IEEE TANSACTIONS ON POWE EECTONICS, VO. 18, NO. 2, MACH 2003 539 A Novel, obust DSP-Based Indirect otor Position Estimation for Permanent Magnet AC Motors Without otor Saliency i Ying and Nesimi Ertugrul, Member, IEEE Abstract This aer rooses and imlements a novel rotor osition sensorless technique for PM ac motor drives, which allows acceleration from standstill and can oerate under various ractical oerating conditions including transient seed changes. The technique develoed here relies on the measurement of the hase voltages and currents of the motor. It uses the incremental values of flux linkage, and the back-emf functions to estimate incremental rotor osition. Using a hase-locked loo (P) algorithm, an internal closed-loo correction algorithm can correct rotor osition estimation drift, which may be due to the motor arameter variations or measurement inaccuracies. The method is imlemented in closed-loo using a digital signal rocessor (DSP), and details of the imlementation are rovided in the aer. To demonstrate accuracy, robustness and reliability of the osition estimation scheme, the aer resents a number of real-time exerimental results, including dynamic oerating conditions. Index Terms DSP based motor control, ermanent magnet motors, osition estimation, sensorless oeration. I. INTODUCTION ONE of the most active areas of research in ermanent magnet (PM) ac motor controls during recent years has been the investigation of new techniques for eliminating the rotor osition sensor that is normally required for selfsynchronization. Elimination of the shaft-mounted osition sensor is a very desirable objective in many alications since such sensor is often one of the most exensive and fragile comonents in the entire drive system. The exected benefits of the indirect rotor osition sensing technique are: elimination of electrical connections to sensors, reduction in size, insuscetibility to environmental factors, and imroved reliability. In addition, when absolute rotor osition sensors are considered, oeration at zero and low seeds are also desirable features of an indirect rotor osition detection method. A number of indirect rotor osition detection techniques have been roosed in the literature for PM ac motor drives. These techniques can broadly be classified in three grous. The first grou is based on back-emf sensing [1] [3]. Since the back-emf voltages of a PM ac motor are functions of the rotor osition, the most common aroach to estimate the Manuscrit received October 18, 2002; revised October 22, 2002. ecommended by Associate Editor S. B. eeb. The authors are with the Deartment of Electrical and Electronics Engineering, Adelaide University, Adelaide 5005, Australia. Digital Object Identifier 10.1109/TPE.2003.809377 rotor osition is to extract the rotor osition information from the back-emf waveform of an unexcited hase. However, the back-emf voltages of the PM ac motors are too small to be sensed at low seeds. In addition, the method is affected by the switching transients from the other current carrying hases. Therefore, it is not suitable for PM ac motors with continuous current conduction and is not suitable for low-seed oeration. The second grou is based on estimation techniques that usually utilize hase voltages and currents of the motor. By using these quantities, the rotor osition of the motor can be determined using a state observer [4] [6], or a alman filtering technique [7], [8], or by direct calculations [9] [11]. However, these techniques are comutationally intensive, and large rotor osition detection errors may occur because of quantization and truncation errors, and measurement inaccuracies. Moreover, variation in the motor arameters due to temerature changes and magnetic saturation significantly affect the estimated rotor osition data. Furthermore, the estimation erformance may suffer under low-seed oeration, mainly due to drift of the integration functions used in the algorithms. Therefore the roblems listed above make the revious methods not suitable for the ractical motor drives. Finally, the third grou of indirect rotor osition detection techniques is based on the detection of the rotor saliency in PM ac motors, which occurs due to the asymmetrical rotor structure or magnetic saturation [12], [13]. In this grou, the rotor osition information can also be extracted from resonses of an injected high frequency test signal [14], [15]. This method is not deendent uon the motor seed and hence can oerate at low seeds including standstill. However, these techniques are not suitable for nonsalient PM motors, such as surface mount PM ac motors that have no rotor saliency. The rincial aims of this aer are to overcome the roblems of the revious methods and to roose a robust solution that is suitable for ractical PM ac motor drives. The osition estimation and the ractical imlementation issues of the roosed method are discussed in the subsequent sections of this aer. In this novel method, three hase flux linkage increments (hence no integration is required) are calculated using the measured three-hase voltages and currents, which is the main source of the estimation error in the revious techniques. Then the flux linkage increments and back-emf functions of the motor are utilized to derive a single rotor osition increment and the corresonding rotor osition information is calculated. In the method, with the hel of a hase-locked 0885-8993/03$17.00 2003 IEEE
540 IEEE TANSACTIONS ON POWE EECTONICS, VO. 18, NO. 2, MACH 2003 loo (P) algorithm, an internal closed-loo can correct the osition drift that may be caused by the deviations of the motor arameters and/or by the measurement inaccuracies. As will be demonstrated in the results section, this novel method can accurately estimate the rotor osition over a wide range of oerating seeds, and is robust with resect to arameter variations of the motor and measurement errors in the system. In addition, the roosed estimation scheme is not comutationally intensive, which makes the real-time imlementation of the method ossible with a commercially available DSP (Analog Devices ADMC300). In addition, while the motor drive oerating in closed-loo without a conventional rotor osition sensor, a number of real-time exerimental results are obtained to demonstrate the robustness, the reliability and the erformance of the novel osition estimation scheme under various ractical oerating conditions [16]. II. PINCIPES OF THE AGOITHM The method develoed here is suitable for a wide range of PM ac motors. However, a three-hase surface-mounted PM ac motor is considered in the develoment of the osition estimation algorithm. The surface-mounted PM ac motor has identical direct and quadrature inductances, so that the rotor saliency does not exist, and thus it is not ossible to use methods which rely on rotor saliency. Under ideal conditions, however, a ossible solution to obtain the rotor osition data is to utilize the relationshis with the three-hase flux linkages that are established by the ermanent magnets. This aroach is considered in this study. A. Mathematical Model of the Motor In order to obtain a general algorithm, the three-hase a-b-c modeling aroach is used in this aer. Under ideal conditions, a three-hase star-connected PM motor can be modeled by a network consisting of a winding resistance, an equivalent winding inductance, and a back EMF source er hase, all connected in series. If it is assumed that the stator resistances of the windings are identical and the self and mutual inductances are constant, which is correct in the motor tye considered (no rotor saliency), the voltage equations of the motor can be given in a matrix form as Here,, and are the hase voltages; is the winding resistance;,, and are the hase currents; is the equivalent winding inductance and is equal to where is the self inductance and M is the mutual inductance of the winding; and,, are the back-emf voltages induced in each hase winding due to the flux linkages of PMs. In the PM ac motor, the back EMF voltages are functions of the rotor osition and the angular seed. Hence, for the motor (1) with sinusoidal back-emf s, the three-hase back-emf voltages can be exressed as where is the back EMF constant, is the rotor angular seed,, and are defined as the back EMF functions that varies with the rotor osition, and is the electrical rotor osition that can be given by (2) (3) where is the number of ole airs in the motor. B. Position Increment Estimation In the above voltage equations, the three-hase currents and voltages are directly measurable quantities. It can be seen that there is only one ossible solution to derive the rotor osition information from the measurable quantities and the ideal model of the motor. The aroach used to determine the rotor osition here is based on the relationshi between the rotor osition and the flux linkage of the ermanent magnets or the back-emf voltages. However, if the relationshi between the rotor osition and the back-emf voltages is used, the osition estimation scheme may not oerate accurately at low seeds due to the small induced back-emf voltages. Furthermore, if the relationshi between the rotor osition and the flux linkage of the ermanent magnets is utilized to calculate the total flux linkages of the windings, some form of digital integration is needed. However, digital integration is difficult to accurately realize in the real-time systems. This is due to motor arameter variations and measurement errors such as DC offsets, quantization and truncation errors. All these errors can cause integration drift and ose a significant roblem in the estimation of the flux linkages, secifically at low seeds. To overcome the drawbacks discussed above, a novel osition estimation scheme is roosed here. In the new method, the calculation of the flux linkage by digital integration is eliminated and a direct calculation of the flux linkage increment change using the voltage equations is utilized. In addition, the back-emf voltages are disassembled as the multilication of the angular seed and the unit back-emf functions, so that the estimation of the back-emf function becomes indeendent of the angular seed. Substituting (2) into (1), the voltage equations can be rewritten as As can be seen in the above equation, if the samling frequency is high enough in a ractical measurement system, the (4)
YING AND ETUGU: NOVE, OBUST DSP-BASED INDIECT OTO POSITION ESTIMATION 541 rotor osition increment within one samle cycle can be derived in the discrete form as (5) where t is the samling interval,, and are the current increments within the samling interval of the threehase currents,, and are defined as the flux linkage increments within the samling interval of each hase. Ideally, each motor hase should roduce identical rotor osition increment. In ractice, however, any estimation errors could cause variations in the estimated rotor osition increment. In this study, a single value of osition increment is obtained by averaging the three values of the osition increments estimated in (5). In addition, assuming that the revious value of the rotor osition estimation is known, an udated value of the rotor osition can be estimated simly by (6) k k k (7) where, is an integer reresenting the estimation of discrete data at the th instant of time. C. Position Estimation Algorithm As can be seen in (5), since the back EMF function of each hase becomes zero at the corresonding rotor ole, the rotor osition increment estimation under this condition may roduce an infinitely high value. However, the remaining two hases can rovide a finite and more accurate rotor osition value. This means that each hase has its own otimal sensing region, where the rotor osition increment estimation is most accurate. Although (6) can be used to calculate the single value of rotor osition increment, in a more ractical algorithm, the three rotor osition increments should be weighted or adjusted with resect to their otimal sensing regions in order to revent the loss of rotor osition information and the reduction of the accuracy. In order to utilize the otimal sensing region of each hase fully and to imrove the osition estimation accuracy, (5) should be rewritten in the format given as follows: In (8), if the two sides of the equations inside the matrix are multilied by, and resectively, and the (8) three equations are summed, a single rotor osition increment can be obtained as The above equation is the basis of the incremental rotor osition estimation, which can be considered as a weighted average which takes into account the otimum regions for accurate osition estimation for each hase. In a very noisy environments however, a more selective range filtering may be required. The osition estimation algorithm in this study utilizes (7) (9). Equation (8) is used to calculate the flux linkage increments using the measured hase currents and voltages. Then, the flux linkage increments and the back EMF functions are utilized to determine the rotor osition increment by (9), and the final rotor osition is estimated by (7). It should be noted here that the back EMF functions are roduced using their waveform functions and the estimated osition signal, which form an internal closed-loo. The algorithm has several advantages. Firstly, it is simle and not mathematically intensive, which makes it very ractical to be used in DSP based control systems. Secondly, the algorithm is indeendent of the shae of back-emfs, hence is suitable for both sinusoidal and traezoidal PM ac motors (or for any other PM motors with nonideal back EMFs). Finally, the calculation of the flux linkages does not include an integration algorithm, so that integration related errors are eliminated. Although a simle integration algorithm still exists in the osition calculation (7), the internal closed-loo roduced by the back-emf function feedbacks stabilizes the osition integration and corrects the osition drift. This is the most imortant feature of the novel algorithm. In other words, the method moves the integration from the flux linkage calculations to the osition calculation level and hence the roblems of the integration drift are solved by the internal closed-loo correction. Furthermore, this internal correction loo imroves the robustness of the rotor osition estimation, which would otherwise be sensitive to arameter variations and measurement errors. It should be noted here that further imrovements were done to the osition estimation algorithm to enhance the accuracy of the estimation, which is illustrated in Fig. 1. In this figure, the basic algorithm described above unchanged and two additional blocks are added to the left side of the diagram: Back-EMF Functions and Phase Difference. III. ANAYSIS OF OBUSTNESS AND IMPOVEMENTS Under ideal conditions, the algorithm described above can roduce accurate rotor osition estimates. In ractice, however, the arameters of the motor may vary for various reasons, such as temerature rise or magnetic saturation. In addition, there are no ideal measurement circuits in reality. Practical measurement circuits can be affected by electromagnetically noisy environment. Therefore arameter deviations and measurement inaccuracies need to be considered in real-time motor control systems as they directly affect the reliability and the robustness of the control algorithm. (9)
542 IEEE TANSACTIONS ON POWE EECTONICS, VO. 18, NO. 2, MACH 2003 where, is the amlitude of the flux linkage increment. As can be seen from the auto-correction function given in (10), in ideal conditions, the rotor osition is equal to the hase angle of the flux linkage increments, and the estimated rotor osition increment is directly roortional to the amlitude of the flux linkage increments. If an error causes the estimated rotor osition to differ, the difference is fed back to the loo via the back-emf functions and the next ste value of the osition increment estimation is corrected within a range of osition For examle, if the estimated rotor osition leads the hase angle of flux linkage increments, the hase difference roduced by the feedback reduces the new estimated value of the osition increment. Conversely, if the estimated rotor osition lags the hase angle of flux linkage increments, the hase difference increases the new estimated value of the osition increment. Fig. 1. Block diagram of the imroved algorithm. A. Theoretical Analyzes of obustness In a ractical motor drive, the motor equivalent circuit arameters are nonlinear functions of time, temerature and various other arameters. Therefore, the accurate rediction of the measurement errors and noise is a challenging issue in the software/hardware integrated ower electronics systems, which is difficult to redict. It can be seen from the basic algorithm described earlier that any arameter variations or measurement inaccuracies can cause osition increment errors. If no corrective action is taken, the osition error may accumulate over the integration eriod and may cause a catastrohic failure in the drive, such as loss of synchronism. As can be seen in (8), if the back EMF functions are ideal sinusoidal waveforms, three-hase flux linkage increments should also be ideal sinusoidal waveforms. Hence, the estimated osition increment value only deends on the amlitude of the flux linkage increments. However, disturbances may occur in a nonideal (ractical) system causing an error in the estimated osition increment. If this error is fed back to the back-emf functions via the internal closed-loo, it causes a hase difference between the flux linkage increments and the back-emf functions. et us assume that the flux linkage increments have a hase angle of, which reflects the actual rotor osition value. Then the estimated rotor osition increment based on the basic algorithm can be rewritten as (10) B. Imrovements As discussed above, the osition estimation algorithm is robust with resect to some of the measurement errors and can oerate accurately within a range of osition. However some static estimation errors also occur in ractice, which is mainly due to the arameter variations and/or the measurement inaccuracies. The auto-correction ability is directly roortional to the motor seed. In high-seed oeration, the static errors are accetable in ractical alications. At slower seeds, however, the static errors accumulate via the integration due to the oor auto-correction ability. This results in the estimated rotor osition laging the flux linkage increments. To make the osition estimation algorithm resistant to static errors, a hase-locked loo (P) is imlemented, which is roven to be very effective. In the P, the three-hase flux linkage increments and the three-hase back-emf functions are considered as vectors. By using the vector roduct, the hase difference between the two quantities are exressed aroximately as (11) Using the above equation in the P, the hase difference between the hase angle of the flux linkage increments and the estimated rotor osition can be estimated. Then the value is then utilized to comensate the incremental osition errors, which may be in error due to the arameter variations and/or the measurement inaccuracies. The block diagram of the imroved algorithm is given in Fig. 1, where the basic algorithm remains unchanged. If there are any arameter deviations or measurement inaccuracies in the system, however, the redicted values may be in error. Therefore, the back-emf functions generated by the redicted rotor osition will have a different hase angle from the functions generated using the flux linkage increments. The P calculates the hase difference and comensates the redicted rotor osition to rectify the rotor osition value in the consecutive ste. Therefore, the imroved rotor osition estimation algorithm is called the rediction-rectification method.
YING AND ETUGU: NOVE, OBUST DSP-BASED INDIECT OTO POSITION ESTIMATION 543 C. Comuter Simulation esults To demonstrate the effectiveness of the algorithm exlained above and to give some quantitative results, extensive simulation studies were erformed on a samle motor, which has the arameters given in the Aendix. The simulation studies were carried out under the steadystate conditions with a dc link voltage of 150 V and under the following arameter changes of the motor: 20%, 20% e and 20% (the winding resistance, the back-emf constant, and the equivalent inductance errors resectively), and under the stator winding imbalances. A PWM current controller with modulation frequency of 5 khz is also included in the simulation. Fig. 2 shows a set of simulation results, which aims to demonstrate the robustness with resect to the motor arameter variations. It can be concluded from the simulation results that if the arameters of the osition estimator and the motor are identical, the estimated rotor osition can accurately follow the actual rotor osition both in the basic and in the imroved algorithms. When the arameters of the motor vary by 20%, the osition estimation errors do occur, but are limited to 2 3% by the basic algorithm with the hel of auto-correctional action. This is an accetable osition error in a ractical osition sensorless motor drive, which demonstrates a degree of robustness in the basic algorithm. However, the basic algorithm cannot eliminate static osition estimation errors and the auto-correctional ability of the basic algorithm is oor at the lower seed range. By using the P, however, the imroved algorithm significantly reduces the static estimation errors as shown in Fig. 2. It can be seen in the figure showing the osition errors that the static osition errors caused by the winding resistance and the back-emf constant variations can be almost eliminated using the imroved algorithm. However, the osition estimation errors caused by the equivalent inductance variations are still relatively high. This is because the variations of equivalent inductance can affect the hase of the flux linkage increments, and therefore the estimated hase of the flux linkage increments may different from the actual value if the equivalent inductance is in error. As mentioned above, the stator winding imbalance was also studied under two different settings (, ; and, ). The result indicated that there is no benefit of the imroved algorithm on the stator winding imbalance. Therefore, the P cannot roduce accurate values to rectify the errors in the rotor osition estimation. It should be emhasised here that in a ractical nonsalient PM ac motor, the equivalent inductance is more stable than the other motor arameters under normal oeration conditions. Therefore, it is recommended in a ractical osition sensorless drive system that the equivalent inductance should be measured accurately in order to minimize the osition estimation errors further. Further simulations studies were also carried out to observe the effects of voltage and current measurement errors ( 10%). In this study, the motor arameters are not changed and the similar control settings as in Fig. 2 are used. The results indicated that the basic algorithm can also limit the osition errors due Fig. 2. Comuter simulation results under the arameter changes of the motor: 620%, 620% e and 620%, with a command current of 2.5 A and at a steady-state seed of 25 Hz. The figure shows the rotor osition (to), the osition errors between the actual and the estimated osition signals with the basic algorithm (middle) and the osition errors with the imroved algorithm (bottom). to measurement errors but the resence of the static estimation errors limit the oeration at slower seeds. The imroved algorithm, however, reduces the static estimation errors and extends the oerating range of the motor. IV. EA-TIME EXPEIMENTA ESUTS To test the roosed osition estimation algorithm to see if it is suitable for the ractical alications, a real-time exerimental setu is imlemented. This includes a three-hase inverter board (IMDAC3, International ectifiers, 460 V, 3 h) and a DSP-based motor controller from Analog Devices (ADMC 300). In addition, a PM ac motor (which has the secifications given in the aendix), a two channel incremental encoder to verify the estimated rotor osition, and three high bandwidth voltage and two high bandwidth current transducers are used in the exerimental setu. A. Oen oo Oeration In the oen loo test, the motor drive is synchronously controlled using the shaft mounted encoder. In the DSP, a standard PWM current controller with a PWM frequency of 5 Hz is used to modulate the currents of the motor. In addition, a ab- VIEW based data acquisition system is used to samle the real data of the motor drive at a samling frequency of 100 Hz. Then, the measured voltage and the current data can be used to estimate the rotor osition of the motor off-line and comare it with the measured rotor osition. In this section, as in the simulation studies, various degrees of artificial errors are introduced to the motor arameters of the osition estimator and to the measured voltage and the current data. The erformance of the algorithm has been tested under these synthetic errors. The test results are illustrated in Fig. 3 and Fig. 4. It was observed that the osition estimation algorithm can still estimate
544 IEEE TANSACTIONS ON POWE EECTONICS, VO. 18, NO. 2, MACH 2003 Fig. 5. Block diagram of the closed-loo osition sensorless PM ac motor drive system. Fig. 3. Oen-loo oeration exerimental results to demonstrate the robustness with resect to the arameter variations: the actual rotor osition (to), the osition estimation error using the basic algorithm (middle), and the osition estimation error using the imroved algorithm (bottom). Fig. 4. Oen-loo oeration exerimental results to demonstrate the robustness with resect to the measurement errors: the actual rotor osition (to), the osition estimation error using the basic algorithm (middle), and the osition estimation error using the imroved algorithm (bottom). the rotor osition accurately ( 3 4%). Although the imroved algorithm generates larger estimation noise, its static errors are smaller than the estimation errors of the basic algorithm. B. Closed-oo Oeration To imlement osition sensorless motor drive, the encoder is eliminated from the control loo, but is utilized to verify the estimated rotor osition. Fig. 5 illustrates the comlete block diagram of the osition sensorless motor drive system, where the osition estimator relaces the shaft mounted osition sensor. Since the DSP used in this study has only five A/D converter channels, three hase voltages and only two hase currents are measured in real-time. The third hase current that is required in the algorithm is calculated using the two measured hase currents. For the nonsalient motor, if the current waveforms are in hase with the rotor osition, the electromagnetic torque is roortional to the amlitude of the excitation current. Therefore, to generate the three-hase current commands using the estimated rotor osition and the current amlitude, a look-u table for a sinusoidal function is established in the DSP as the current waveform command generator. A PI seed controller is imlemented in the motor drive, which is considered as the torque command of the motor drive. Finally, the three-hase command currents are comared with the measured three-hase currents and the results are used as the duty cycle signals to generate the three-hase PWM signals for the switching ower devices (IGBTs). As known, in a digital motion control system, the duty cycle value can be udated once (or twice if the double udate PWM mode is used) in each PWM cycle. In a conventional motor controller with a osition sensor, there is only one interrution service routine, which has the same frequency as the PWM. In the osition sensorless motor controller, however, the osition sensorless algorithm requires high bandwidth voltage measurements. Therefore, two different interrution service routines are required. In the method imlemented, one of the routines is used to estimate the rotor osition signals, and the second routine is used to emloy the conventional motor control algorithms. This is because when three hases are excited with currents, the voltage of one hase has 6 ossible values in each PWM cycle. Therefore, in order to samle the values of the hase voltages accurately, the A/D converter should have much higher samling rate than the PWM frequency. It should be emhasised here that the accuracy of the osition estimation is directly roortional to the samling frequency. Exeriences indicate that the frequency of the interrution service routine should be at least 6 times the PWM frequency. The highest ossible samling rate of the A/D converter used in this study is 31.5 khz. Therefore, the frequency of PWM and the motor control interrution service routine of the osition sensorless motor drive is selected as 5208 Hz. So, the samling rate of the A/D converter is 6 times higher than the PWM frequency.
YING AND ETUGU: NOVE, OBUST DSP-BASED INDIECT OTO POSITION ESTIMATION 545 Fig. 6. The real-time exerimental results obtained from the closed-loo motor drive oerating at 107 rm without the shaft mounted osition sensor: three-hase measured currents (to), measured osition (middle) and estimated osition (bottom). Since the estimated rotor osition values are used only once in the motor control interrution service routine er PWM cycle, the six estimated rotor osition values within one PWM cycle are averaged in the real time system. Therefore, the estimation noises are reduced by this averaging method, and the closed-loo sensorless osition estimator was imlemented successfully. C. Starting Strategy in the eal Time Drive Since there is no rotor osition data available at standstill, most of the osition sensorless techniques resented in the literatures are not self-starting. Therefore, a secial starting strategy should be accommodated in the controller until the osition algorithm generates an accurate estimation of the rotor osition. In the osition estimation method roosed in this aer, an initial value of the rotor osition is required. Fortunately, the auto-correctional feature of the algorithm not only resonds to the arameter variations and the measurement errors but also corrects the initial osition value. For examle, if the redetermined initial osition is different than the actual rotor osition, the hase difference between the initial rotor osition and the hase angle of the flux linkage increments is fed back through the internal loo of the algorithm. Using the hase difference, the robust algorithm corrects the rotor osition increment and udates the rotor osition value, and after few samling cycles, the estimated rotor osition can converge to the actual value. As will be demonstrated later, the roosed method can be used to start the PMAC motor from standstill in real time. This imlies that the osition estimation algorithm can redict the rotor osition from a random initial value (such as zero). If the estimated rotor osition is used as the osition feedback in the controller, the motor may roduce lower or even negative electromagnetic torque initially, which may affect the starting erformance of the motor drive slightly. However, the estimated Fig. 7. Measured dynamic starting erformance of the closed-loo osition sensorless motor drive: Phase currents (to), the estimated rotor osition (middle) and the estimated seed (bottom). osition can converge to the actual osition within the first electrical cycle and can thus imlement synchronous control from standstill. In comarison with other oen-loo starting strategies, it was demonstrated exerimentally that this method has shorter starting time and a higher dynamic erformance, and it was observed that the starting rocedure is smooth. D. eal-time Exerimental esults (Without the Shaft Position Sensor) To demonstrate the effectiveness of the osition estimation algorithm, a number of real time exeriments have been erformed at various oerating conditions. Fig. 6 rovides a set of steady-state test results while the sensorless motor drive oerates at a seed of 107 rm (about 50 Hz). The figure illustrates the waveforms of the measured three-hase currents, the measured rotor osition and the estimated rotor osition of the motor. As can be seen in the osition waveforms, there is a negligible discreancy between the estimated and the measured osition data, and the actual current waveforms are very close to the desired waveforms (sinusoidal) that are generated using the estimated rotor osition data. The real-time exerimental results were also obtained from the closed-loo motor drive oerating at 10.7 rm (about 5 Hz). A very good agreement between the estimated and the measured rotor osition is also found in this test. The osition errors in these tests were less than 3%. However, significant variations were observed on the actual hase currents of the real motor. The main reason for this is the small mechanical load of the real drive at the low seeds, which was difficult to rectify. A low inertia PM ac generator is used as a load that is attached to a three-hase resistive load bank. Finally, a dynamic test was erformed and the results are given in Fig. 7. In this exeriment, the osition sensorless motor
546 IEEE TANSACTIONS ON POWE EECTONICS, VO. 18, NO. 2, MACH 2003 drive was accelerated from standstill to 107 rm. The results demonstrate that the osition sensorless motor drive can start smoothly without the hel of any secial starting strategy, and a reasonable dynamic erformance is achieved. V. CONCUSION The aer has roosed a novel osition sensorless technique suitable for a wide range of PM ac motors. Although, the rinciles of the method are develoed and exlained for the motors without rotor saliency, the method is also alicable to rotors with saliency. Here the osition sensing is much easier as the variations of the inductance with osition can be utilized. The method described here is based on an incremental fluxlinkage algorithm, which can form an internal closed loo and uses the real-time voltages and current of the motor. In addition, with the hel of the hase-locked loo algorithm, the internal closed loo can eliminate the roblems associated with the integration drift, which exists in the revious methods. It was also demonstrated using the real data and some synthetic errors that the method has high robustness and reliability against arameter changes of the motor and various measurement errors. The osition estimation algorithm is simle and not mathematically intensive, which makes the real-time imlementation ossible. By using the DSP based real-time system, it was demonstrated that the algorithm develoed here can start from standstill and can estimate the rotor osition accurately under the ractical oerating conditions, including the static and dynamic erformance. The starting from standstill requires an initial value that need not be correct. An incorrect starting osition influences the starting dynamics only, and in the worst scenario it is corrected within one electrical cycle. In comarison with revious osition sensorless techniques, it can be concluded that this novel method has two major features. Firstly, the algorithm has high robustness with resect to the arameter variations and the measurement errors and hence is suitable for ractical alications. Secondly, the auto-correctional ability of the method makes it alicable for starting and oeration at a wider seed range, including slower seeds. APPENDIX The arameters of the exeriment motor. Back EMF constant, : 3.785 V/rad/s. Number of oles air, : 28. Winding resistance, : 6.4. Equivalent winding inductance, : 32.8 Mh. EFEENCES [1]. Iizuka and H. Uzuhashi et al., Microcomuter control for sensorless brushless motor, IEEE Trans. Ind. Alicat., vol. 21,. 595 601, May/June 1985. [2] J. C. Moreira, Indirect sensing for rotor flux osition of ermanent magnet AC motors oeration over a wide seed range, in Proc. IEEE-IAS Annu. Meeting, 1994,. 401 407. [3] S. Ogasawara and H. Akagi, An aroach to osition sensorless drive for brushless DC motor, IEEE Trans. Ind. Alicat., vol. 27,. 928 933, Set./Oct. 1991. [4]. A. Jones and J. H. ang, A state observer for the ermanent magnet synchronous motor, IEEE Trans. Ind. Electron., vol. 36,. 374 382, Aug. 1989. [5] J. S. im and S.. Sul, High erformance PMSM drives without rotational osition sensors using reduced order observer, in Proc. Conf. IEEE IAS Annu. Meeting, 1995,. 75 82. [6] M. Tomita and T. Senjyu et al., New sensorless control for brushless DC motor using disturbance observers and adative velocity estimations, IEEE Trans. Ind. Electron., vol. 45,. 274 282, Ar. 1998. [7]. Dhaouadi, N. Mohan, and. Norum, Design and imlementation of an extended alman filter for the state estimation of a ermanent magnet synchronous motor, IEEE Trans. Power Electron., vol. 6,. 491 497, July 1991. [8] S. Bolognani,. Oboe, and M. Ziglitto, Sensorless full-digital PMSM drive with EF estimation of seed and rotor osition, IEEE Trans. Ind. Electron., vol. 46,. 184 191, Feb. 1999. [9] W. usong and G.. Slemon, A ermanent magnet motor drive without a shaft sensor, in Proc. IEEE IAS Annu. Meeting, 1990,. 553 558. [10] A. Consoli and S. Musumeci et al., Sensorless vector and seed control of brushless motor drives, IEEE Trans. Ind. Electron., vol. 41,. 91 96, Feb. 1994. [11] N. Ertugrul and P. P. Acarnley, A new algorithm for sensorless oeration of ermanent magnet motors, IEEE Trans. Ind. Alicat., vol. 30,. 126 133, Jan./Feb. 1994. [12] A. B. ulkarni and M. Ehsani, A novel osition sensor elimination technique for the interior ermanent magnet synchronous motor drive, IEEE Trans. Ind. Alicat., vol. 28,. 144 150, Jan./Feb. 1992. [13] S. Ogasawara and H. Akagi, Imlementation and osition control erformance of a osition-sensorless IPM motor drive system based on magnetic saliency, IEEE Trans. Ind. Alicat., vol. 34,. 806 812, July/Aug. 1998. [14] M. J. Corley and. D. orenz, otor osition and velocity estimation for a salient-ole ermanent magnet synchronous machine at standstill and high seeds, IEEE Trans. Ind. Alicat., vol. 34,. 784 789, July/Aug. 1998. [15] A. H. Wijenayake, J. M. Bailey, and M. Naidu, A DSP-based osition sensor elimination method with an on-line arameter identification scheme for ermanent magnet synchronous motor drives, in Proc. IEEE IAS Annu. Meeting, 1995,. 207 215. [16]. Ying and N. Ertugrul, A novel osition sensorless control for ermanent magnet AC motors, in Proc. Int. Power Electron. Motion Control Conf. (IPEMC 00), Beijing, China, 2000,. 169 174. i Ying received the B.Sc. and M.Sc. degrees in electrical and electronic engineering from the China University of Mining and Technology, China, in 1983 and 1986, resectively, and the Ph.D. degree from the University of Adelaide, Adelaide, Australia. From 1987 to 1998, he was with Yunnan Polytechnic University, China. His research interests include real time control of motor drives, DSP-based alications, high efficiency and high erformance motor drive design, and intelligent control systems in ower electronics. Nesimi Ertugrul (M 95) received the B.Sc. and M.Sc. degrees from the Istanbul Technical University, Istanbul, Turkey, in 1985 and 1989, resectively, and the Ph.D. degree from the University of Newcastle uon Tyne, U.., in 1993. He joined the University of Adelaide, Adelaide, Austrial, where since 1994, he has been a Senior ecturer. He is the author of abview for Electric Circuits, Machines, Drives and aboratories (Englewood Cliffs, NJ: Prentice-Hall, 2002). His research toics include sensorless oeration and real time control of switched motor drives, fault tolerant motor drives, condition monitoring, and electric vehicles. His recent interests are macro machines and human machine interfaces. Dr. Ertugrul serves on the Editorial Advisory Board for the International Journal of Engineering Education.