝐴𝑋 + 𝑊) 𝑇 𝐸 (𝐹𝑋) 𝑇can be guaranteed, the state observer is stable. 𝐸 𝑇 −I 0 < 0 (22)The adaptive scheme for speed estimation is given 𝐹𝑋 0 −𝐼by If X* and W*is a feasible solution to linearω 𝑟= ( 𝐾𝑝+ K𝑖 ) (𝜓 𝑠 𝑇 ) J (i 𝑠 - is) (17) matrix inequality (22),then u= W*(X*)-1 𝑥is a state 𝑃 feedbackH∞ controller of system(21). So, K= W*(X*)-1 .the observer gain matrix can be obtained from H=KC-1 Table I Parameters of IMFig. 4 DTC-SVM with Adaptive Stator fluxobserverB. Observer Gain Matrix Computation Let’s introduce a theorem about quadraticstability of uncertainty system before design theobserver gain matrix. Lemma: Uncertainty system𝑥 𝑡 = ( A0 + ΔA(t))𝑥(t),𝑥(0)= 𝑥0 (18)is quadratic stable, if and only if A0 is Stable and IV. SIMULATIONS To verify the DTC-SVM scheme without 𝐹(sI − A0 )−1 E ∥∞ < 1 (19) controller, with PI controller and with adaptive stator flux observer simulations are performed in this Where A0 is nominal matrix, which is section. The block diagram of the proposed systemsupposed to be Well Know ΔA=E𝛿F is represent the is shown in Fig. 4. The parameters of the inductionun certainties on A due to unmodeled behavior or motor used in simulation results are as Table I.parameters drift ,E and F are the uncertaintystructure matrices of the system, 𝛿 is uncertainty Case A: DTC without controllercoefficient. The reference stator flux used is 0.8 WbIf ΔAR is also written as ΔAR = E𝛿F, so system (16) and the command speed value is 1420 rpm in bothis quadratic stable,if and only if A0+ωrAω+HC is two systems. The speed and torque response curvesstable and of conventional DTC and proposed DTC-SVM are shown Fig. 6- Fig. 14. At startup, the system is 𝐹(sI − A0 − ωrAω − HC )−1 E ∥∞ < 1 (20) unloaded, the load torque is changed to 2 Nm at t=0.3s, then the load torque is changed from 2 Nm toSupposing K= HC quadratic stability problem of 1 Nm at t=0.6 s. The stator flux observer curves aresystem (12) can be transformed to static state shown in Figs. 8 and 9.feedback H∞ control problem for the system The torque ripple is calculated using the equation 𝑇 𝑚𝑎𝑥 − 𝑇 𝑚𝑖𝑛 𝑇 𝑟𝑖𝑝𝑝𝑙𝑒 (%) = ∗ 100A State –Space realization of Fig.1 is as (21) 𝑇 𝑟𝑒𝑓 299 | P a g e
  4. 4. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302Fig. 6Torque waveform Fig. 10Torque waveformFig. 7Speed waveform Fig. 11Speed waveformFig. 8Stator Flux waveforms Fig. 12Stator Flux waveformsFig. 9Stator flux TrajectoryCase B: DTC with PI controller Fig. 13Stator flux Trajectory Case C: DTC with Stator Flux observer 300 | P a g e
  5. 5. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302 stator flux well and truly. The torque ripple for all the three cases at different load torques is shown in Table II. Load T=2N T=4N T=6N T=8N T=10N Torque m m m m m Method Conventio 50% 25% 16.6% 12.5% 10% nal Conventio 6% 3% 2% 1.5% 1.2% nal withFig. 14Torque waveform PI Conventio 5% 2.5% 1.66% 1.25% 1% nal with flux observer V.CONCLUSION A novel DTC-SVM scheme has been developed for the IMdrive system, In this control method, a SVPWM inverter is used tofeed the motor, the stator voltage vector is obtained to fullyFig. 15Speed waveform compensate the stator flux and torque errors. Furthermore, a robustfull-order adaptive flux observer is designed for a speed sensor-less DTC- SVM system. The stator flux and speed are estimated synchronously. By designing the constant observer gain matrix, the robustness and based on state feedback stability of the observer systems is ensured. Therefore, the proposed sensor-less drive system is capable of steadily working in very low speed, has much smaller torque ripple and exhibits good dynamic and steady-state performance. REFERENCESFig. 16Stator Flux waveforms [1] I. Takahashi and T. Noguchi, “A new quick-response and high efficiency control strategy of an induction motor,” IEEE Trans. Ind. Appl.,vol. IA-22, no. 5, pp. 820–827, 1986. [2] Y. S. Lai and J. H. Chen, “A new approach to direct torque control ofinduction motor drives for constant inverter switching frequency andtorque ripple reduction,” IEEE Trans. Energy Convers., vol. 16, no. 3,pp. 220–227, 2001. [3] S. Mir, M. E. Elbuluk, and D. S. Zinger, “PI and fuzzy estimators for tuning the stator resistance in direct torque control of induction machines,” IEEE Trans. Power Electron., vol. 13, no. 2, pp. 279–287,1998.Fig. 17Stator flux Trajectory [4] F. Bacha, R. Dhifaoui, and H. Buyse, “Real-time implementation ofdirect torque Compared with conventional DTC, the control of an induction machine by fuzzyDTC with PI controller has smaller torque ripple, logic controller,” in Proc. ICEMS, 2001,furthermore the DTC with Stator flux observer has vol. 2, pp. 1244–1249.much smaller torque ripple. From Fig.17, it can be [5] A. Arias, J. L. Romeral, and E. Aldabas,seen that the adaptive observer can estimate the “Fuzzy logic direct torquecontrol,” in Proc. 301 | P a g e
  6. 6. Srinivasa Rao jalluri, Dr.B.V.Sanker Ram / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.297-302 IEEE ISIE, 2000, vol. 1, pp. 253–258. [6] D. Seyoum, M. F. Rahman, and C. Grantham, “Simplified flux estimation for control application in induction machines,” in IEMDC’03,2003, vol. 2, pp. 691–695. [7] G. Xi, H. Gao, and W. Xu et al., “A method to determine gain matrixof stator flux full order observer,” J. Cent. South Univ.(Science andTechnology),vol. 39, no.4, pp. 793–798, 2008. [8] J. Soltani1, G. R. A. Markadeh, and N. R. Abjadi3 et al., “A new adaptive direct torque control (DTC) scheme based-on SVM for adjustable speed sensorless induction motor drive,” in ICEMS 2007, Seoul, Korea, Oct. 8–11, 2007, pp. 497– 502. 302 | P a g e

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