New Approach for the Low Speed Operation of PMSM Drives Without Rotational Position Sensors Power Electronics, IEEE Transactions on 512 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 11, NO 3, MAY 1996 N[.]
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 11, NO 3, MAY 1996 512 New Approach for the Low-Speed Operation of PMSM Drives Without Rotational Position Sensors Joohn-Sheok IOm, Student, IEEE and Seung-Ki sul, Member, IEEE Abstract- A new approach to the position sensor elimination of permanent magnet synchronous machine (PMSM) drives for low-speed operation is presented in this paper Using the position sensing characteristics of PMSM itself, the actual rotor position, as well as the machine speed, can be obtained even in the transient state Since the essential back-EMF information is obtained from direct measurement during a special test cycle called MCDI, the operating speed range of the sensorless drives can be extended to 10 rpm Moreover, the chronic starting problem of the PMSM drives can be simply settled by the proposed algorithm In order to verify the feasibility of the proposed scheme, experimental results in the low-speed range of about 10 100 rpm are also presented - I INTRODUCTION P to now, machine drive systems without rotational position sensors, the so-called sensorless drives, have gained increased popularity in industrial applications because of the inherent drawbacks of rotational sensors In general, the rotational encoder-type sensors are used to obtain speed or position information of the machine The major drawback of these sensors is the performance degradation caused by vibration or humidity Furthermore, these extemal sensors will result in added cost and increase the size of the drives [ 11-[6] By these reasons, there has been considerable interest in developing techniques to achieve the position and speed information for the sinusoidal back-EMF-type permanent magnet synchronous machine (PMSM) without extemal position sensors The PMSM of this type has widely found its application fields on the high-performance machine drive because of the ripple-free torque characteristics and simple control rule However, since none of the parameters of the PMSM with sinusoidal back-EMF varies as a function of the rotor position, it is very difficult to get the rotor position information without rotational position sensors in this drives Basically, most previous studies about the sensorless drives for the PMSM with sinusoidal back-EMF-type start on the foundation of the voltage equation of the machine and the information of the machine terminal quantities, such as line voltage and phase current Using this information with machine model, the rotor angle and speed were estimated directly or indirectly based on the back-EMF information by various sensorless strategies [ 11-[5] In all cases, however, since the machine parameters should be well-known for the proper sensorless operation, the sensitivity to the machine Manuscript received July 13, 199.5; revised November 30, 199.5 The authors are with the School of Electrical Engineering, Seoul National University, Seoul 15 1-742, Korea Publisher Item Identifier S 088S-S993(96)03SS2-1 parameter is a major drawback Another important demerit of the previous studies is the limitation of the controllable speed range, especially in low speed range In the previous studies, the essential back-EMF information was estimated using the terminal quantities, such as currents and voltages But these quantities are very noisy because of the PWM operation of the power stage Especially in the low-speed range, the actual voltage information on the machine terminal can be hardly detected because of the small back-EMF of the machine and the system noise For instance, when a typical machine with 2000 rpm-rated speed is operated at 50 rpm, the back-EMF is about 1.5 V only Considering the precision of the terminal voltage in PWM fashion and the system noise produced by the nonlinear characteristics of the switching devices [lo], the controllable lower speed range of the conventional sensorless drives is generally limited to the value of around 100 rpm Furthermore, another problem to be considered in the sensorless drives for PMSM is the starting capability At standstill state of the machine, the essential back-EMF information cannot be achieved in the conventional drive algorithm for itself In the literature [6]-[8], some special starting algorithm or initial position detection algorithm were studied for just machine starting However, in the case of sinusoidal back-EMF-type PMSM with symmetrical machine parameters, it is quite difficult to apply these methods to machine drive system In this paper, new drive technique for the sinusoidal backEMF-type PMSM drives without rotational position sensor is presented As described above, the rotor position of the PMSM is related only to the phase of the back-EMF So, the information about the back-EMF of the machine plays the important role of the sensorless drives The back-EMF has a sinusoidal waveform of which magnitude is proportional to the rotor angular speed This means that the PMSM itself has a position sensor characteristic like the resolver-type rotational sensors In the proposed method, the back-EMF information is obtained by direct measuring at the machine terminal not by indirect estimation For the purpose of direct back-EMF measurement, a special test cycle, called maximum current decaying interval (MCDI), is introduced Since the back-EMF information is obtained from the direct measurement, the controllable speed range in sensorless drives can be extended to 10 rpm without parameter dependency Additionally, the chronic starting problem of the PMSM drives without rotational sensors or with sensors like the incremental encoder can be solved using the proposed direct-voltage measuring strategy For the successful starting of the general PMSM 0885-8993/96$0.5.00 1996 IEEE KIM AND S U L LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTA1’IONAL POSITION SENSORS P qr se (- vbs Ld Fig Space vector diagram for the PMSM drives, the standstill rotor angle should be known even if a rotational sensor, such as incremental type encoder, is adopted for angle detection By detecting the small back-EMF quantity produced by an initial test current, the initial rotor angle can be easily determined within several ones [“I in mechanical degree As a result, the proposed direct back-EMF measuring strategy can be applied to the general sensorless drive system to increase the controllable lower speed range and to ensure the initial starting capability To verify the feasibility of the proposed method, some experimental tests are conducted for the low speed range (10 N 100rpm) 11 SYSTEMDESCRIPTION A System Modeling The general equivalent space vector diagram for the PMSM is illustrated in Fig It is well-known that none of the parameters of the PMSM with sinusoidal back-EMF are varied according to the rotor position [l], [2] Therefore, the machine model based on the d-q reference frame theory can be described in simple form as R, i!pL,] (Super script s denotes the stationary reference frame.) As shown in (l), the terminal voltage of the machine consists of the voltage drop terms related to the stator resistance R, and stator inductance L,, and the back-EMF term including the rotor speed w, and the back-EMF constant Kp? It is generally assumed that the back-EMF has the true sinusoidal waveform related to the rotor position, and its magnitude is proportional to the rotor speed Therefore, in this aspect, the PMSM with sinusoidal back-EMF has the positiori sensor characteristics in itself like the resolver, and the essential information about rotor angle and speed can be simply obtained from the back-EMF in the stationary reference frame So the back-EMF quantity plays an important roll in the machine drive system without rotational sensor Generally speaking, this quantity can be obtained using the terminal voltage and the information about the voltage drop terms In most previous 513 studies about sensorless drives, the rotor angle and speed are achieved using a specialized estimation algorithm about the back-EMF quantity However, the value of the back-EMF constant is just several 10’s V/krpm in the general commercial PMSM for servo applications Considering the value of K E , it is easily surmised that the back-EMF quantity should have a value about several 1’s V when the machine is operated with 100 rpm mechanical speed Therefore, on the low-speed operating condition, it is quite difficult to obtain the back-EMF information by the conventional estimation method using the machine terminal quantities B Back-EMF Detection Strategy for Low-Speed Operation The back-EMF may be detected at the machine terminal through removing the corresponding voltage drops But, since each machine terminal is connected to the center point of the inverter arms in which the pole voltages have two voltage levels, such as zero or dc-link voltage, it is very difficult to achieve the actual terminal voltage when this voltage is very small In this instance, if the machine terminals are disconnected from the inverter stage, there is one method to detect the small machine voltage at the machine terminal In this paper, the back-EMF information is obtained by direct measurement of the terminal voltage As previously mentioned, the back-EMF will appear at the machine terminal when the voltage drop associated with stator resistance and stator inductance is removed A simple way of removing the voltage drops is to hold the machine currents to zero When the machine terminal currents remain zero, the terminal voltage matches the back-EMF And to measure the terminal voltage in analog fashion, the machine terminal should be disconnected from the inverter arms However, it is not easy to actually disconnect the machine and power stage For the purpose of the implementation of disconnection effect, a third state of the inverter pole voltage is introduced in this paper The states of the inverter pole voltages are always determined by the gating signals Thus, each pole voltage has zero value or DC-link value according to the gating signals When the pole voltages are different from each other, some active voltage is applied to the machine Let’s define this state as the ‘first state’ of inverter In the other case, all the pole voltages have the same value to apply zero voltage to the machine and this condition is defined as the ‘second state’ of inverter In the conventional inverter operation strategy, the machine voltages are generated using these two pole voltage states However, if all the gating signals are removed from the switching devices, the third switching state can be implemented on the inverter side As shown in Fig 2, when the machine currents flow through the machine terminals, the phase current would hold its current state because of the inherent characteristics of the stator winding inductance In the normal operation state, the gating signals for upper or lower switching device are always given by the on state alternately, except during dead time interval As shown in Fig 2(a), if the gating signal for the lower device is on, the normal current named, I,,,, flows through the lower switching device, and the current will flow through the upper IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 11, NO 3, MAY 1996 514 , Inverter, Fig Current flow at the inverter state of all gating off diode attached to each switching device in the other case If the current flows from machine to power stage, the opposite state takes place, as shown in Fig 2(b) However, if all the gating signals for switching devices are in the off state, the machine current named io^ will unconditionally flow through the upper or lower diode according to its direction, as shown in Fig Therefore, in this state, the pole voltages of the inverter are just determined by the machine current direction This phenomenon has been utilized for establishing the basic idea of the dead-time compensation strategy also During this third switching state, the stored energy in the stator inductance is recovered on the dc-link side effectively For example, as shown in Fig 2, the machine current is injected to the dclink voltage through upper diode or derived from the zero voltage of the inverter side through the lower diode This means that the negative largest output voltage is applied to the machine terminal, and the terminal currents should be decayed to zero with the maximum rate When the stored energy is fully recovered and all machine currents reach zero value, the terminal voltages are determined by the back-EMF because of the absence of the voltage drop Therefore, the machine terminals keep the electrically open state as the disconnection state In this paper, the third state of inverter action is utilized in the MCDI test cycle to measure the machine back-EMF Considering the voltage equation of the MCDI test interval leads that the terminal currents can be reduced to zero within a few tenths of a microsecond For instance, when a PMSM with 5-mH winding inductance is operated under 310-V dclink voltage condition, 5-A stator current will be reduced to zero within 13 ps : 5[A1 = 13[psec] at % L , ?;avid c = [mH] $ 310 [VI Fig Back-EMF measurement circuit Y T,,= 3.6msec I I I I E,', EA' detect & Speed Control Fig MCDI test cycle estimation method [9] Another considerable point is the effect of the parasitic capacitors on the switching devices Because of this parasitic capacitor and the leakage inductance of the terminal lines, some resonant phenomenon takes place during the MCDI test cycle and the machine current does not diminish rapidly, as expected in (2) To prevent this resonance, some damping resistors are inserted between the machine terminal in Y -connection form With the consideration of the imaginary neutral point of the PMSM, the phase back-EMF can be derived as follows E: + Et + E,"= O Therefore, the d-q components of the back-EMF on the stationary frame can be obtained simply as, (2) At the end of this MCDI test cycle, the back-EMF that appears at the machine terminal can be directly measured with analog fashion Since the neutral point of the PMSM is not generally available, the back-EMF should be obtained from the line-to-line voltage, as shown in Fig The voltage measurement circuit can be constructed with a laser-trimmed differential-type isolation amplifier and some additional components The maximum measurable line-to-line back-EMF is clamped to V by the back-to-back-connected zener diodes and 10 k resistance Therefore, the maximum operation speed is limited to several hundred rpm In the upper speed range, the back-EMF quantities can be properly estimated using an E" = (2Ez - E{ - E,")/3 E: =(E," - El)/& (4) 111 SENSORLESS CONTROLSTRATEGY A Rotor-Angle Detection Strategy The back-EMF measurement is performed by adding an MCDI test cycle to the current control algorithm, as shown in Fig In this figure, Test means the sampling interval for MCDI test cycle and for the rotor quantity estimation process At the beginning of the MCDI test cycle, all gating signals for the inverter are blocked When the stator currents reach the zero value, the back-EMF is measured 1; is the 515 KIM AND SUL: LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTATIONAL POSITION SENSORS I r$ I I - J ' Fig The overall control diagram for low-speed sensorless drive algorithm torque component current in the synchronous frame fixed to rotor position After TdlP interval, normal current regulation process is performed for torque generation Therefore, in the proposed sensorless algorithm, consequential high-frequency torque ripple would appear in the case of large viscous friction load condition However, this ripple can be negligible if a sufficient inertia is mounted on the machine shaft Considering the general load pattern that the load quantity would be increased according to the machine speed, the applicability of the proposed drive scheme is not damaged Furthermore, since the ripple frequency determined by the sampling interval Test is considerably high, this torque ripple is not critical in the aspect of drive Another choice of the sexisorless drive for low-speed operation is the usage of the PMSM with trapezoidal back-EMF In this case, the back-EMF also can be directly measured at the nonconducting phase [ ] However, since the torque ripple inherently produced by the two-phases conducting method is quite severe, it is very difficult to generate continuously stable electrical torque So the controllable lower-speed range would be limited about several hundred rpm in the loaded operating condition From the measured back-EMF, the actual rotor angle can be achieved as follows E: = E -E COS(^,) sin(0,) : { COS(^,) 1, E = J-.sign(4$) =Ei/E sin(8,) = -E;/E However, when some errors occur at the back-EMF detection instance, the control angle might be influenced by these errors directly, and this results in the system instability Therefore, instead of above angle detection method, the rotor angle is achieved using arc-tangent function and an angle compensation algorithm is introduced in this paper First, the rotor angle is achieved as follows -E: E; - Kew, sin(0,) Kew, cos(8,) sin(0,) - cos(8,) - tan(8,) It is noticeable that the sign of the rotor speed should be considered at the angle calculation because the speed information is canceled by the division operation of the arctangent function When the machine speed has negative value, the rotor angle can be described by -E: E; - sin(0, - 180') K,w, sin(0,) - - sin(0,) K,w, COS(^,) - COS(^,) COS(^, - 180') = tan(0, - 180') : 8, = tan 2-'(-E:, E,")+ 180' (7) Therefore, the rotor angle is represented as follows 0, = 0, + 7r (8) The speed direction can be identified using the calculated rotor angle as follows : sign(w,) = if A&,, -1 if A0,,,, > < (9) To avoid the conflict between (8) and (9), a hysteresis with some bands is added to the rotor speed direction determination process In Fig 5, the overall rotor angle estimation process is depicted The lower area enclosed by a dashed box corresponds to the speed direction detection process with hysteresis function And the upper area enclosed by another dashed box represents the angle compensation algorithm In this algorithm, the deviation of the calculated rotor angle is limited to some value according to the rotor speed to stabilize the control angle in the transient state The basic operation concept is that the rotor angle deviation during one estimation step has the same value of the time integral value of the rotor speed Thus, the maximum deviation will be limited by following value AO, = 1.5 x ILF(&)I Test AQmin=-AO,,, (10) E E E TRANSACTIONS ON POWER ELECTRONICS, VOL 11, NO 3, MAY 1996 516 machine would be slightly rotated to arbitrary direction The rotor angle deviation between the initial point and moved point is very small, but the angular speed would be sufficiently great to detect the rotor angle Whenever the machine speed is higher than 10 rpm, the essential back-EMF can be directly measured, and the initial angle detection process can be accomplished through the proposed angle detection strategy Therefore, within several ones ["I deviation of the rotor shaft in mechanical degree, the initial rotor angle can be easily detected Just after the initial angle determination cycle, a proper starting torque is generated with the information about the electrical initial rotor angle, and the rotor is smoothly rotated according to the direction of the speed command This important feature also can be applied to the general PMSM drives with an incremental encoder type position sensor for smooth machine starting When the incremental encoder is used, the actual rotor position can be achieved when the first zero pulse is encountered Therefore, in most B Speed-Detection Algorithm drives, a special type encoder that provides U, V, W pulses From the basic machine equation (I), the back-EMF inforis used for the initial starting However, the rotor position mation can be utilized for the accurate rotor angular speed w, information with just 60" precision is available using this as follows special encoder at the initial starting instance Moreover, in order to measure these pulses, an additional six lines should w, = sign( ' d m / K E be connected between machine and controller for only the initial starting Using the proposed simple voltage measuring speed can be Every MCD1 test cyc1e, the equipment that can be mounted on the control board with from the back-EMF and speed control algorithm is performed minimum area and smallest wiring, the initial position angle guaranteed in Although the above equation is can be easily detected within reasonable range operating condition, the following remark should be made on the back-EMF constant For an accurate determination of w,, it is necessary to IV EXPERIMENTAL RESULTS know the correct back-EMF constant K E This parameter Experimental tests are conducted to evaluate the performay be uncertain or may be varying according to the thermal mance of the proposed back-EMF detection strategy and the environment Changing this parameter will cause steady-state feasibility of the new position sensor elimination technique error of the estimated speed This uncertainty can be overcome for low speed operation The overall PMSM drive system for by the back-EMF compensation algorithm [9] The basic idea the laboratory prototype test is illustrated in Fig The tested of this algorithm is that the back-EMF constant slowly varies drive system consists of a six-pole Y-connected 0.47 [kW] according to thermal condition and the long-term average of PMSM and an electric dynamometer load The rating and the time differentiation value of rotor angle has the same value parameters of the PMSM are presented in Table I The power of the actual rotor speed With the help of this algorithm, stage comprises the IGBT inverter with 8.33-kHz switching not only the parameter variation but also the measurement frequency and 200-V dc link And, high-performance digital error of the back-EMF can be compensated easily Because signal processor (DSP), TMS320C30 controller specially deof the direct rotor position measuring strategy, the back-EMF signed for machine drive is used to implement the overall constant can be modified to the suitable value to remove the proposed sensorless algorithm, based on C language The steady-state error of the estimated speed whole experimental results including current, machine speed, and angle traces are illustrated by the multichannel oscilloC Starting Strategy scope through D/A converter equipped on the main controller Generally, in the PMSM drives, the information about the Moreover, for monitoring purposes only, an additional increstandstill rotor angle is required at the initial start-up instant to mental encoder with 2000 ppr resolution is attached to the produce a proper electrical torque for starting In the case of machine shaft The actual machine speed and rotor angle are the drive system without position sensors, a specially designed taken from this sensor starting algorithm should be included in the drive algorithm The experimental waveforms of the proposed MCDI test because the back-EMF is not available at the start-up [6] cycle are shown in Fig The PMSM is operated with 50 rpm However, if the proposed direct back-EMF detection strategy constant speed by the proposed sensorless control algorithm In is adopted for the machine drive system, the starting capability Fig 7(a), the actual rotor angle in electrical angular degrees is displayed The estimated rotor angle from the proposed anglecan be given to the drive system in itself At the start-up instant, a test current with short pulse form estimation strategy is shown in Fig (b), and the detected is injected to the machine current By this test current, the back-EMF quantity on the stationary q-axis is shown in the (The L F ( ) function means the low-pass filter.) If the angle deviation is smaller than these maximum values, the control angle Bc always follows the rotor angle , calculated from the measured back-EMF However, if the deviation of the control angle exceeds the maximum value, this deviation is restricted to the maximum value and the control angle is more slowly changed than the calculated angle With the help of this angle compensation algorithm, the control angle is always maintained to the actual angle with sufficiently negligible error, even if some measurement errors occur At the end of the MCDI test cycle, the gating signals are returned to their original state, and the normal current control sequence is restarted In this study, the current sampling interval is chosen to be 60 ps, and the current control algorithm based on space voltage vector is used for high-performance current regulation $) KIM AND SUL: LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTATIONAL POSITION SENSORS I l"32OC30 DSP Controller 517 -.L > L : > - Fig Laboratory experimental setup TABLE I PMSM RATINGAND PARAMETERS 3-phase 6pole Sinusoidal back-EMF PMSM I Rate Power I R" KE i (DC equivalent model) Iyo+a(DCequivalent model) 0rate I (IIb - 0.47 [kWl ,_ 1.26 r- ni - _ 6.5 [mH] 0.03 [ V/rpm] 5.2 [AI I 2000.0 [rpm] - Fig Speed control performance (10 rpm) (a) and (b) Detected synchronous q-axis and d-axis back-EMF (c) and (d) Actual and estimated rotor angle (elec angle) (e) and (f) Actual and estimated rotor speed (d) v m l ] ? d T L T Fig Experiment waveforms of the MCDI test cycle (a) Actual rotor angle (elec angle) (b) Estimated rotor angle (elec angle) (c) Detected stationary q-axis back-EMF (d) Synchronous q-axis current (enlarged time base) next figure As shown in these figures, using the proposed MCDI test cycle, the essential back-EMF quantities can be clearly detected and the new sensor elimination control :scheme for the low-speed operation has performed very well In the last figure, Fig 7(d), the torque component current of the machine is presented in the sampled data fashion To show the MCDI test interval precisely, the time duration between two anrows in the other figures is enlarged in this figure At the initial points of each test cycle, the machine currents are quickly diminished to zero value to directly measure the back-EMF When the back-EMF is completely detected, the machine currents are rapidly stabilized to produce the required electrical torque Of course, the whole electrical torque is affected by the test cycle for back-EMF detection, and the maximum conlhuous output power of the proposed control strategy is limited to some value However, this sensor elimination technique can be effectually utilized to some applications in which a continuous full torque operation is not needed and an effective low speed operation is required without position sensors Fig shows the speed-control performance of the proposed algorithm with 10 rpm speed reference In Fig 8(a) and (b), the traces of the measured back-EMF are shown As shown in these figures, some low order harmonics are included in the back-EMF waveform These harmonic components appear actually in the machine itself because of the slightly small misalignment of the stator winding or inherent flux distribution of the permanent magnet However, this harmonic component would be negligible in the higher speed range because the magnitudes of this harmonics are nearly constant irrespective of the magnitude of the fundamental back-EMF In Fig 8(c) IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 11, NO 3, MAY 1996 518 -1001 I t -14 -4 '0 I sec] 2' (c) (d) 50 [rpm]) (a) Initial angle difference E 70°, No load (b) Initial angle difference Fig 10 Starting performance of the proposed algorithm (0 5Z -120°, No load (c) Initial angle difference 5Z -40' 1/4 load (d) Initial angle difference -150°, 1/4 load (In each figure, first traces: actual rotor angle (elec.); second traces: estimated rotor angle (elec.); third traces: actual machine speed; last traces: torque component current command on the reference frame fixed to 8est.) i and (d), the actual rotor angle and the rotor angle calculated from the back-EMF are shown And, the actual rotor speed and calculated speed are displayed in Fig 8(e) and (0 The rotor speed quantities are fluctuated owing to the harmonic component of the back-EMF If a higher control band width is selected for speed controller, this speed fluctuation can be decreased to some degree In Fig 9, the step response of the proposed sensorless PMSM control algorithm is depicted when the speed reference is changed from 20 to 100 rpm and back with 40% rating load From these experimental results, it can be seen that the measured back-EMF can be successfully used to obtain the necessary position and speed information for replacing a shaft sensor at low speed range (10 150 rpm) However, this proposed sensorless method cannot be applied to the system that has large viscous friction load at low speed operation range, because the current decaying operation in the MCDI test circuit may result in the mechanical resonance when high current flows to machine In the upper speed range, over 150 rpm, the basic machine-model-based method, such as [9], may be adopted for the sensorless drives In Fig 10, the starting performance of the proposed scheme is presented As described above, since the initial rotor position - can be detected through the injected test current and voltage measurement system, the direct back-EMF measuring strategy gives good starting ability to the control system As shown in the lowest trace of Fig 10(a), the test current for producing arbitrary torque is injected with the initial control angle, which is always maintained at zero on the stationary reference frame at the power-up instance During the test current injection cycles, the whole rotor angle estimation process previously mentioned is performed And within a sufficiently short time, the information about the initial rotor angle can be obtained Therefore, at the end of the test cycle, the machine gets started by the proposed sensor elimination control scheme As shown in Fig 1O(c) and (d), the starting process is successfully applied, even in the same loaded case Considering that the outer load is generally given by the pattern that is proportional to the machine speed or the square value of the machine speed, the machine starting under a general loaded condition is no more a critical problem V CONCLUSION A new approach to the position sensor elimination of the PMSM drives for low-speed operation is presented in this KIM AND SUL: LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTATIONAL POSITION SENSORS paper It is shown that the actual rotor position, as well as the machine speed, can be achieved strictly using the: MCDI test cyc1e and direct measuring the back-EMF with a simp1e measurement circuit Additionally, a relatively smooth start can be achieved by the injection of a simple test current to the machine To avoid the steady state-speed estimation error caused by the parameter variations, the back-EMF constant compensation algorithm is also proposed The experimental results show the important features of the new methold in the low speed region (10-100 [rpm]) with acceptable accuracy REFERENCES [ I ] R Wu and G R Slemon, “A permanent magnet motor drive without a shaft sensor,” ZEEE Trans Znd Applicat., vol 27, no 5, pp 1005-1011, 1991 [2] K Iizuka, H Uzuhashi, M Kano, T Endo, and K Mohri, “Microcomputer control for sensorless brushless motor,” ZEEE Trans Znd 4ppZicat., vol IA-21, no 4, pp 595401, 1985 [3] N Matsui and M Shigyo, “Brushless dc motor control without position and speed sensors,” ZEEE Trans Znd Applicat., vol 28, no 1, pp 120-127, 1992 [4] R Dhaouadi, N Mohan, and L Norum, “Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor,” IEEE Trans Power Electron., vol 6, no 3, pp 491497, 1991 [5] S Bolognani, R Oboe, and M Zigliotto, “DSP-based extended Kalman filter estimation of speed and rotor position of a pm synchronous motor,” ZECON Conf Rec, pp 2097-2102, 1994 [6] R Krishnan and R Ghosh “Starting algorithm and performance of a pm dc brushless motor drive system with no position sensor,” PLSC Conf R e c , pp 815-821, 1986 [7] M Matsui and T Takeshita, “A novel starting method of censorless salient-pole brushless motor,” ZAS Conf Rec , pp 386-392, 1994 [8] S Kondo, A Takahashi, and T Nishida, “Armature current locus based estimation method of rotor position of permanent magnet synchronous motor without mechanical sensor,” ZAS Conf Rec , pp 55-60 1995 519 [9] J S Kim and S K SUI,“New approach for high performance PMSM drives without rotational position sensors,’’ APEC Con5 Rec., pp 381-386, 1995 [lo] J S Kim, J W Choi, and S K SUI, “Analysis and compensation of voltage distortion by zero current clamping in voltage-fed PWM inverter,”Yokohama ZPEC Conf Rec., pp 265-270, 1995 Joohn-Sheok Kim (S’92) was born in Korea in 1965 He received the B.S and M.S degrees in electrical engineering from Seoul National University, Korea, in 1989 and 1992, respectively, where he is working toward the Ph.D degree in the area of power electronics His major interests are adjustable speed ac drives and static power converter Seung-Ki SUI (S’78-M’87) received the B S , M S , and P h D degrees in electrical engineering from Seoul National University, Korea, in 1980, 1983, and 1986, respectively He was with the Department of Electncal and Computer Engineering, University of Wisconsin, Madison, as a Research Associate from 1986 to 1988 He joined Gold-Star Industnal Systems Company as Principal Research Engineer in 1988, where he remained until 1990 Since 1991 he has been with the Department of Electrical Engineenng, Seoul National University His present research interests are in high-performance electnc machine control using power electronics He is performing vanous research projects for industnal systems and some of the results are applied to the fields of industrial high-power electric machine control ... the zero value, the back-EMF is measured 1; is the 515 KIM AND SUL: LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTATIONAL POSITION SENSORS I r$ I I - J '' Fig The overall control diagram for low-speed. .. condition is no more a critical problem V CONCLUSION A new approach to the position sensor elimination of the PMSM drives for low-speed operation is presented in this KIM AND SUL: LOW-SPEED OPERATION. .. L LOW-SPEED OPERATION OF PMSM DRIVES WITHOUT ROTA1’IONAL POSITION SENSORS P qr se (- vbs Ld Fig Space vector diagram for the PMSM drives, the standstill rotor angle should be known even if a rotational