A Simplified Position Control of a Transverse Flux Type Linear Synchronous Motor Using Hall Sensors

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1 A Simplifie Position Control of a Transverse Flux Type Linear Synchronous Motor Using Hall Sensors Qi Zhao, Ruijuan Guo,Takafumi Koseki Department of Electrical Engineering an Information Systems, The University of Tokyo Tokyo, Japan r_guo@koseki.t.u-tokyo.ac.jp Abstract For position feeback control in long linear synchronous rives, high-resolution sensors such as linear encoers are often expensive for inustrial applications. Furthermore, their fine precision comes along a higher sensitivity to contamination an isturbance. We propose an economic position sensing metho which uses two Hall sensors for position control of long linear synchronous motor rives where fiel flux istribution can be approximate to sinusoial. We obtain position signal from the Hall sensors. Two methos to erive spee signal from the position signal given by the Hall sensors have been compare. The first is an approximate ifferential operation of position with low-pass filter. The secon is application of state observer incluing external loa force in its state variables. In aition, the performance of the cascae position control feeback is verifie to satisfy technical requirements in numerical stuies. Keywors Transverse Flux; Linear Synchronous Motor; Hall Sensors; Cascae Position Control; State Observer; Position Sensing I. INTRODUCTION The Linear Synchronous Motor is attracting attention in recent years an it is wiely use in inustrial applications [1]. High-resolution position sensors such as optical linear encoers for precise position control of linear motors are costly an elicate, especially for long linear rives [2]. Hence, economic position sensors are neee for long linear motor position control system in inustrial applications. We propose to use a couple of Hall sensors on a mover to achieve economic position sensing in long linear rives. A Transverse Flux linear Synchronous Motor, which prouces high thrust ue to its small pole pitch an multipolar configuration [3] has been introuce to our research on economic position control for long linear rives. Contrary to position sensing for rotary motor, which requires only a 36-egree-angle sensing, the first problem of position sensing for long linear rive is that the sensor cost is proportional to the linear motor stroke. The longer the stroke, the higher the cost for a linear encoer. The secon problem is that many environments of inustrial applications have contamination an isturbance to an optical linear encoer. Hence, we propose to use an economic an robust position sensing scheme for long linear position control system. There have been many stuies on the riving methos of rotary synchronous motor with Hall sensors [4]-[6]. Since DC brushless rives are fe with 12 electrical egrees square-wave currents, they require a 6-egree resolution for motor position sensing. Inexpensive Hall sensors can provie this resolution. Digital Hall sensors an aitional harware for low-cost AC linear synchronous rives have been propose by S. Morimoto [4]. This metho obtaine highresolution position information by processing the lowresolution position measurements. Constant spee was assume throughout a 6-egree block. However, this assumption is not vali in accelerating operation from zero spee. Hall sensors can also be use for position control in combination with a sensorless algorithm [5]. The combination of sensorless algorithm an Hall sensors have also been use with a combination of ual observer an position sensor offset compensation strategy [6], which overcome some harware problems. But those methos are epenent on the electrical moel of motors. We have stuie on riving methos of linear synchronous motor with Hall sensors an propose alternating position an spee control of long linear synchronous motor base on Hall sensors [7]. Sensors were combine to a ual-rate sampling observer to estimate motor spee an position. In this work, the observer time constant was varying in relation to motor spee. This metho coul estimate the motor position an spee, an coul suppress oscillation when spee becomes low in numerical stuies. Parameters for the spee controller were also varying in relation to motor spee. Thus, if we can obtain approximate continuous position signal irectly from a simple sensor, the control algorithm woul become much simpler. This paper proposes an economic position sensing metho from low-cost Hall sensors installe on the mover of a transverse flux linear synchronous motor. It also compares two methos to obtain spee from position signal from Hall sensors. The first is an approximate ifferential operation of position with low-pass filter an the secon is a single sample rate state observer which inclues external loa force estimation. Furthermore, position error in a cascae control is also analyze. The system consists of two Hall sensors an generates two quarature analog waveforms. This paper is organize in five sections. Principle, structure an avantages of Transverse Flux Linear Synchronous Motor will be

2 presente in the secon section following this introuction. Funamental iea to use Hall sensors to etect position will then be shown in the thir section. Methos to obtain signals requeste to cascae control will be analyze in the fourth section. The last section conclues the paper. II. PRINCIPLE, STRUCTURE AND ADVANTAGES OF TRANSVERSE FLUX TYPE LINEAR SYNCHRONOUS MOTOR Transverse flux rotary machines were propose by H. Weh in 1986 [8]. Fig. 1 shows the rectilinear moel of a single sie TFM [9]. As this figure shows, the funamental principle can be irectly applicable to linear synchronous motors. Its stator consists of iniviual C cores of laminate steel positione aroun the machine an winings.the rotor consists of two rows of alternately polarize surface mounte permanent magnets an a series of laminate steel elements. This kin of structure guies the main flux through a path transverse to the irection of motor movement. When the winings are excite with a sinusoial alternating current, continuous torque will be prouce an motor moves. TFM esigns ha complex structural problems in the early stage. Many researchers i lots of work on transverse flux machines. Recently, H.J. Kim [3] propose a tunnel actuator, which is a transverse flux linear motor with C stator core an coreless mover. This kin of structure contributes to reuce mover mass an bearing loa. On account of low power factor of transverse flux machine, Y. Yamamoto [1], consiere on structure an material of rotary transverse flux linear motor stator, which enhance the motor power factor over.8. A. Avantages of Transverse Flux Machine TFM can achieve high thrust because short pole-pitch can be realize without substantial increase of leakage flux. The short pole pitch allows for a low spee mechanical rive with high armature electric frequency without any mechanical spee reuction. Therefore, the motor is beneficial for irect rives. B. Requirements for long an fast rive combine with position feeback control Firstly low-cost Hall sensors are neee to obtain economic position sensing for long linear synchronous motor position rive system. Seconly, position controller shoul respon fast, in our research 16 msec level is satisfie. Thirly, the position error between position comman an real one shoul be smaller than 1mm. That is to say, the error between position feeback signal from Hall sensors an real position shoul be also smaller than 1mm. Fourthly, effects of unmoele isturbance force such as friction force of linear bearing, shall be sufficiently suppresse. Feeforwar isturbance compensation is useful for the isturbance suppression. position rive system. However, Hall sensors cannot irectly give out linear position signals, so we have to process the analog signal from Hall sensors to linear position information neee for position feeback control. A. Cascae feeback controller esign for position control Cascae position control rive system consists in a current loop, a spee loop an a position loop, as shown in Fig. 2. The q-control signals use the position information from Hall sensors for the coorinate transformation, which guarantees three phase control signals sent to the motor. The three control loops are esigne base on Kessler s canonical form. Then the current loop an spee loop can be consiere as a first orer system in sequence, which is convenient for the next loop esign. (a) (b) Fig. 1. The Structure of TFM propose by H. Weh [9]. (a) Schematic configuration; (b) implementation to a rotary machine. III. FUNDAMENTAL IDEA TO USE HALL SENSORS TO DETECT POSITION As state above, the cost of linear encoer is proportional to motor stroke an high-resolution position sensors is also elicate to environment, especially optical linear encoers. Hence, we propose to use low-cost Hall sensors to obtain the position information for long linear synchronous motor Fig. 2. Cascae position controller.

3 Output voltage of Hall sensors (V) Fig. 3. The output voltage signals of two Hall sensors. The time constants of current, spee an position loops are approximately set into 1 msec, 4 msec an 16 msec respectively. Furthermore, the three controllers possess a filter to reuce overshoot. B. Measurements of fiel magnetic flux with a couple of Hall sensors The longituinal magnetic fiel of the motor is consiere as a sinusoial fiel; The output of Hall sensor is proportional to the magnetic fiel. In our metho, two A1324 Hall sensors are installe on the mover an the interval between them is 6.75mm, which is the half pole pitch. Taking the saturation of Hall sensors output into consieration, the Hall sensors plate was set up about 1mm away from the permanent magnet plate. The output signals of the two Hall sensors are shown in Fig. 3. Theoretically, the signal from Hall sensors shoul be a sinusoial wave with the same amplitue in every perio; however, in reality the amplitue of the output signal is not a stanar sine wave as Fig. 3 shows. C. Metho to etect position In orer to get the position of the motor from the output signal of Hall sensors, we must know the mapping between them. When a Hall sensor moves with the mover, the output signal of this Hall sensor s is a sinusoial wave theoretically, which can be expresse as follows: s A sin τ π x + ϕ = pole _ pitch where τ pole_pitch = 13.5mm, A is the maximum amplitue, φ is the phase at x = m. As Fig. 3 shows, when the motor moves from the start position (x = m) to the en position (x =.2m), the output signals of Hall sensors are recore. Here we pick up the peak, trough an zero points in each perio of the signal; then the signal is ivie into several sections accoring to these points, each section is a quarter of one perio (Fig. 4). We assume that the signal in each quarter (1) matches (1) strictly. In each quarter, we can pick up the maximum value s max (peak) or the minimum value s min (trough), which is the value of A in (1), this value changes in each quarter. We also can pick up the value s of the signal when x = m; then φ can be calculate as follows: s ϕ = arcsin (2) A here φ remains constant in every quarter. Finally, in each quarter the output value of Hall sensor at every position can be calculate by (1) an we get a mapping table which shows the relationship between the output value of Hall sensor an the motor position. When the motor moves, Hall sensors outputs are rea in an we can get the position of motor by look up table at each time. However, the output of one Hall sensor changes perioically. Its value maybe correspons to several position along the motor stroke in the table. Here when look up table, we fin the position in a small subsection aroun motor position at the previous time. There are two subsections in Fig. 5. In subsection 1, the signal of Hall sensor 1 in the table is monotonically increasing so that one value of the signal correspons to one position. The range of this subsection is etermine by the max spee of the motor. However, when motor moves closely to the position where the output signal of Hall sensor 1 is aroun the peak of the waveform, the signal of Hall sensor 1 in the table is not monotonous as shown in subsection 2 in Fig. 5. But at this time output of Hall sensor 2 which has a 9-egree phase ifference must be monotonous. In a wor, no matter what the outputs of sensor 1 or 2 are, the signal which is monotonous having one to one corresponence to motor position in the look up range is use to look up table, then the motor position is obtaine. We use our metho to estimate the motor position from the output signals of Hall sensors. Here we obtaine the following result. Fig. 6 is the position from the Hall sensors an linear encoer. Fig. 7 is the position ifference between the Hall sensors an linear encoer. We calculate that the position error is less than.3mm. It satisfies the requirement from the secon section which is that the error between position Output voltage of Hall sensors (V) one quarter peak zero trough Fig. 4. The ivision of the signal of One Hall sensor.

4 Output voltage of Hall sensors (V) Fig. 5. The subsection of the signal of Hall sensors. feeback signal from the Hall sensors an real position must be smaller than 1mm. IV. METHODS TO OBTAIN SIGNALS REQUESTED TO THE CASCADE CONTROL A. Metho 1: Approximate iffrential operation for LP-filter spee signal By consiering spee as the ifferential of position, we can express it in the S-omain as: s v = x (3) 1 +τs Where τ is the time constant of the low-pass filter. Consiering the stability of spee control loop, we choose the low-pass filter time constant τ as 4 millisecon. The sampling time T is.1ms so that the spee expression in Z- omain is shown as: Time (s) Fig. 6. Position from Hall sensors an a linear encoer τ 2τ v[ n] = x[ n] x[ n 1] 1 v[ n 1] 1 + (4) T T T T Fig. 6 an 7 are the position information obtaine from Hall sensors. They are use to o numerical calculation. An in orer to compare the two methos of calculating spee, ieal spee from perfect position in our simulation is use as the comparison object. Base on (4), spee is shown in Fig. 8. It shows that spee from metho 1 has small vibration. It also has certain elay. B. Metho 2: Single sample rate state observer (incluing external loa force estimation) Single sample rate state observer uses current an position information to estimate motor position, spee an mechanical loa force treate as an external isturbance [11]. The ynamic characteristics of motor in continuous omain are expresse in the following: t x v = F 1 x 1 Kt v + i M M F q x 1 v (5) F, y = [ ] Time (s) Fig. 7. Difference between position signals from a linear encoer an Hall sensors. In iscrete omain, the sampling time T is.1ms in our research. Observer time constant is also 4 millisecon. Therefore, accoring to Kessler s canonical from, three poles in S- omain can be obtaine. Then three poles in Z- omain are also fixe. Finally, accoring to observer stable principle, observer gain is esigne by applying the pole placement metho to the following observer characteristic equation: et[ zi ( A L C A )] = (6) where subscript means the iscretize matrix.

5 Fig. 8. Spee obtaine from approximate ifferential of position with lowpass filter. The previous research use position pulses of Hall sensors combine to a ual-rate sampling observer to obtain motor position. The observer time constant shoul change with spee to guarantee the estimation of motor position an spee. Then we use alternating position an spee controller for position control. Previous research uses position pulses from Hall sensors, which enhance accuracy of position. But it nees to switch between ifferent controllers resulting in transient process. An system response time is slow. In this paper, we irectly use analog output signal of Hall sensors to obtain motor position. Spee is erive from two methos. Then we use cascae position control for motor rive. It is no nee to switch between ifferent controllers so that transient process can be eliminate. An system response time is fast than previous research. Fig. 9. Spee obtaine from single rate observer. 16ms Estimate spee from the observer is shown in Fig. 9. It has very small oscillation. C. Comparison among the two methos an their performance The two methos are compare by consiering the spee response an position performance. Consiering the spee, about metho 1, as shown in Fig. 8, its avantage is that spee can be calculate irectly from position from Hall sensors inepenent on system moel. But it has one isavantage that spee waveform has small vibration compare to estimate spee waveform from metho 2. About metho 2, as shown in Fig. 9, the avantage is that spee waveform has very small vibration. But metho 2 is epenent on the accuracy of system moel. If the system moel is not very accurate, the observer performance will become ba. Consiering the position performance, Fig. 1 an Fig. 11 are position feeback performance in cascae control base on metho 1 an metho 2. Both of position feeback signals have elay of position comman about 16ms. It satisfies the requirement from the secon section that position controller must respon fast in a level of 16 msec. Finally, because that position ifference from Hall sensors escribe in the fourth section is less than.3mm, so the position error between position comman an position feeback signal is also less than.3mm. It satisfies the requirement in the secon section that position error between position comman an real one must smaller than 1mm in numerical stuies. Fig. 1. Position comman an position obtaine from Hall sensors without use of observer (metho 1). 16ms Fig. 11. Position comman an estimate position from observer (metho 2).

6 V. CONCLUSIONS In this paper, we propose an economic position sensing for position feeback control in long transverse flux linear synchronous motor rive. By assuming sinusoial waveform of longituinal flux istribution, two economy Hall sensors give an inicate of the motor position with a position error less than.3mm, which is smaller than 1mm as we require. Two methos to erive spee signal from the position signal from Hall sensors have been presente an compare. One is approximate ifferential operation of position with lowpass filter. The other is to use state observer incluing external loa force in its state variables. Although the first metho nees no system moeling, the erive spee has a elay an the suppression of the measurement noise is insufficient. The secon metho can prouce a fast an smooth spee signal from position signal of Hall sensors, which is base on a sufficiently goo system moel. The transient responses of cascae position control feeback performances base on position signals from a conventional linear encoer an from the propose Hall sensors are calculate an compare. The numerical stuy shows that the position feeback control base on the economic Hall sensors has goo performance with a setting time shorter than 16msec an an accuracy of.3mm when it is combine with a simple single rate igital state observer. Future work inclues experimental verification of the technical feasibility of the propose position feeback control using Hall sensors as position sensors. [7] Qi Zhao, T. Koseki, Alternating position an spee control of long stroke linear synchornous motor base on Hall sensors, Technical meeting on linear rives, IEEJ, vol. LD-14-7, Aug.214. [8] H. Weh, H. May, Achievable force ensities for permanent magnet excite machines in new configurations, Proceeing of the International Conference on Electrical Machines an Drives, 1986, vol. 3, pp [9] H. Weh, H. Hoffman, an J. Lanrath, New permanent magnet excite synchronous machine with high efficiency at low spees, Proceeing of the International Conference on Electrical Machines an Drives, 1988, vol. 3, pp [1] Y. Yamamoto, R. Watanabe, Y. Takaa, T. Koseki, an Y. Aoyama, Design using simple moeling an experimental stuy on irect-rive isk-type motor with ense stator configuration, Eupean Conference on Power Electronics an Applications, Sep. 213, pp [11] L. Kovuhikulrungsri, T. Koseki, Precise spee estimation from a lowresolution encoer by ual-sampling-rate observer, IEEE / ASME Trans. Mechatronics, vol. 11, no. 6, pp , Dec. 26. ACKNOWLEDGMENT The authors are corially grateful to Mr. J. Shin, Mr. Y. Takaa, an Mr. H. Narita for their technical support an avices in our measurements of the linear synchronous motor. REFERENCES [1] P. Giangrane, F. Cupertino, an G. Pellegrino, "Moelling of linear motor en-effects for saliency base sensorless control," IEEE Energy Conversion Congress an Exposition (ECCE), Sep. 21, pp [2] M. Huikuri, N. Nevaranta, M. Niemela, an J. Pyrhonen, Sensorless Positioning of a Non-Salient Permanent Magnet Linear Motor by Combining Open-loop Current Angle Rotation Metho an Back-EMF Estimator, IEEE Annu. Inustrial Electronics Society. Conf., Oct.213, No 1, pp [3] H.J. Kim, J. Nakatsugawa, K. Sakai, an H. Shibata, High-acceleration linear motor, Tunnel Actuator, Journal of Magnetics Society of Japan, vol. 29, no. 3, pp , 25. (in Japanese) [4] S. Morimoto, M. Sanaa, an Y. Takea, Sinusoial current rive system of permanent magnet synchronous motor with low resolution position sensor, Proc. IEEE IAS Annu. Meeting, Oct. 1996, pp [5] S. Zaim, J.P. Martin, B. Nahi-Mobarakeh, an F. Meiboy-Tabar, High performance low cost control of a permanent magnet wheel motor using a hall effect position sensor, IEEE Vehicle Power an Propulsion Conference, Sep.211, pp [6] Y. Anno, S. Seung-Ki, L. Dong-Cheol, an J. Cha-Seung, Novel spee an rotor position estimation strategy using a ual observer for lowresolution position sensors, IEEE Transactions on Power Electronics, vol. 24, no. 12, pp , December 29.