Position Sensorless Vector Control of                   Permanent Magnet Synchronous Motors                     for Electr...
qc        q                                                                                      dVc    =    R     dc + PL...
(13)                                                                                q     1 + TiqS   qcCt)r       -Y      ...
From Fig. 3, the transfer function from Vd to id is                                 input                                 ...
V. SIMULATION AND EXPERIMENT                                                                                              ...
is set to 900 ts, and the computation interval of (11) and(14) is set to 500is.   Fig. 6 shows the simulation result of th...
12 shows the motor current and motor frequency signalwaveforn recorded while the motor was accelerating. Inthis case, the ...
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Position sensorless vector control of pmsm for electrical household applicances

  1. 1. Position Sensorless Vector Control of Permanent Magnet Synchronous Motors for Electrical Household Appliances Kiyoshi Sakamoto*, Yoshitaka Iwaj i*, Tsunehiro Endo* *, Tsukasa Taniguchi*, Toru Niki***, Mitsuhisa Kawamata***, and Atsuo Kawamura**** * Hitachi Research Laboratory, Hitachi Ltd., Ibaraki, JAPAN ** Power and Industrial Systems Division, Hitachi Ltd., Ibaraki, JAPAN * ** Hitachi Appliances, Inc., Ibaraki, JAPAN * ** * Yokohama National University, Yokohama, JAPAN Abstract-A position sensorless vector control for a have focused on this control [1-3]. However the position Permanent Magnet Synchronous Motor (PMSM) suitable estimation methods proposed by the papers, such as the for electrical household appliance motor drives is described Kalman filter, the state observer, and the disturbance in this paper. As a position sensorless control, a simple position estimate equation is presented. The derivation of observer, are relatively complicated and their calculation the equation is described. A simplified vector control requirements are large. Furthermore, vector control, method for position sensorless PMSMs is proposed. The which includes a speed-control loop and current-control proposed method does not employ any automatic speed loop, requires a short control interval. Therefore, a high regulator or automatic current regulator. However, since performance Micro-Controller Unit (MCU) or Digital the motor supply voltage Vd and Vq are calculated on the Signal Processor (DSP) is needed for the implementation control rotation axis, the drive performance of our method is almost the same as that of a conventional vector control of the control. Adoption of such an expensive under a steady-state condition, i.e. constant load and controller/processor is unrealistic for electrical household constant speed. Simulation and experimental results are appliance motor drives. shown. Finally, the authors applied the proposed method to In this paper, a simplified vector-control method a battery-driven cordless vacuum cleaner. By experiment, a suitable for implementation with a low-cost typical MCU stable drive of 50,000 min1 was confirmed. is proposed. The position estimation algorithm proposed by the authors is described. The configuration of the Index Terms-position sensorless control; vector control; proposed controller and the gain design methodology are permanent magnet synchronous motor; cordless vacuum presented. Simulation results are given to verify the cleaner. effectiveness of the proposed drive system. Finally, the I. INTRODUCTION authors applied the proposed control to a battery-driven cordless vacuum cleaner (maximum motor speed is In the field of electrical household appliances, 50,000 min-), demonstrating the high-speed motor drive especially air-conditioners and refrigerators, Permanent capability of the proposed method. Magnet Synchronous Motors (PMSM) have become the standard ac motors for variable speed drives, because of II. POSITION ESTIMATION ALGORITHM their several advantages, such as superior power density In this section, the derivation process of the proposed and high efficiency, compared with induction motors. position estimation algorithm of PMSM [6] is described. The first air-conditioner product, which uses an inverter driven PMSM, was developed in 1982 in Japan. Since A. Voltage Equation of Salient Pole PMSM 1998, the ratio of inverter-driven household air- The well-known voltage equation of the salient pole conditioners sold in Japan has risen to over 90 percent. PMSM in the synchronous reference frame d-q axis is as This trend might spread over the world given recent follows: global energy and environmental problems. As a drive method for PMSM for electrical household [V ] R]+P[Ld i +wr[ L i i [Es] (1) appliances, a position-sensorless trapezoidal current drive, i.e. 120-degree commutation drive, is widely used where cor is the rotor angular velocity; Ld, Lq are the d and because of its simplicity and low-cost implementation. q axes inductances; Vd, vq are the d and q axes voltages; id, However, the distorted current waveform generates iq are the d and q axes currents; R is the stator winding pulsating motor torque and motor loss. Presently, the use resistance; p is the differential operator with respect to of sinusoidal current drive, i.e. 180-degree commutation time; and Eo is the voltage of the back electromotive drive, is increasing. force (EMF). A major example of a sinusoidal current drive is the In the sensorless control system, rotor angular position position-sensorless vector control. Many research papers and velocity o,r are not measured; thus voltages and1-4244-0844-X/07/$20.00 ©2007 IEEE. 1 11 9
  2. 2. qc q dVc = R dc + PLd + 2 coL, i q 1 (6) dt L i 1 Ox cosAO] However, equation (6) includes 0cr, which is an unobservable value of the controller. Substituting rdc equation (6) into dAO/dt of equation (7), equation (8) is obtained: d AO(d-=d d)d d- p (7) d) ( dt dt dt 2rFig. 1. Relation between two synchronous reference frames. The d dV = R d +PLd 1 d +CDLqi c (8) axis is the rotor frame and the dc axis is the assumed rotor frame.currents onthe d-q axis cannot be obtained. Therefor +dAS L -ia+ UsinA00 (L d -L q) [coOxsynchronous reference frame dc-qc axis, which is fion the assumed rotor, is introduced. Equation (8) does not include 0r, and is suitable for Fig. shows the two rotating axes of the PM deriving the position error equation.where the assumed dc-qc axis is shifted from the real Combining the Eo, term, equation (9) is obtained:axis. The difference between the two axes is definedposition error AO given in (2): EOx coA = v1Ri-PLd - i I-d LqL i (9) AO=Odc Odwhere Od is the real angular position of the d-axis relati ive - ~~~~~~~~~dt ( d q) i Hto the stationary a-axis and Odc is the assumed angular To obtain the position error information, the size of theposition of the dc-axis relative to the stationary a-axis. Converting from the dc-qc axis value into the d-q a) extended EMF is not necessary but the phase angle of thevalue, equation (3) can be used: extended EMF is important. Getting tangent tanzl0, the size of the extended EMF Eo, is eliminated: V cossAO -sinAO Vdc [Vq] si:AO cos AO ][vqc] tanAOVdC -( R+pLd )idC +{(Ld Lq)(pAO)} q (10)B. Position Error Equation Vqc- (R +PLd)qc -{|L Lq)(PAO)} dc The voltage equation (1) can be transformed ianother expression as follows: Equation (10) includes the time derivation ofthe motor [d R[ d +PLd[. d] 2 Lq[L q] current and the position error zAS. We assume that the time derivative of the motor current is negligible under ±v Q d±P(L 2q d the condition where motor load and motor speed are constant. We also assume that the time derivation of the [KE2 ° r + p Ld) iq ±2 °(Ld Lq) id.J position error zlObecomes zero under the same conditions. Eliminating the time derivation values, a practicalThe fourth term of (4) is the summation of the back E position error equation can be obtained as follows:and induced voltage caused by motor pole saliency.term is called the extended EMF [4]. In the folloMN AOc = tan dc Rid +0) iLq *qc] (1 1)explanation, Eo, expresses the extended EMF term Vqc -R jiqc -aCILq * dcjfollows: where /10, is the estimated position error value. Note that E0 =KE r+ P(Lq Ld) iq + r(Ld Lq) id by substituting L-Lq =L in (l1), an equation for non- (5) salient PMSMs can be obtained. The voltage equation of the dc-qc axis is obtained by III. SIMPLIFIED VECTOR CONTROLsolving as follows: In this section the authors would like to propose a simplified vector control for position sensorless PMSMs. The proposed control structure is shown in Fig. 2. A characteristic of our method is that the control structure of the proposed control is very simple compared with the 1120
  3. 3. (13) q 1 + TiqS qcCt)r -Y Since the detected motor current iqc changes withSpeedReference motor load variation, the value of the q-axis current command is adjusted properly. Note that determining the time constant parameter of the LPF (13) is important. The response of the LPF output should be designed to be lower than the response of the PLL controller described in the following. C. PLL controller The position error ASO expresses the lead-lag relationship between the assumed axis and the actual axis. Using this lead-lag relation, the PLL controller adjustsFig. 2. Simplified vector control system for position sensorless PMSM the assumed rotor speed o,, i.e. the inverter output drive. frequency.conventional one. This simplified vector control structure Actually, the PLL controller is implemented in the usewas reported on in the 1980s for use in induction of proportional control as follows:machines [5]. The authors apply the idea to PMSM drives. A1 = -KPsAOC. (14) As shown in Fig. 2, our method does not use anautomatic speed regulator (ASR) or automatic current If z1O, is positive, the assumed axis is ahead of theregulator (ACR). Thus, the proposed method has no actual axis, and the PLL controller reduces the assumedadvantage over the conventional vector control especially rotor speed o,. Similarly, if z1O, is negative, the assumedpertaining to the case of disturbance load torque. axis is lagging the actual one, and the PLL controller However, since the motor supply voltages Vd and Vq increases co,.are calculated on the dc-qc axis, the drive performance of The dc-axis phase Odc is obtained by an integrationour method under the steady state condition, i.e. constant calculation as follows,load and constant speed conditions, is almost the same asthat of the conventional vector control. This is an Odc =frdt. (15)important difference between the well-known V/F typecontrol and our method. Another feature of the proposed control is that number D. Other comments concerning the proposed methodof control parameters is smaller than for the conventional The setting of the d-axis current command id* ismethod. Thus, controller adjustment is finished with less important for high efficient drive. The current referencework. of the d-axis, id*, is set to minimize the amplitude of the The proposed simplified vector control is characterized motor current in order to decrease losses.by using a voltage command calculator, a q-axis current Changing the speed reference oi) * at a rapid rate iscommand generator, and a PLL controller. We describe limited because the voltage command is calculated fromthe detail of each constituent block below. the speed reference directly as shown in (12). To generateA. Voltage command calculator c)r , the use of a ramp function is recommended. This part calculates the voltage command Vdc* and vqc*using the motor electrical parameters, motor frequency IV. GAIN DESIGNreference, and current reference. The calculating formulais shown in equation (12), which is obtained by The proposed control has two control parameters, aneglecting the time derivative term of equation (1). time constant parameter of the LPF (13) and a gain Kp of the PLL controller. In the following, the gain design Vd method, based on the resonant characteristics of PMSM [vc]R[] + L .J+LK l] : clc ] 0 cI 0 C9 I 0 d [d E 1 (12) is described. A. Resonant characteristics of PMSMwhere o, * is frequency reference of the motor. Fig. 3 shows a salient pole PMSM motor model in theB. q-axis current command generator rotational reference frame. The relation between the In the conventional vector control, the ASR determines voltage and current shown in Fig. 3 is obtained from thethe q-axis current command, iq*, as a motor torque voltage equation (1). To analyze the electrical response ofcommand. On the other hand, in our method, the q-axis the motor, we assume that the motor speed co, is constant.current command is generated through the LPF equation For simplicity, we also assume that the position error A1O(13) from detected motor current as follows: equals zero and the motor speed PoV2 is substituted by c] - 1121
  4. 4. From Fig. 3, the transfer function from Vd to id is input outputobtained as follows: Vd - > id = R + sLq (16) s2LdLq + s R(Ld + Lq)+ R2 + 012LdLq G= Using the motor parameters of Table 1, the transfercharacteristics of Go can be plotted as Fig. 4. Fig. 4shows that Go has resonant characteristic and the resonantpeak becomes sharp with higher o, values. In order to find the resonant characteristics, equation(16) is changed to a 2nd_order system equation as follows: Fig. 3. A model of salient pole PMSM in the rotational reference frame. R + sLq C 2 = q - (17) ° R2 + C LLS &si i C. ct Q.) 2 R (,01 +LL 90 91=0 100 =25% °1=50% p1=75% p1 100% (233Hz)where (18) ........... ........... ....... L~LqR . (Ld + Lq) 10 .0 ...0.0 . . . . . . . ....... . ... .... 2VLE (R2+ 2LdLq) -90 ,_ 10 ioo 100 O Equation (17) indicates that the resonant frequency CoI Inverter frequency[Hz] Fig. 4. Transfer characteristics from d-axis voltage to d-axis currentand the damping coefficient 4 vary with changing tl. If t), is the higher value, ozh, comes close to o, and the value Actual Position Estimatedof 4 is reduced. Thus, the resonant oscillation of PMSM position error positioncan hardly be damped at higher rotation speed. Od AO K 0dcB. Resonant suppression strategy of Simplified Vector +SControl PLL controller Generally, in order to suppress the resonance of the Fig. 5. Simplified model of PLL controller.PMSM mentioned above, a decoupling control isemployed. The decoupling controller calculates the d-qaxis interference value and compensates the voltage R *(Ld + Lq) COn (20)command reference. However, complete decoupling is 2*LdLqimpossible, because the computation interval of thecontroller output is limited and the motors electrical Here we call the right value of (20) a critical dampingparameters are different from the actual values. frequency tnO: Simplified vector control avoids the resonance inanother way. The method is limiting the variation of the R (Ld + Lq) (21)voltage command reference. If the frequency of the 0)nO 2 LdLqvoltage reference is lower than the resonant frequency ozI,no resonant oscillation occurs and the PMSM systembecomes stable. C. Gain Design Methodology In the following, we clarify the critical resonant The PLL gain Kp should be set at the critical dampingcondition. The relation between the resonant frequency frequency tnO(I)n and the damping coefficient X is expressed byequation (19): Kps = 0) n0 (22) R-(Ld+Lq) (19) Selecting the gain Kp as shown in equation (22), the 2- LdLq * transfer characteristic from AS0 to Odc becomes the LPF n response and the cutoff frequency is COJo because the PLLThe case of coefficient 4=1 is known as the critical controller can be simplified as Fig. 5. Therefore, thedamping condition. Thus, we can derive the stable frequency component PLL controller output is less thancondition by solving for ; >1.0 Equation (19) is . 0nO and the PMSM system becomes stable. Note that the response speed of the LPF (13) is alsochanged to the following inequality: important. It is recommended that the LPF setting be about 0.1 times slower than the PLL response. 1122
  5. 5. V. SIMULATION AND EXPERIMENT frequency is set to 5kHz. The 3-phase voltage reference is To confirm the validity of the proposed control, several computed every 1OOVts. The computation interval of (12)simulations and experiments were made. Thespecifications for the test motor used in this simulationare shown in Table 1. TABLE 1. SPECIFICATIONS OF THE TEST MOTOR. In this case, the critical damping frequency C0o Rated Power 3.7 kWbecomes 74rad/s. Therefore we set the control parameters Rated Speed 3500 r/minto K, =80rad/s and Tiq=125ms. The PWM carrier signal Pole Number P 8 Inductance Ld, Lq 2.5, 3.3 niH 200 Resistor R 0.21 Q ---.---.---------.---......................................... Rotor Inertia 0.0034 kg cm2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 20 0 -20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 150 100 . A . 50 ........... -50 °0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 20 lo ............ ............ 10 . -20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 40 20 (a) Phase current and inverter frequency > 20 _ . . -40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 150 100. - 50 50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6[s] Fig. 6. Performance of speed response. (Simulation) 240 30 . 220 (0 0.1 0.2 0.3 0.4 0.5 0.6 40 (b) Phase current and estimated axis error AOc L20 -20 r 40 °H-lIE .;il ltil lb,,i.;: IL... .1 i Fig. 7. Performance of speed response. (Experimental result) -.C:) 0 0.1 0.2 0.3 0.4 0.5 0.66 ct 0 - 200 t 100t a) LI 0 -4- ;z 0 M. 0 -50 -4- 0 0.1 0.2 0.3 0.4 0.5 0.6 40 20 -2 ......................................................................... -40 0 0.1 0.2 0.3 0.4 0.5 0.6 40 . -20 i -40 0 0.1 0.2 0.3 0.4 0.5 0.6 200 .iqc 100 --............... ..... 0* .-I-._ 0 0.1 0.2 0.3 0.4 0.5 0.6 Is] Fig. 8. Load torque variation response. (Simulation). Fig. 9. Load variation response. (Experimental result) 1123
  6. 6. is set to 900 ts, and the computation interval of (11) and(14) is set to 500is. Fig. 6 shows the simulation result of the speedresponse. In this simulation, the load torque of the testmotor is set to zero. The frequency reference increasesfrom 30Hz to 230Hz. The result of this simulation shows that the motortorque rise is delayed, and furthermore, that ASO occurs atthe speed variation point. However, zAO becomes zeroduring speed up. Within this simulation, the proposedcontrol method has adequate capability. Fig. 1U. External view o0 the test motor. Fig. 7 shows the experimental result of applying ourcontrol system to an actual apparatus. The motor phase DC24Vcurrent, inverter frequency, o,, and estimated positionerror zIO, are shown. The motor current amplitude isdifferent from the simulation because of the wind loss ofthe actual motor. Except for this point, the experimenttends to agree well with the simulation results. Fig. 8 shows the simulation result of the torque step measurementresponse. In this simulation, 100% load torque is added to Fig. 11. Experimental apparatus.the motor during the maximum rated rotation speed.From this increase in the load the motor speed 0crdecreases, and the inverter frequency, o,, follows cr, TABLE 2. SPECIFICATIONS OF THE TEST SYSTEM.After applying the load, the motor torque Tm is adjusted Maximum Ratedfor about 0.4s to balance with the load. Speed 50,000 r/min Fig. 9 shows an experimental result of the torque step Pole Number P 2response. The motor current is quite similar to thesimulation but its amplitude is fluctuating. It seems that Inverter Output 500 Wthe mechanical model difference causes the fluctuation. DC voltage 24 VWe chose a simple 1-mass model for the motormechanical model of the simulation.VI. APPLICATION EXAMPLE OF HOUSEHOLD APPLIANCES The proposed method has been applied to varioushousehold appliances, such as room air conditioners andrefrigerators [7]. In this paper, we will outline itsapplication to a cordless vacuum cleaner as one case. A cordless vacuum cleaner has some drawbacksbecause all the power is supplied from a battery. Forexample, the problem is that the suction power is poorand available operating time is short. These problemsresult from the use of a commutator motor. To improvethe performance, substituting a PMSM for thecommutator motor has been investigated [8]. Fig. 12. Startup waveforms. In order to boost the suction power, a rotation speed ofabout 50,000r/min is necessary for the PMSM. Thus, themotor driver of cordless vacuum cleaner requires highrotation-speed drive capability. The authors applied thesimplified vector control to driving such a high-speedmotor. Fig. 10 shows the external view of the test motor. Thespecifications of the test motor are shown in Table 2. Thetest motor is designed to operate using a 24V DC battery.The structure is an interior permanent-magnetsynchronous type. The output power of the drive circuit is500W. As a micro-controller unit, a 32bit SH7046 RISCprocessor made by Renesas Technology is employed. PWM carrier frequency: 8kHz The experimental apparatus is shown in Fig. 11. Fig. Fig. 13. Motor phase current waveform in high-speed region (50000minm1). 1124
  7. 7. 12 shows the motor current and motor frequency signalwaveforn recorded while the motor was accelerating. Inthis case, the acceleration to 50,000r/min (top speed) was REFERENCEScompleted in just 5s. [1] T. Takeshita, M. Ichikawa, J-S Lee, and N. Matsui, "Back Here, it is necessary to explain the start sequence in EMF Estimation-Based Sensorless Salient-Pole Brushlessdetail. At the beginning of rotation, an open-loop start-up DC Motor Drives", T IEE Japan, Vol. 11 7-D, No. ] pp. 98-method, i.e. the synchronous drive method, is used in this 104 (1997-1) (in Japanese) [2] L. A. Jones and J. H. Lang, "A state observer forexperiment. The start-up method flows more current than permanent magnet synchronous motor," IEEE Trans.the vector control. You can find the start-up period by the Industrial Electronics, Vol. 36, No. 3, 1989, pp. 374-382.difference of motor current amplitude shown in Fig. 12. [3] S. Bolognani, R. Oboe, and M. Zigliotto, "Sensorless full- After the start-up, the proposed simplified vector digital PMSM drive with EKF estimation of speed andcontrol is activated. During acceleration to the top speed, rotor position," IEEE Trans. Industrial Electronics, Vol. 46,significant fluctuation of the motor current was not No. 1, Feb. 1999, pp. 184-191.observed. Fig. 13 shows a close-up of the motor current [4] S. Ichikawa, Z. Chen, M. Tomita, S. Doki, and S. Okuma, "Sensorless Controls of Salient-Pole Permanent Magnetwaveforn at the top speed. The motor current involves a Synchronous Motors Using Extended Electromotive Forcehigh frequency component. These components are caused Models", T. IEE Japan, Vol.122-D, No.12 pp.1088-1096,by the back electromotive force with harmonic distortion Dec. 2002. (in Japanese).and use of the pulse width modulation (PWM) control. In [5] T. Okuyama, N. Fujimoto, and H. Fujii, "Simplifiedthis experiment, the PWM carrier frequency was set to Vector Control System without Speed and Voltage8kHz. Sensors", T. IEE Japan, Vol.1 10-D, No.5 pp.477-486, May 1990. (in Japanese). We conclude from the experiment described above [6] K. Sakamoto, Y. Iwaji, T. Endo, and Y. Takakura,that the proposed simplified vector control can be applied "Position and Speed Sensorless Control for PMSM Driveto a high speed PMSM drive. The proposed control might Using Direct Position Error Estimation," Proc. ofbe applied not only to vacuum cleaners but also high- Industrial Electronics Society, 2001. IECON 01. The 27thspeed fan motor drives and spindle motor drives. Annual Conference ofthe IEEE, vol.3, pp.1680-1685, 2001 [7] D. Li, T. Suzuki, K. Sakamoto, Y. Notohara, T. Endo, C. Tanaka, T. Ando, "Sensorless Control and PMSM Drive VII. CONCLUSIONS System for Compressor Applications." Proc. of Power A simplified vector control for position sensorless Electronics and Motion Control Conference, 2006. IPEMCPMSMs is proposed. Configuration of the proposed 06. CESIIEEE 5th International, vol.2, pp. 1-5, Aug. 2006method and the position estimation method are shown. [8] T. Taniguchi, H. Mikami, K. Sakamoto, K. Ide, H. Harada,The methodology of the control gain setting is introduced. F. Jyoraku, "Basic Study of High-Speed Brushless DC motor with Battery System," Proc. of The 2005The effectiveness of the proposed control is verified by International Power Electronics Conference, IPEC 2005,simulation and experiments. pp. 1033-1037, April. 2005 Using the results of this paper, the cordless vacuumcleaner, type CV-XG20, shown in Fig. 14 has been madeavailable in stores since October 2003. Fig. 14. Cordless vacuum cleaner. CV-XG20 1125