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14. a variable speed, sensorless, induction motor drive
 

14. a variable speed, sensorless, induction motor drive

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    14. a variable speed, sensorless, induction motor drive 14. a variable speed, sensorless, induction motor drive Document Transcript

    • A Variable-Speed, Sensorless, Induction Motor Drive Using DC Link Measurements S. B. Bodkhe M. V. Aware Department of Electrical Engineering Department of Electrical Engineering G. H. Raisoni College of Engineering Visvesvarya National Institute of Technology Nagpur, India Nagpur, India s_b_bodkhe@yahoo.co.in mva_win@yahoo.com Abstract— This paper presents a new control strategy for on applying speed sensorless FOC to high performancethree-phase induction motor which includes independent speed & applications that is based on estimation of rotor speed by usingtorque control loops and the current regulation thereby the machine parameters, instantaneous stator currents andovercoming the limitation (i.e. sluggish response) of volts per voltages [1]-[6]. The benefits of speed sensorless control arehertz controlled industrial drives. For close-loop control, the the increased reliability of overall system with the removal offeedback signals including the rotor speed, flux and torque arenot measured directly but are estimated by means of an mechanical sensors, thereby reducing sensor noise and driftalgorithm. The inputs to this algorithm are the reconstructed effects as well as cost and size. However to exploit thewaveforms of stator currents and voltages obtained from the dc benefits of sensorless control, the speed estimation methodslink and not measured directly on stator side. The proposed drive must achieve robustness against model and parameterthus requires only one sensor in the dc link to implement the uncertainties over a wide speed range. To address this issue, aclose-loop speed and torque control of a three-phase induction variety of approaches have been proposed.motor. The simulation results on a 2.2 kW induction motor drive The adaptive observers (AO) like Luenberger observer or thein Matlab/Simulink software show fast dynamic response and extended Kalman filter [1], [5] gets accurate estimates undergood agreement between the actual values and the estimated detuned operating conditions but these solutions arevalues of torque and speed. Replacement of the open-loop controlstrategy of existing v/f drive by the proposed close-loop strategy computationally intensive, require more memory space and areappears to be possible without requiring any additional power difficult to tune because the initial values of three covariancecomponents and sensors. matrices have to be assumed and selected after much trial and error. So their application in low cost drives is limited. The Index Terms— Speed-sensorless, estimation, dc link, band-pass model reference adaptive system is also an AO technique [7],filter, reconstruction, three-phase induction motor, space-vector. where the same quantity is calculated by two different ways. One of them is independent of variable to be estimated while NOMENCLATURE the other one is dependent on it. The two computed quantitiesRs Rr Stator and rotor resistances ( Ω ) are used to formulate the error signal. The error signal is then Magnetizing and rotor inductances (Henry) fed to an adaptation mechanism which in most cases is a PILm Lr controller. The output of the adaptation mechanism is the I. INTRODUCTION estimated quantity. While all the speed sensorless techniques eliminate the useThe widespread industrial use of induction motor (IM) has of mechanical speed sensor, they require the stator current andbeen stimulated over the years by their relative cheapness, low stator voltage signals as input. This requires at-least twomaintenance and high reliability. The control of IM variable current sensors and two voltage sensors on the stator side. It isspeed drives [1] often requires control of machine currents, difficult to get current sensors with equal gains over the widewhich is normally achieved by using a voltage source inverter. range of frequencies, voltages and currents used in a practicalA large number of control strategies have been registered so inverter. The problem is exacerbated if the motor windings arefar [2]-[4]. The volts per hertz (v/f) IM drives with inverters not perfectly balanced or if the current sensors have some dcare widely used in a number of industrial applications offset. Over last few years, techniques of stator currentpromising not only energy saving, but also improvement in reconstruction from the dc link current have been suggested inproductivity and quality. The low cost applications usually literature [8]-[9].adopt v/f scalar control when no particular performance is In this paper, a new speed sensorless control strategy for IMrequired. Variable-speed pumps, fans are the examples. is proposed that includes the speed control, torque control and For those applications which require higher dynamic current regulation. Unlike conventional close loop estimators,performance than v/f control, the dc motor like control of IM it involves less computation and is less dependent on machinethat is called, the field oriented control (FOC) is preferred. parameters. The stator currents and stator voltages areDuring the last few years, a particular interest has been noted978-1-4244-2800-7/09/$25.00 ©2009 IEEE 3591 ICIEA 2009
    • reconstructed from dc link quantities and the inverter recovery effect of diode, this leg is in fact shorted through atswitching signals. For faithful reconstruction of currents, use this moment such that a positive current spike will appear atof adaptable gain band-pass filter is proposed in the scheme. the dc link side. To establish the basic relationship between dcThe simulation results of proposed scheme shows fast link current, winding currents and inverter switching pattern,performance as compared to v/f control and therefore can be the switches shown in Fig. 2 are considered as ideal; the dioderegarded as an improvement. For the close loop speed control, recovery effect and the snubber action are not considered.a single current sensor in the dc link is sufficient. Thus it issuitable for low-cost, moderate performance, sensorless IMdrive applications. The proposed drive is modeled inMatlab/Simulink software for a 2.2 kW IM. The simulationresults are presented to verify the workability of proposedstrategy. II. PROPOSED SCHEMEFig. 1 shows the block diagram of the proposed scheme. Itconsists of a speed (frequency loop), a torque loop, and a Figure 2. Voltage source inverter fed induction motor drivecurrent regulator. The output of speed/frequency regulatorrepresents the torque reference for the torque loop. The torque A. Space-Vectorsregulator generates the q-axis current command iqe∗ . The d- During normal state, there are eight switching states of inverter which can be expressed as space voltage vector (SA,SB,SC) suchaxis current command i ∗ is directly generated from the as (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0) and dereference rotor flux ψ r * as given by (1) [1]. This eliminates (1,1,1). SA =1 means upper switch of leg A is on while the lower one is off, and vice versa. The same logic is applicable toan additional PI controller and reduces the computational SB and SC also. Amongst above eight voltage vectors, (0,0,0)burden. These dc commands expressed in synchronously and (1,1,1) are termed as zero vectors while the other six asrotating reference after transformation to the three phase active vectors. The switching vectors describe the invertercurrent commands are than compared with the actual three- output voltages.phase currents (reconstructed waveforms) to generate theswitching signals for the inverter. In the proposed scheme, all B. Basic Principle of Phase Voltage & Line Currentthe feedback signals including the stator currents and stator Reconstructionvoltages are estimated/reconstructed from the dc link For different voltage vectors, the phase voltage that willquantities. appear across stator winding can be determined by circuit * ψ * (1) observation. This is summarized in Table 1. It is assumed that i = r de Lm the stator winding is star connected. From this table, the expressions for the reconstruction of three phase voltages are III. RECONSTRUCTION OF STATOR VOLTAGES & CURRENTS as follows (assuming no dwelling time): FROM DC LINK ~ V v = dc (2S − S − S ) (2) a A B CAs indicated in [1], [6], the stator flux, torque and speed can 3be derived from the stator voltages and currents expressed in ~ Vdc (3) vb = (−S A + 2SB − SC )d-q reference frame. The phase currents and voltages are 3 Vdc (4)related to the dc link current and voltage by inverter switching ~ vc = (−S A − SB + 2SC )states. A voltage source inverter-IM drive is shown in Fig. 2 3where Vdc is the dc link voltage, Idc is the instantaneous dc link The stator voltages as expressed in stationary d-q frame are: ~ s ~ V (5)current and ia, ib, ic are the instantaneous three-phase winding vqs = va = dc ( 2 S A − S B − SC )currents. Generally, IGBTs associated with snubber protection 3and feedback diode are used as switch in inverters. When a ~ s 1 ~ ~ V vds = (vb − vc ) = dc (SB − SC ) (6)switch is being turned-on and the conducting diode at the same 3 3leg is being blocked off by this turn-on, because of the reverse TABLE I. DC LINK CURRENT & PHASE VOLTAGES Voltage Vector va (V) vb (V) vc (V) Idc (A) (SA,SB,SC) (0,0,0) 0 0 0 0 (0,0,1) -Vdc/3 -Vdc/3 2Vdc/3 + ic (0,1,0) -Vdc/3 2Vdc/3 -Vdc/3 + ib (0,1,1) -2Vdc/3 Vdc/3 Vdc/3 - ia (1,0,0) 2Vdc/3 -Vdc/3 -Vdc/3 + ia (1,0,1) Vdc/3 -2Vdc/3 Vdc/3 - ib (1,1,0) Vdc/3 Vdc/3 -2Vdc/3 - icFigure 1. Block diagram of the proposed scheme. (1,1,1) 0 0 0 0 3592
    • The relationship between the applied active vectors and the can be obtained on integration of the phase voltage minusphase currents measured from the dc link is also shown in voltage drop in the stator resistance Rs [1]:Table 1. It is clear that at-most, one phase current can be ψ = (v ~ ds ~ s − R ~ s ) dt ∫ ds si ds (15)related to the dc.-link current at every instant. The qs = ∫ (v qs ~ ψ ~ s − R ~ s ) dt (16)reconstruction of phase currents from the dc-link current can s iqsbe achieved easily only if two active vectors are present for at ~ ~ ~ ψ s = ψ ds 2 + ψ qs 2 (17)least enough time to be sampled. Fortunately, as indicated in ~ ~ ~ ψ ~ ψ cos θ e = ~ ; sin θ e = ~ (18)[10], for most PWM strategies, two phase currents can be ds qssampled by looking at the dc link current over every PWM ψ s ψ speriod. If the PWM frequency is high enough, the phase ~ where θ e is the stator flux angle with respect to the q-axis ofcurrent does not change much over one PWM period. Hence, a the stationary d-q frame.reconstructed current derived from the dc link current gives areasonable approximation of the actual current. In terms of B. Estimation of Torqueswitching states and Idc, the three ac line currents can be The electromagnetic torque can be expressed in terms of statorderived as follows: currents and stator flux as follows [1]: S ~ a S i = I (S − B − C ) dc A 2 2 (7) T = e (ψ i −ψ i ) ~ 3P ~ ~ s ~ ~ s 4 ds qs qs ds (19) ~ S SC (8) ib = I dc (− A + SB − ) C. Estimation of Synchronous Speed &Rotor Speed 2 2 S A SB ~ The synchronous speed ωe can be calculated from the ~ ic = Idc (− − + SC ) (9) 2 2 expression of the angle of stator flux as:The stator currents as expressed in stationary d-q frame are: ~ ~ ψ θe = tan−1 ~ds (20) ~ s ~ ~ s 1 ~ ~ (10) i =i ; qs i = a (2 i + i ) ds b a ψ qs 3 ~ ~ s ~ ~ s −1 ~ ~ (11) ~ dθ e (21) or iqs = ia ; ids = ( 2 ic + ia ) ωe = 3 dt ~ To obtain the rotor speed ωr , simple slip compensation can be ~ s ~ ~ or iqs = −( ib − ic ); ~ s ids = 1 ~ ~ ( i + ic ) (12) 3 b derived using the steady-state torque speed curve for the machine being used:C. Filter Stage ~ ~ ω = KsTe (22)The dc link current Idc consists of a train of short duration slpulses and has information about the stator currents of all the where Ks is the rated slip frequency/rated torque and it can bethree phases. By using (7)-(9), these pulses can be segregated derived from the name plate of the machine. Alternately, if theinto three ac line currents. Generally, an active or passive-type rotor flux ψ r is assumed as constant, the slip speed can alsolow-pass filter (LPF) with narrow bandwidth is used to filter be calculated as:out the high frequency components in the ac current waveform ~ s ~ R iqs (23)thus obtained from Idc. This filter actually works as an ω = r ~ sl Lr ids sintegrator. However, a LPF causes phase lag and amplitudeattenuation that vary with fundamental frequency [11]. In this The rotor speed is than given by, ~ ~ ~ ωr = ωe − ωsl (24)paper, we propose the use of band-pass filter with adaptablegain to overcome this problem. The transfer function of thefilter is given below: V. PROPOSED CONTROL STRATEGY ⎡⎛ sT ⎞⎛ T ⎞⎤ (13) Majority of IM drives are of open-loop, constant-v/f, voltage- y= ⎢⎜ 1 + sT ⎟⎜ 1 + sT ⎟⎥ x ⎣⎝ ⎠⎝ ⎠⎦ source-inverter type. These drives are cost effective but they offer sluggish response. Due to high current transients duringwhere x, y and T are input, output and time constant of the the torque changes, they are subject to undesirable trips. Toband-pass filter. For sT >>1; (1+sT) ≅ 1. Therefore, avoid the un-necessary trips, the control parameters like 1 (14) acceleration/deceleration rate has to be adjusted (reduced) y= x s according to the load. This results in underutilization of torque capability of the motor. Thus the drawback of v/f drive can be IV. ESTIMATION OF FEEDBACK SIGNALS FROM attributed to lack of torque control. This is the reason why RECONSTRUCTED QUANTITIES open-loop, constant-v/f drives are mostly used in lowThe feedback signals required to simulate the proposed performance fan and pump type loads. In this paper, wescheme i.e., flux, torque and rotor speed are estimated as: propose a modified control scheme that includes the torque control and a current regulated PWM inverter to avoid theA. Estimation of Flux undesirable trips due to transient currents.The stator flux in stationary d-q frame ψ s ,ψ qs s and thus ψ s As shown in Fig.1, the feedback signals i.e. torque and rotor ds speed are obtained from the dc link quantities and hence from 3593
    • the reconstructed line currents and phase voltages. The 500accuracy of reconstructed waveforms depends upon the a ) v (V 0sampling rate [8], [9]. Higher the sampling rate less is the error -500between the actual and reconstructed waveforms. In a hard- 0.05 0.06 0.07 0.08 0.09 0.1switching inverter, the switching frequency is limited to a 500typical value of a few kHz. This limits the sampling rate of dc b ) v (V 0current and hence the update rate of torque and rotor speed.Consequently, closing the loop directly on the instantaneous -500 0.05 0.06 0.07 0.08 0.09 0.1value of the estimated torque now becomes difficult because 500estimation error during a PWM cycle could become c ) v (Vsignificantly high. In order to use the estimated torque in a 0more robust manner, a control strategy should use the -500averaged torque instead of the instantaneous value. This leads 0.05 0.06 0.07 0.08 Tim e (s ) 0.09 0.1to the control strategy depicted in Fig.1. In this system, two P- (a)I controllers are used to regulate the average value of torque iAind lin ( ) c kA 5and speed. The output of the P-I regulators forms the q-axis 0reference in a synchronously rotating reference frame. -5 1.78 1.8 1.82 1.84 VI. SIMULATION STUDIES iBind lin ( ) c kA 5In order to predict the behavior of the drive during steady-state 0and transient conditions, detailed simulation studies of the -5scheme shown in Fig.1 are carried out on a 2.2kW IM by 1.78 1.8 1.82 1.84 iC d lin ( ) in c k A 5using Simulink software. Fig. 3. shows the internal structure ofthe controller that consists of the speed loop, torque loop and 0the current regulation loop in synchronously rotating frame of -5 1.78 1.8 1.82 1.84reference. The switching signals for inverter are generated by Time (A) (b)comparing the command ac currents with reconstructed ac Figure 4. Reconstructed waveforms of (a) three phase voltages and (b) threecurrents. For the reconstruction of stator voltages and ac line line currents separated from the dc link current.currents, the dc link quantities with Vdc = 600V are sampledwith a sampling time of 2e-6 seconds and than segregated into values of time constants T for the band-pass filter are selectedthe three-phase voltages and three ac currents as per (2)-(4) by trial and error. The simulation output of band-pass filterand (7)-(9) respectively. The simulation was carried out for which represents the reconstructed ac line currents is shown infive different operating conditions as is presented ahead. A Fig.5(a). For the sake of comparison, the actual ac linevariable- step ode23tb(stiff/TR-BDF2) solver was used. The currents are illustrated in Fig.5(b). The reconstructed andwaveforms of reconstructed phase voltages and the three ac actual waveforms of ac line currents during 100% speedline currents as reflected in the dc current, are presented in reversal at no-load are presented in Fig.6(a) & (b). TheFig.4. From these waveforms, it is clear that the samples of response of speed sensorless drive during differentphase currents available in the dc link current are not evenly ) econstructed line currents a,b,c,(A 5spread and being discontinuous, the set of resulting points do 0not constitute an acceptable reconstruction. Therefore a zero-order hold is employed followed by a band-pass filter. The -5 R 1.78 1.8 1.82 1.84 Tim e (s ) (a) c re tsab ( ) ur n , ,c A 5 c a e Atu l lin 0 -5 1.78 1.8 1.82 1.84 Time (s) (b) Figure 5. Stator currents at rated load (a) reconstructed (b) actual waveforms R c n tr c d 10 e o s u te c r e ts ( ) ur n A 0 -10 1.1 1.2 1.3 Time (s)Figure 3. Simulink model of control strategy (a) 3594
    • outer speed loop and is very similar to open-loop v/f drive in A tu l c r e ts( ) c a ur n A 10 0 terms of power components and sensors required. Due to the -10 inclusion of torque control loop, the drive response is fast and 1.1 1.2 1.3 stable. Simulation results confirm the effectiveness of the Time (A) proposed scheme. The technique uses only dc link voltage and (b) dc link current measurements to generate the estimates ofFigure 6. Stator currents during reversal at no-load (a) reconstructed E tim te toq e( .u E t a ds e d( .u) s a d r u p ) sim te p e p .waveform (b) actual waveform 1 0.5dynamic conditions was studied in detail. To check theaccuracy of estimated variables, these variables were obtained 0 0 0.1 0.2 0.3 0.4 0.5by two different methods. In the first one, the machine 15 10variables which include the flux, torque, synchronous-speed, 5slip-speed and rotor-speed are estimated by using (15)-(24) 0and in the second method, these variables are calculated with -5 0 0.1 0.2 0.3 0.4 0.5the help of dynamic model of IM [1] by using the stator Tim e (s ) (a)currents and voltages measured directly. The simulation cu l p e pu) At a s e d( . .results of the first method were treated as estimated values 1while those of the latter method as actual values. 0.5 Case 1: Free acceleration characteristics: 0The machine was allowed to accelerate from zero speed to 0 0.1 0.2 0.3 0.4 0.5 cu l oq e pu) 15 At a t r u ( . .rated speed at no-load. The steady-state was reached at 0.3 10seconds. The waveform of estimated speed show faster 5 0response (less damped) as compared to its actual counterpart. -5This is shown in Fig. 7(a) & (b). 0 0.1 0.2 0.3 Tim e (s ) 0.4 0.5 Case 2: Step change in speed reference: (b)Step change in speed reference was applied two times. At 0.5 Figure 7. Free-acceleration characteristics (a) estimated & (b) actual valuessec., from +100% to +60% and vice-versa at 1 sec. was Et a dt r u ( .u Et ae s e d p .) simt oq e p .) simt d pe ( .uapplied. The response is shown in Fig.8. The torque becomes 1negative during the first change to decelerate the motor. Upon 0.5reaching steady state, the torque becomes equal to the load 0torque. The response time of the drive for this step change is 10 0.4 0.6 0.8 1 1.2100ms. The estimated values of torque and speed vary in 0accordance with their corresponding actual values. e -10 Case 3: Speed reversal: 0.4 0.6 0.8 1 1.2A step change in speed reference from +100% to -100% is Time (s) (a)applied at 1.5 seconds. This step change is equivalent to 100% A tu l s e d(p .) c a p e .u 1speed change. The response is shown in Fig. 9. The phasesequence reverses to rotate the motor in reverse direction. The 0.5drive reaches steady state after the change in reference speed 0 0.4 0.6 0.8 1 1.2in 700 ms. this proves that the speed estimation is stable even A tu l to u (p .) 10 c a rq e .uat very low speeds. Case 4: Step change in load: 0A step change in load is applied at 0.5 seconds. The response -10of the drive is shown in Fig.10. The electromagnetic torque 0.4 0.6 0.8 Tim e (s ) 1 1.2increases to correct the speed error. Upon reaching the steady (b)state, the torque becomes equal to the load torque. The rotor Figure 8. Variation in rotor speed and electromagnetic torque for stepspeed, after an initial droop attains back its earlier speed . The changes in reference speed (a) estimated values, (b) actual valuesmotor reaches the steady state in 300ms. s a d oq e p . s a d p e p .) E timte t r u ( .u)E timte s e d( .u Case 5: Low speed operation: 1The response of the drive at 40% and 20% of rated speed is 0shown in Fig.11. For the machine under consideration, 20% -1corresponds to 3.14 rad/sec angular mechanical speed. The 1.4 1.6 1.8 2 2.2speed estimation is very stable even at this low speed range. 5 0 VII. CONCLUSION -5 -10In this paper, a new control strategy for induction motor drive 1.4 1.6 1.8 Time (s) 2 2.2is proposed. The drive is operated under torque control with an (a) 3595
    • A tu l s e d(p .) phase voltages, line currents, flux, torque and rotor speed. If c a p e .u 1 0 the dc link voltage is assumed as constant, only one current -1 sensor in the dc link is sufficient to give the estimates of all 1.4 1.6 1.8 2 2.2 required feedback variables. Moreover, the same current sensor that is already available in the dc link of an open-loop A a to u (p .) 5 ctu l rq e .u 0 v/f drive for protection purpose can be used. Thus the open- -5 loop control strategy in an existing v/f drive can be replaced -10 by the proposed close-loop control strategy without requiring 1.4 1.6 1.8 Time (s) 2 2.2 any additional power components or the physical sensors. The (b) proposed strategy appears to be a good compromise betweenFigure 9. Variation in rotor speed and electromagnetic torque during reversal the high-cost, high-performance field-oriented drives and the(a) estimated values, (b) actual values low-cost, low-performance v/f drives. Practical implementation of the proposed scheme on a 16 E tim te toq e( .u E tim te s e d(p .) s a d r u p .) s a d p e .u 1 bits floating point arithmetic Texas Instrument TMS320C31 processor are the subject of future follow-up research work. 0.5 APPENDIX 0 0 0.2 0.4 0.6 0.8 1 MACHINE PARAMETERS 15 10 Rs = 11.1Ω; R’r = 2.2605Ω 5 Ls = 0.7329H; L’r = 0.7329H 0 Lm = 0.71469H; P = 4 -5 0 0.2 0.4 0.6 0.8 1 Time (s) (a) REFERENCES [1] B. K. Bose, Power Electronics and Motor Drives, Delhi, c a p e p .) A tu l s e d( .u 1 India, Pearson Education, Inc., 2003. 0.5 [2] M. Rodic and K. Jezernik, “Speed-sensorless sliding-mode torque control of induction motor,” IEEE Trans. Ind. 0 0 0.2 0.4 0.6 0.8 1 Electron., vol. 49, no. 1, pp. 87-95, Feb. 2002. c a r u p .) 15 [3] L. Harnefors, M. Jansson, R. Ottersten, and K. Pietilainen, A tu l toq e( .u 10 5 “Unified sensorless vector control of synchronous and 0 induction motors,” IEEE Trans. Ind. Electron., vol. 50, no. 1, -5 pp. 153-160, Feb. 2003. 0 0.2 0.4 0.6 0.8 1 Time (sec) [4] M. Comanescu and L. Xu, “An improved flux observer based (b) on PLL frequency estimator for sensorless vector control ofFigure 10. Variation in rotor speed and electromagnetic torque with step rise induction motors,” IEEE Trans. Ind. Electron., vol. 53, no. 1,in load(a) estimated values, (b) actual values pp. 50-56, Feb. 2006. [5] Radu Bojoi, Paolo Guglielmi and Gian-Mario Pellegrino, s a d r u p .) s a d p e p .) E timte toq e( .u E timte s e d( .u “Sensorless direct field-oriented control of three-phase 1 induction motor drives for low-cost applications,” IEEE 0.5 Trans. Ind. Appl., vol. 44, no. 2, pp. 475-481, Mar. 2008. 0 [6] I. Boldea and S. A. Nasar, Electric Drives, New York: Taylor 20 0 0.5 1 1.5 & Francis, 2006. [7] S. Maiti, C. Chakraborty, Y. Hori, and Minh. C. Ta, “Model 0 reference adaptive controller-based rotor resistance and speed estimation techniques for vector controlled induction motor -20 0 0.5 1 1.5 drive utilizing reactive power,” IEEE. Trans. Ind. Electron. Time (s) (a) vol. 55, no. 2, pp. 594-601, Feb. 2008. [8] B. Saritha and P. A. Janakiraman, “Sinusoidal three-phase c a p e p .) A tu l s e d( .u 1 current reconstruction and control using a dc-link current 0.5 sensor and a curve-fitting observer,” IEEE Trans. Ind. 0 Electron., vol. 54, no. 5, pp. 2657-2662, Oct. 2007. 0 0.5 1 1.5 [9] H. Kim and T. M. Jahns, “Current control for AC motor c a r u p .) A tu l toq e( .u 20 drives using a single dc-link current sensor and measurement 0 voltage vectors,” IEEE Trans. Ind. Appl., vol. 42, no. 6, pp. 1539-1546, Nov./Dec. 2006. -20 0 0.5 1 1.5 [10] P. Vas, Sensorless Vector and Direct Torque Control, Oxford, U.K. Oxford Science, 1998. Time (s) (b) [11] J. Zhao, B. K. Bose, “Neural-network-based waveformFigure 11. Variation in rotor speed and electromagnetic torque in low-speed processing and delayless filtering in power electronics andregion (a) estimated values, (b) actual values AC drives,” IEEE Trans. Ind. Electron., vol. 51, no. 5, pp. 981-991, Oct. 2004. 3596