Position Sensorless Control for an Interior Permanent Magnet Synchronous Motor SVM Drive with ANN Based Stator Flux Estimator

Transcription

1 International Journal of Computer an Electrical Engineering, Vol., No. 3, June, 1 Position Sensorless Control for an Interior Permanent Magnet Synchronous Motor SVM Drive with ANN Base Stator Flux Estimator Kalyan Kumar Haler, Naruttam Kumar Roy an B.C. Ghosh Abstract An Interior Permanent Magnet Synchronous Motor (IPMSM) rive fe by Space Vector Moulate (SVM) inverter without rotor position sensor is propose in this paper. The control system estimates the motor stator flux an its position through a Real Time Recurrent Neural Network (RTRNN). The RTRNN is traine off-line to estimate stator flux from the spee error an stationary α- an β- axis current components obtaine through Park s transformation. Vector control of the motor is achieve through comman torue an magnetizing current components generation an necessary transformations. The estimate flux an rotor angle are foun to match accurately with their corresponing actual values. A Proportional plus Integral (PI) controller is use to control the motor variables in close loop. The effectiveness of the rive system is teste for ifferent operating conitions. The propose system is foun to work satisfactorily uner these conitions an perturbations of parameters. Inex Terms PI controller, Park s transformation, real time recurrent neural network, space vector moulation, an sensorless control. I. INTRODUCTION Interior permanent magnet motors are recently introuce in inustries an omestic appliances for their large torue/weight ratio an constant operating spee with high performance [1]-[6]. Both the constant torue an fiel weakening moes of operation are stuie in etail in [1]. The authors of this paper escribe four uarant operation of the rive system implemente in a microprocessor-base system. Fuzzy logic an four switch (IGBT) converter base IPMSM rive is escribe in []. Digital Signal Processor (DSP) with hysteresis current control is use for their rive system implementation. The same authors apply Fuzzy Logic Control (FLC) to achieve inirect vector control of IPMSM [3]. A moifie current control mechanism for VSI-fe IPMSM rive is introuce in [4]. DSP environment is use for practical implementation in this paper. A etaile simulation stuy an microprocessor-base implementation is propose in [5] for application of IPMSM in vehicle. Simple current control mechanism is shown to work effectively in this paper. Maximum torue/ampere control is shown in [6]. Interior permanent magnet motors has -component inuctance, L higher than the -component, L that reuires proper moeling for controller esign. A etaile analysis of IPM lumpe parameter moel starting from variable inuctance an mutual coupling is presente in [7]. The paper shows the - euivalent circuit an escribes methoology to measure the lumpe parameters of the machine. Machine inuctances base on angle epenent reluctances are consiere in [8] for ynamic analysis. Simulate results those comply with their proposal are shown in this paper. Normally, IPM motors are of small size an have applications in low power converting systems. The cost of rives therefore shoul be kept as small as possible. The rive system avois position an spee sensors are shown in [9]-[11]. IPM motors posses magnetic saliency that introuces harmonics in the motor current. This phenomenon is introuce in [9] to fin out position an spee of the IPM rive. An extene inuce voltage moel base sensing of back emf an rotor position is presente in [1]. It uses a position error estimator to calculate spee an rotor position. A sliing moe observer base estimation of back emfs along stationary mutually perpenicular reference frames is shown in [11]. The estimate back emfs are then use to fin out the rotor position. Interior permanent magnet synchronous motors reuire position sensors with the motor to etect the rotor fiel position. Generally, resolvers or shaft encoers are use for this purpose. This paper proposes a rotor position estimator using stator flux components base on RTRNN. The stator flux components along stationary mutually perpenicular axes are use to calculate instantaneous position of the rotor. Space vector moulation techniue is use to reuce the ripple in torue. Manuscript receive July 9, 9. Kalyan Kumar Haler is with the epartment of Electrical an Electronic Engineering of the Khulna University of Engineering an Technology, Khulna, Banglaesh (corresponing author to provie phone: ; kalyan_kuet@ yahoo.com). Naruttam Kumar Roy an B.C. Ghosh are with the epartment of Electrical an Electronic Engineering of the Khulna University of Engineering an Technology, Khulna, Banglaesh ( nkroy@ yahoo.com, bcg@eee.kuet.ac.b). 475 II. MATHEMATICAL MODEL The flux of permanent magnet in an IPM machine is assume to act along -axis of synchronously rotating frame. The stator voltages an currents act along the physical symmetric a-, b-, c-, coils represente as stationary axes. The torue an magnetizing current components i t an i m respectively, act along mutually perpenicular axes. The

2 International Journal of Computer an Electrical Engineering, Vol., No. 3, June, 1 stationary axes a-, b-, c-, their two phase euivalents α-, β-, an the rotating axes are shown in Fig. 1. In this representation δ is the torue angle an ψ is the instantaneous angle of the reference pole of IPMSM. β V b i t δ ψ α V a V c Fig. 1 Stationary an rotating axes of IPMSM The mathematical euations of the IPMSM motor in - axes are written below [7] v = Ri pl i ω ψ ω L i (1) v r r f r = Ri pl i ω L i () Flux Linkages along the fictitious - an -axis are: λ = L i (3) λ = ψ f L i (4) The evelope electromagnetic torue is written as: 3Pp T e = ( ψ f i ( L L ) ii ) (5) The torue balance euation for the motor spee ynamics is given by Te = TL J m pω m Bmωm (6) where, the symbols have their usual meanings. i m III. PROPOSED CONTROL SCHEME A control scheme propose to implement the SVM base vector controlle IPMSM rive is shown in Fig.. The high performance control strategy is implemente in close loop using PI controller in spee loop. The spee error is processe to generate the torue proucing component of the stator current (i t ). The torue angle δ is a function of (i t / i m ) an in this stuy is: i t δ = tan (7) im The - an - axis reference current components are formulate as follows [1]: i = i cosδ I sin δ (8) m t i = it cosδ I m sin δ (9) The reference voltage components V an V are calculate using (1) an (). The reference voltage vector u an the inverter switching time are calculate using the formula presente in [13]. If γ is the angle between the resultant voltage vector an -axis then V γ = tan (1) V If ψ is the angle of resultant stator flux with α- axis then Estimate angle of voltage vector, λ βs ψ = tan (11) λαs θ γ ψ = (1) V c Flux Program i m Axes trans. i i Control voltage calculation V V u = V V u SVM switching control V a V b V c Inverter ω re Σ - ω m E ω PI controller i t γ = V tan ( ) V γ Σ ψ Stator flux an angle estimator θ I αs I βs a-b-c to α-β trans. I a I b I c IPMSM Spee Sensor Fig. Propose Control Scheme of the IPMSM 476

3 International Journal of Computer an Electrical Engineering, Vol., No. 3, June, 1 IV. REAL TIME RECURRENT NEURAL NETORK (RTRNN) BASED STATOR FLUX ESTIMATION In the propose algorithm stator flux components are estimate from stationary α-, β- axis stator currents an spee error, E ω. An euivalent RTRNN is then propose which results in the following matrix euation [14]: λαs ( k 1) 11p λαs 11 iαs λβs ( k 1) = p λβs iβs Eω (13) 3 where 11p, p, 11, etc. are the weights of the RTRNN, which is shown in Fig. 3. i αs (k) i βs (k) E ω (k) Fig. 3 Stationary α- an β-axis stator flux estimation by Real Time Recurrent Neural Network (RTRNN) V. SIMULATION RESULTS The propose control scheme was teste by simulation in a Pentium-base PC with C environment. Solution of ifferential euations was carrie out using R-K 4 th orer metho. The rating an motor parameters use in this simulation are given in Appenix. The space vectors generate with ifferent switching seuences are use to obtain phase voltages. The sampling time interval is 5 μs. The stator phase voltages are shown in the Figs. 4, & (c) respectively. Voltage in volt z z p 13 V a p λ αs ( k 1) λ βs ( k 1) Voltage in volt Voltage in volt V b V c (c) Fig. 4 Stator voltages for phase a, phase b, (c) phase c. A. Performance of RTRNN to Estimate Stator Flux an Rotor Angle The control system an machine moel was simulate simultaneously to visualize the accuracy of the RTRNN flux estimator. The RTRNN was traine off-line uner ifferent operating conitions with the exact values obtaine from the mathematical moel. The estimate an actual values of α- & β-axis stator flux components are shown in Figs. 5 an 5. Position of the rotor is estimate using these flux components an applying to (11). A comparison of estimate value with the actual position from an arbitrary reference is inicate in Fig. 5(c). Perfect matching of the values can be visualize from this figure that inicates the acceptability of the RTRNN to obtain the flux of the IPMSM. Flux in wb Estimate

4 International Journal of Computer an Electrical Engineering, Vol., No. 3, June, 1 Flux in wb Estimate Angle in raian Estimate Fig. 6 Simulate spee response, Develope electromagnetic torue uner transient an steay-state conitions. C. Performance uner Different Operating Conitions 1) Suen Change of Loa Torue The motor was starte from stanstill conition with loa torue 1. N m. Suenly at t=1. s loa torue is increase to 4. N m. The evelope electromagnetic torue an spee response with change of loa at t=1. s is given in Figs. 7 an. Suen application of loa torue causes a negligible oscillation in spee. The steay-state error is almost negligible. (c) Fig. 5 α-axis components of estimate an actual stator flux, β-axis components of estimate an actual stator flux, an (c) Estimate an actual rotor angle for the IPMSM rive. B. Starting Performance of IPMSM rive The motor was starte with a comman spee of 955 rpm from stanstill conition. Fig. 6 shows the simulate spee response of the rive. It is observe that this rive follows the comman spee very fast an reaches the set value at t=. s. Fig. 6 shows the evelope torue that oscillates aroun the loa torue when the motor reaches the set spee. It is notice that higher electromagnetic torue is generate uring the motor acceleration. Some pulsations in electromagnetic torue is notice which is ue to switching voltage isturbances of the evices with SVM. Spee in rpm 1 Reference spee spee Spee in rpm Reference spee spee Loa torue suenly increase here Fig. 7 Develope electromagnetic torue, Simulate spee response for the IPMSM rive for change of loa torue (1. N m to 4. N m). ) Variation of Stator Parameters The effect of mismatch in the value of stator resistance on angle estimation was stuie by increasing it to ouble its 478

5 International Journal of Computer an Electrical Engineering, Vol., No. 3, June, 1 nominal value suenly at t=.5 s. Fig. 8 shows the effect of stator resistance change on angle estimation. The estimate angle still follows the actual angle. Thus the change in resistance has negligible effect on the accuracy of rotor position estimation. Fig. 8 shows the effect of stator inuctance change on angle estimation. The - an -axis inuctances are ouble at t=.5 s. It is note that change in inuctances oes not affect the rotor position estimation. Thus the rive performance is insensitive to stator parameter variation. Angle in raian Angle in raian 1 8 Estimate Estimate Fig. 8 Estimate an actual rotor angle for the IPMSM rive for change in stator resistance (R to R) stator inuctances (L to L an L to L). 3) Reversal of Spee Fig. 9 shows the spee response for reversal of spee. It is observe that the rive system follows a very fast spee response an takes almost ouble time when the spee is reverse from 955 rpm to -955 rpm or vice versa in comparison to starting conition ( to 955 rpm). Fig. 9 shows corresponing evelope electromagnetic torue. Spee in rpm 1 Reference spee spee Fig. 9 Simulate spee response an Develope electromagnetic torue for the IPMSM rive for change in reference spee from 955 rpm to -955 rpm an again to 955 rpm. VI. CONCLUSION The control methoology propose in this paper is foun to work satisfactorily without any position sensor. It nees only a spee transucer an simple 3-phase voltage regulate SVM inverter. The RTRNN flux estimator is accurate an robust uner parameter eviation conitions. The propose control scheme is sufficiently stable an robust to loa isturbances, an spee reversal. Very fast response of the system without oscillation inicates the effectiveness of the propose control scheme. APPENDIX The motor parameters, PI gains an weights use in the system are summarize below: Interior permanent magnet synchronous motor, Rating: 3-phase, 1 hp, 3 V, 3A, 5 Hz, -pole pair. Parameters: Stator resistance, R = 5.8 Ω -axis inuctance, L =.448 H -axis inuctance, L =.14 H Motor inertia, J m =.87 Kg m Rate torue, T b = 6 N m Friction coefficient, B m =.8 Nm/ra/sec Magnetic flux constant, ψ f (rms) =.533 b Spee loop: K p =.3, K i =.16 eights of the RTRNN: 11p = p =.96, 11 = =.5, 1 = - 1 =.8, 13 = 3 =.1 479

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