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Position Estimation in Salient PM Synchronous Motors Based on PWM Excitation Transients Vladan Petrovic´, Member, IEEE, Aleksandar M. Stankovic´, Senior Member, IEEE, and Vladimir Blaˇsko, Senior Member, IEEE
Abstract—This paper presents a position and speed estimation algorithm based on magnetic saliency of permanent-magnet synchronous motors. The proposed method uses inherent high-frequency content of motor pulsewidth-modulation (PWM) excitation to measure position-dependent inductance parameters, which are then processed using a simple nonlinear observer to produce the position and speed estimates. To ensure persistent excitation at all operating voltages (speeds), a novel PWM algorithm with full voltage output is developed and presented. The efficiency of the modified excitation was evaluated and compared to the efficiency of the standard position-sensorless motor drive excitation. Experimental results are presented as well, showing good algorithm performance in a wide speed range, including zero, and for various load torques. Index Terms—Motor drives, permanent-magnet (PM) motors, position estimation, position-sensorless control.
I. INTRODUCTION
P
ERMANENT-MAGNET synchronous motors (PMSMs) became increasingly popular in high-performance variable-frequency drives. In many applications PMSMs are the preferred choice due to their favorable characteristics: high efficiency, compactness, high torque-to-inertia ratio, rapid dynamic response, and simple modeling and control. To achieve proper field orientation in motion control of PMSMs, it is necessary to obtain the actual position of the rotor magnets. Although a position sensor mounted on the motor shaft (encoder, resolver, Hall-effect sensor, etc.) is typically used for this purpose, there is a significant interest in removing those sensors since they are often complex and rather fragile. Their removal thus results in reduced overall system cost (both in terms of parts and in maintenance), and in improved reliability. The industrial interest in position-sensorless operation of ac motor drives has triggered intensive research in this area in the past several years. Broadly speaking, there are two approaches Paper IPCSD 02–034, presented at the 2001 Industry Applications Society Annual Meeting, Chicago, IL, September 30–October 5, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 15, 2001 and released for publication February 24, 2003. This work was supported in part by the National Science Foundation under Grant ECS-9502636 and Grant ECS-9820977, and by the Office of Naval Research under Grant N14-95-1-0723. V. Petrovic´ is with Aware Inc., Bedford, MA 01730 USA (e-mail:
[email protected]). A. M. Stankovic´ is with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA (e-mail:
[email protected]). V. Blaˇsko is with Otis Elevator Company, Farmington, CT 06032 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TIA.2003.811776
to the rotor position estimation reported in the literature. The first approach concentrates on estimation of the motor back electromotive force (EMF) and subsequent extraction of position information from this signal [1]–[4]. The common characteristic of the back-EMF-based algorithms is that their performance degrades at low speeds, since the back-EMF term vanishes close to standstill. To avoid this singularity, the second approach relies on position dependence of motor inductances due to magnetic saliency. The methods in this group usually involve injection of an auxiliary signal to probe the motor electrical subsystem, and use the response to such excitation to estimate the position [5]–[10]. Corley and Lorenz [5] propose the method similar in operation to a resolver and resolver-to-digital converter (RTDC), where the motor actually acts as the electromagnetic resolver. Sinusoidal injection is applied with the power converter and the current response is processed with an RTDC chip in hardware. In [6], a similar method with a lower injection signal frequency is used, but both the generation and processing of the test signals are performed without the additional hardware. The methods in [8] and [9] use motor saliency only for the startup, and continue with back-EMF-based algorithms at higher speeds. The first of those two methods uses pulse and the second sinusoidal signal injection. Another method that combines the two position sensing principles is presented in [10]. In this work, the authors use injected waveforms natural for inverters (the so-called INFORM method) for position estimation at low speeds, and switch to the back-EMF method at higher speeds. In addition, a Kalman filter is used for the estimation of the mechanical variables and load torque. The majority of techniques operational at low speeds involve auxiliary signal injection. However, a different approach to system excitation for parameter estimation was proposed by Ogasawara and Akagi [11], [12]. The authors suggest the use of the high-frequency content of pulsewidth-modulation (PWM) voltage signal, instead of an auxiliary injection signal, for the system identification. A similar approach was adopted in [13] where the authors use PWM transients in a back-EMF-based position estimation with saliency-based startup. In our work, we start with a model discretization similar to [11] in order to exploit the current transients within a PWM period. Then, we use the current and voltage data and the PMSM electrical subsystem model to construct a novel least-squares problem intended for the estimation of the position-dependent motor parameters. Computationally intensive least-squares problem solution is avoided with a careful problem reformulation which reduces the online parameter estimation procedure to a simple matrix-vector multiplication.
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The algorithm then employs a nonlinear observer to extract position and speed from the parameter estimates. To accommodate the requirements of the position estimation algorithm, a new PWM scheme achieving full voltage output (and, thus, speed) range is developed. The efficiency of the proposed excitation is also evaluated and compared with the efficiency of the standard algorithms. The resulting position and speed estimation algorithm is tested in laboratory experiments in closed loop with a two-loop proportional-plus-integral (PI) controller, and the results show good performance in a wide range of motor speeds and load torques. II.
MODEL OF A PMSM WITH ROTOR SALIENCY
As a result of the rotor geometrical saliency and nonuniform motor steel saturation, stator inductances depend on the rotor position. In general, stationary frame inductances have dc and all even higher harmonics in [14]. However, the harmonic magnitudes decay rapidly with increasing harmonic number, so the usual approximation is to keep only the dc and second harmonic components. The resulting stator inductance matrix in is then of the following form: stationary frame (1) , and with subsystem model is now given with
. The electrical
(2)
are the vectors of voltages, currents, and where , , and is the matrix magnet fluxes, respectively, of stator phase resistances, and is the effective resistance materm as well since trix which contains the inductance matrix (1) is not constant. The torque produced by the motor comprises reluctance and mutual components (the cogging torque ripple is neglected), and it is given with (3) where is the number of pole pairs. The mutual torque ripple components are also often neglected, and the rotor magnet flux back-EMF constant can then be expressed in terms of the as . The mechanical behavior of the motor is modeled with the viscous friction and inertia yielding the following model of the mechanical subsystem:
(4) where and are the moment of inertia and the friction constant (both normalized with ), and is the load torque. The
Fig. 1.
Current and voltage waveforms in one PWM period.
position and angular velocity dians and rad/sec, respectively.
are measured in electrical ra-
III. POSITION ESTIMATION ALGORITHM The electrical subsystem model (2), with (1), is the basis for the position information extraction from the voltage and current measurements. In this model, mechanical state variables enter as parameters in the inductance and effective resistance matrices. Position estimation algorithms based on magnetic saliency rely on the fact that the changes in the mechanical variables are much slower than the changes in the electrical ones. Thus, the electrical transients are used to determine the approximately constant parameters of the above system, yielding the information about the mechanical state. A. Parameter Estimation Approach model of a salient PM synchronous motor The complete is given in the previous section. At the PWM frequencies, however, it is reasonable to assume that the resistive term (and, thus, parameters of ) has negligible effect, compared to the inductive term. This can be shown more rigorously using the numerical procedure described in [15], involving Jacobian analysis of the least-squares parameter estimation problem that results from the complete model. The simplified electrical subsystem model then becomes (5) For the discretization of the above system, current and voltage behavior in one PWM period shown in Fig. 1 will ), a be used. Namely, in each PWM subinterval ( , is supplied to the system, and the constant voltage vector current vector changes approximately linearly. The currents are actually parts of exponentials, but the time constants of the electrical subsystem are typically much longer than the PWM period so the linear approximation is well justified. To describe linear changes in currents, it is sufficient to sample them at the
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of these requirements (e.g., when commanded voltage vector is zero, only , are used), and to overcome this problem we propose a modification of the PWM algorithm, which will be presented in Section IV. B. Implementation Simplification The above procedure involves several matrix multiplications and a matrix inversion on every PWM step.1 Note, however, that a computationally less-intensive procedure can be achieved by , and that has the noting that (6) implies , form (1) with parameters , . With such parameterization, (6) can be rewritten as
Fig. 2. Sector numbering, inverter voltage vectors (V ), and desired average voltage vector ( ).
v
subinterval boundaries [11]. With such current sampling, the , ) interval and division by integration of (5) over the ( this interval duration yields
where , and is a number of subintervals in one PWM period. Under the assumption that mechanical variables are approximately constant during one PWM period, the combination of the above equations from two subsequent subintervals eliminates the back-EMF term, yielding (6)
latter equations in one PWM period can be combined and to determine the position-dependent parameters. To this end, notice that the inductance matrix (1) can be parameterized with , and only three parameters equations (6) become
for . Combination (“stacking”) of those equa, where is a tions yields overdetermined system matrix containing current slope measurements, -dimensional vector containing voltage difand is a ferences. The parameter estimates can then be calculated as a . linear least-squares solution [16]: To obtain reliable estimates of inductance parameters, we need to acquire at least two linearly independent equations (6) in each PWM period. It can be shown [17] that this is equivalent to the requirement that the PWM pattern consists of at least three voltage vectors not all lying on the same line (e.g., , , in Fig. 2 are suitable, while , , are not). In addition, to ensure well conditioning of the problem, current differences must dominate the measurement noise, and thus inverter voltage vector durations must be bounded from below. The standard space-vector PWM (SVPWM) [18] does not always satisfy both
for , and the solution of the corresponding least-squares problem now yields parameter estimates as (7) is a matrix containing voltage values, where -dimensional vector containing current slope and is a measurements. can be calculated and stored ofNotice that the matrix fline since it consists of inverter voltage vector values which are determined by a particular PWM pattern and are, thus, known a priori. The real-time parameter estimation procedure in this case reduces only to a matrix-vector multiplication, thus greatly simplifying the practical algorithm implementation. As an illustration, the parameter estimation (7) in the experiments presented in Section V-C requires a total of only 30 multiply–accumulate operations (i.e., 30 digital signal processor (DSP) clock cycles). C. Mechanical State Observer To extract position from inductance parameters in without the need for inverse trigonometric functions, and to reduce the measurement noise, a nonlinear observer of mechanical variables is designed. The approach is similar to that of [19]. The key difference is the introduction of an additional (third) state to reduce the estimation errors during motor transients, which were reported in [19]. The proposed observer has the following form:
where , , and are the estimates of mechanical variables, and is a nonlinear observation error that is used to drive variable estimates to their true values. The error is derived from positionand dependent inductance parameter estimates as
1The actual implementation of such parameter estimation would use the method of normal equations to find the least-squares solution. This method involves computation of Cholesky factorization of and solution of two triangular systems of equations.
C C
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with . The design parameters are chosen to set the poles of the linearized estimation error system to the desired values. The desired poles are selected negative enough to ensure rapid convergence of state estimates that will not affect the dynamics of the rest of the system (i.e., the motor with current and speed controllers). IV. DESIGN
FULL-OUTPUT SIX-VECTOR PWM ALGORITHM
OF THE
Given the components of a desired voltage vector ( ) that a PWM algorithm has to produce, inverter voltage vector duty can be determined from the following three scalar ratios equations: (8) are inverter voltage vectors shown in Fig. 2 (with ). The system (8) consists of three equations with seven unknowns and is thus underdetermined, i.e., has infinitely many solutions. Besides the standard SVPWM solution, another possible approach to this problem is to select the minimum 2-norm solution [11]. While this approach overcomes redundancy in the PWM design, it does not fully exploit the available degrees of freedom. In the following, we will use the redundancy in the PWM pattern design to maximize the voltage output, in addition to accommodating the parameter estimation algorithm requirements. To this end, we propose a PWM scheme with standard sector distribution (shown in Fig. 2) that uses all six nonzero vectors in each PWM period. Since according to (8) linear combinations of inverter vector duty ratios have to be equal to the desired voltage vector and components, we postulate a linear dependence of on those two quantities
where
Some of the unknown constants are determined using (8) and the additional requirement of smooth operation (i.e., continuous change of duty ratios) on sector boundaries, and the remaining redundancy is used to maximize the voltage output achievable by the PWM pattern. The resulting six-vector PWM algorithm has the following duty ratios:
For a desired vector in sector, the above duty ratio forcounmulas are calculated with rotated by terclockwise, and such duty ratios correspond to the inverter rotated by clockwise. voltage vectors This PWM algorithm does not use zero inverter voltage vectors ( , ), but it is still capable of producing the full range of voltages (i.e., all the vectors inside the hexagon in Fig. 2), as the
Fig. 3. Typical phase terminal voltage waveforms in the modified PWM pattern.
standard SVPWM algorithms. In addition, this algorithm satisfies the parameter estimation requirements (e.g., at zero desired voltage, all nonzero voltage vectors are applied for the same and, thus, the singularity of the estimation time problem is avoided). It is interesting to note that the above duty ratios can be rewritten in terms of the duty ratios in the conventional SVPWM scheme as
where , , and are duty ratios of lag, lead, and zero inverter vectors, respectively. Therefore, the proposed six-vector PWM algorithm can be viewed as a modification of the standard PWM algorithm in which all six vectors are used to produce the missing zero vectors. V. EXPERIMENTS AND PRACTICAL ISSUES A. Efficiency of the Modified Excitation In addition to the proper generation of the commanded average voltage, a PWM pattern has to satisfy several performance criteria to be useful in practical applications [18]. The first of them is the amount of losses produced in the semiconductor components during the course of their operation. Since the PWM current ripple averages to zero (by definition), conduction losses are approximately the same in both standard and modified PWM patterns, and are equal to the conduction losses due to the fundamental component. In addition, subinterval voltage vectors in the modified PWM scheme are ordered so that the number of voltage transitions in a PWM period is equal in both schemes (see Fig. 3 for the phase terminal voltage waveforms in the modified PWM algorithm) and, thus, the switching losses in both schemes are approximately the same as well.
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Fig. 4. Dependence of the normalized rms squared current ripple on the normalized desired voltage magnitude m and angle in the first sector for the modified six-vector SVPWM algorithm.
Fig. 5. Dependence of the normalized rms squared current ripple on the normalized desired voltage magnitude m and angle in the first sector for the conventional SVPWM algorithm.
Another important figure of merit of a PWM scheme is the rms value of the current harmonics it produces in addition to the fundamental. This value accounts for the copper losses introduced to the motor drive system due to the switching nature of the stator voltages. Although some of the voltage harmonic content is filtered by the low-pass characteristic of the stator phase impedance, a considerable amount of harmonics still appears in the stator currents. The closed-form analytic expressions for normalized current ripple can be calculated for different PWM patterns [20]. We derived [17] those expressions for the modified and conventional PWM patterns and the resulting ripple dependences on the normalized desired voltage magniand angle in the first sector are plotted in tude Figs. 4 and 5.2 As the plots show, the modified PWM pattern has more copper losses than the standard one. This was expected because the pattern was designed to emphasize current ripple to satisfy the requirements of the parameter estimation algorithm. Since the modified excitation provides both motor drive and sufficient excitation for parameter estimation, the comparison with copper losses in the system with a standard position estimation scheme is more appropriate. In the following, we will compare the proposed estimation algorithm with the modified PWM excitation to the standard injection scheme with the conventional SVPWM excitation in terms of the copper loss performance. The magnitude of the injection current was selected as 3.6% of the rated current of the motor used in experiments.3 The experimental setup presented in Section V-B contains a mH which is driven by an PMSM with inductance V. With such system inverter supplied with voltage parameters, the square rms values of the additional current com-
ponents for the two algorithms are given in Table I for several , , and are PWM frequencies. In this table the total rms values (i.e., composites of the rms values from all three phases) of the fundamental, injection, and current-ripple components, respectively, calculated over the corresponding periods.4 The values relative to the fundamental component at nominal current are also given in the table. From the values shown in Table I, we can see that the sein this example achieves approximately lection of the same copper losses in both estimation schemes. Although produces more the modified PWM scheme with losses, we have used this value in the following experiments in order to achieve a wider speed range where the position estimation algorithm operates well. Namely, the increase in the PWM frequency increases the detrimental effects of the dead time and switch voltage drops, especially at higher speeds (desired voltages) when certain inverter voltage vector durations are short. was found to be a good compromise The selection between the admissible copper losses and good algorithm performance in a wide speed range. Even though the copper losses are higher, a relative contribution to the total losses is still low (0.53% of the total losses at the rated fundamental current), and can be tolerated.
= p
2The relationship between m and the modulation index M defined in triangle comparison PWM algorithms is: m ( 3=2)M ; v is the maximum magnitude of sinusoidal voltage that can be produced by an SVPWM without overmodulation. 3To achieve satisfactory quantization error levels this value was selected such that the injection signal occupies 6 bits of the total A/D conversion range in our experimental setup.
B. Experimental Setup The proposed position estimation algorithm was implemented and tested on a laboratory test bed built around a DS1103 controller board (made by dSPACE). The schematic diagram of the experimental setup is given in Fig. 6. The test stand consists of a 2-hp Kollmorgen Goldline XT motor (model MT306B, with parameters given in Table II), DS1103 controller DSP board, interface electronics, three-phase voltage-source inverter (consisting of six insulated gate bipolar transistors (IGBTs) and gate drivers integrated in a Mitsubishi 4To produce a number suitable for comparison, I~ functions were averaged over the PWM sector (i.e., both over ' and m ) for both modified and standard PWM patterns.
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TABLE I COPPER LOSS COMPARISON FOR DIFFERENT EXCITATION METHODS AND FREQUENCIES
Fig. 7. Block diagram of the motion control system. Fig. 6.
Schematic diagram of the experimental setup. TABLE II MT306B MOTOR PARAMETERS
PM15CSJ060 intelligent power module) supplied from the 200-V programmable power supply, torquemeter and hysteretic load cell mechanically coupled with PMSM, LEM closed-loop Hall-effect current sensors, and an incremental encoder. Rotor position is measured with a two-channel quadrature output incremental encoder with index pulse and line drivers. Each channel produces 2048 pulses per revolution, and the use of the quadrature decoder/counter (contained in the DS1103) results in the position signal with resolution of rad. Motor speed is calculated from position measurements using a backward difference approximation. Although position and speed are measured, they are used only for comparison with the estimates. The motion of the PMSM is controlled by a nested-loop PI controller that uses measured currents and position and speed estimates as feedback. The main
processor in the DS1103 board (Motorola 604e PPC, floating point) is programmed to perform all processing functions in the control system. The system sampling period is set to s by the periodic interrupts of Timer A. The equations of the motion controller and the mechanical variables observer are discretized using a simple first-order Euler approximation and implemented in Timer A interrupt service routine. Timer B is used for aperiodic events associated with the PWM excitation generation, and its interrupt service routine implements the modified SVPWM algorithm of Section IV with frequency and a dead time of 2 s.5 The DS1103 also houses an analog-to-digital (A/D) conversion subsystem including 16- and 12-bit A/D converters. The 12-bit 0.8- s SAR-type A/D converters are used in the discretization of the current feedback signals provided by the Halleffect sensors (currents are measured in two phases only since the motor is Y connected). Phase currents are sampled times in one PWM interval, as described in Section III-A. Sampling occurs right before the voltage transition to avoid the switching noise in measurements. Current samples acquired in this way are then used in the position-estimation algorithm of Section III to produce position and speed estimates. In addition, the samples are used to find the current average values as
5Note that the on-board slave processor (TMS320F240, fixed point) has built-in functions that can generate several standard PWM excitations. This feature was not used in the implementation since our method uses an alternative PWM algorithm for motor excitation.
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Fig. 8. Dynamical response of the motor drive system to several speed reference steps. On the left from top to bottom: actual position, position estimate, and position estimation error. On the right from top to bottom: actual speed, speed estimate, q -axis current, and d-axis current.
which are then fed back to the controller together with the estimates of the mechanical variables. Control is performed in dq frame and estimated position is used for transformation between and frames. The forward transformation is performed to correct for the delays introwith duced to the system by processing of feedback signals, calculation of control action, and nature of the motor excitation [21]. The block diagram of the motion control system is shown in Fig. 7. For easier controller implementation, is set to zero. C. Experimental Results Several experimental tests were performed to verify the transient and steady state behavior of the position estimation algo, rithm. The observer poles were selected as , and the bandwidths of the current and speed closed loops were set to 400 and 30 rad/s, respectively. The dynamical behavior of the closed-loop system in response to several speed reference steps is given in Fig. 8, while Fig. 9 shows the system s response to two torque steps (zero to the rated torque at s). Steady-state position estiand rated torque to zero at mation errors are shown in Figs. 10 and 11 for the full range of speeds and load torques achievable with the experimental motor drive system. As the displayed results show, the proposed algorithm provides accurate speed and position estimates for the closed-loop control in a wide speed range. Motor speed is correctly controlled to both low and high values. The transient position estimation error is determined by the observer design parameters rad electrical for all acceland is kept within erations up to the maximum allowable for the PMSM under test. The steady-state position estimation error is kept within rad electrical even under the worst operating conditions (low speed and high torque). Note also that, even and change at elevated though inductance parameters
Fig. 9. Closed-loop system response to load torque steps. From top to bottom: speed estimate (solid) and speed reference (dash-dotted), position estimation error, q -axis current, and d-axis current.
phase currents (i.e., motor torques) due to magnetic saturation, the position estimation is not affected by parameter variation due to fast dynamics of parameter estimator and mechanical state observer. Most of the high-frequency noise in current measurements is filtered with the observer and does not appear in the mechanical variable estimates. The remaining oscillatory error in the estimates is due to the unmodeled phenomena such as hysteresis and nonlinear characteristic of the motor magnetic materials, and higher harmonics in the inductance (1). This position-de-
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Fig. 10.
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Steady-state position estimation error in the full range of motor speeds.
Fig. 11. Steady-state position estimation error at motor speeds ! to the rated).
= 25 rad/s (on the left) and ! = 12:5 rad/s (on the right) for various load torques (from zero
pendent estimation error is also partially filtered by the observer, but only at medium speeds when the frequency of oscillations increases enough (as can be seen in Fig. 10). At very high speeds (voltages), however, the durations of several PWM subintervals become very small, and the estimation error starts increasing again due to the dead-time and switch voltage drop effects. At the highest speed in Fig. 10, normalized input voltage magni, which is the limit for satisfactory algotude is rithm performance in our setup. We should also point out that, since the speed estimate is used as a feedback, the oscillations in this signal limit the achievable bandwidth of the mechanical closed loop system (as can be seen from the speed loop bandwidth used in the presented experiments). VI. CONCLUSION This paper has presented a position- and speed-estimation algorithm for PMSMs with magnetic saliency. The algorithm re-
lies on the least-squares estimation of position dependent inductance parameters using voltage and current behavior within one PWM period. Position and speed are then extracted from parameter estimates using a three-state nonlinear observer. A novel PWM algorithm achieving full voltage (speed) range was developed to aid the position estimation. The performed analysis shows that, although the modified PWM scheme has more current ripple than the conventional SVPWM, the losses in the system with the modified excitation are comparable to the losses in the standard position-sensorless motor drive. In addition, this analysis confirms that the additional losses are inherent to all saliency-based algorithms as a consequence of additional harmonics introduced to the motor drive system in order to determine its electrical parameters. The proposed algorithm was implemented and evaluated in laboratory tests. The experimental results verify good steady-state and transient performance of the position estimation algorithm in the full range of the motor speeds and load
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torques, demonstrate practical use of the proposed estimation algorithm in a position sensorless motor drive, and point out the dependence of estimation accuracy on modeling assumptions and quality of current feedback. REFERENCES [1] R. B. Sepe and J. H. Lang, “Real-time observer-based (adaptive) control of a permanent-magnet synchronous motor without mechanical sensors,” IEEE Trans. Ind. Applicat., vol. 28, pp. 1345–1352, Nov./Dec. 1992. [2] S. Bolognani, R. Oboe, and M. Zigliotto, “Sensorless full-digital PMSM drive with EKF estimation of speed and rotor position,” IEEE Trans. Ind. Electron., vol. 46, pp. 184–191, Feb. 1999. [3] J.-S. Kim and S.-K. Sul, “New approach for high-performance PMSM drives without rotational position sensors,” IEEE Trans. Power Electron., vol. 12, pp. 904–911, Sept. 1997. [4] K. R. Shouse and D. G. Taylor, “Sensorless velocity control of permanent-magnet synchronous motors,” IEEE Trans. Contr. Syst. Technol., vol. 6, pp. 313–324, May 1998. [5] M. J. Corley and R. D. Lorenz, “Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds,” IEEE Trans. Ind. Applicat., vol. 34, pp. 784–789, July/Aug. 1998. [6] P. L. Jansen and R. D. Lorenz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Applicat., vol. 31, pp. 240–247, Mar./Apr. 1995. [7] J.-M. Kim, S.-J. Kang, and S.-K. Sul, “Vector control of interior permanent magnet synchronous motor without shaft sensor,” in Conf. Proc. IEEE APEC’97, vol. 2, Atlanta, GA, Feb. 1997, pp. 743–748. [8] S. Östlund and M. Brokemper, “Sensorless rotor-position detection from zero to rated speed for an integrated PM synchronous motor drive,” IEEE Trans. Ind. Applicat., vol. 32, pp. 1158–1165, Sept./Oct. 1998. [9] T. Aihara, A. Toba, T. Yanase, A. Mashimo, and K. Endo, “Sensorless torque control of salient-pole synchronous motor at zero-speed operation,” IEEE Trans. Power Electron., vol. 14, pp. 202–208, Jan. 1999. [10] M. Schroedl and P. Weinmeier, “Sensorless control of reluctance machines at arbitrary operating conditions including standstill,” IEEE Trans. Power Electron., vol. 9, pp. 225–231, Mar. 1994. [11] S. Ogasawara and H. Akagi, “Rotor position estimation based on magnetic saliency of an IPM motor,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, St. Louis, MO, Oct. 1998, pp. 460–466. [12] S. Ogasawara and H. Akagi, “Implementation and position control performance of a position-sensorless IPM motor drive system based on magnetic saliency,” IEEE Trans. Ind. Applicat., vol. 34, pp. 806–812, July/Aug. 1998. [13] C. Wang and L. Xu, “A novel approach for sensorless control of PM machines down to zero speed without signal injection or special PWM technique,” in Proc. IEEE APEC’01, vol. 2, Anaheim, CA, Mar. 2001, pp. 857–864. [14] V. Petrovic´ and A. M. Stankovic´, “Modeling of PM synchronous motors for control and estimation tasks,” in Proc. IEEE CDC, vol. 3, Orlando, FL, Dec. 2001, pp. 2229–2234. [15] M. Burth, G. C. Verghese, and M. Vélez-Reyes, “Subset selection for improved parameter estimation in on-line identification of a synchronous generator,” IEEE Trans. Power Syst., vol. 14, pp. 218–225, Feb. 1999. [16] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996. [17] V. Petrovic´, “Saliency-based position estimation in permanent magnet synchronous motors,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Northeastern Univ., Boston, MA, 2001. [18] J. Holtz, “Pulse width modulation for electronic power conversion,” in Power Electronics and Variable Frequency Drives, B. K. Bose, Ed. Piscataway, NJ: IEEE Press, 1997. [19] L. Harnefors and H. -P. Nee, “A general algorithm for speed and position estimation of AC motors,” IEEE Trans. Ind. Electron., vol. 47, pp. 77–83, Feb. 2000. [20] V. Blaˇsko, “Analysis of a hybrid PWM based on modified space-vector and triangle-comparison methods,” IEEE Trans. Ind. Applicat., vol. 33, pp. 756–764, May/June 1997.
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[21] V. Blaˇsko, V. Kaura, and W. Niewiadomski, “Sampling of discontinuous voltage and current signals in electrical drives – A system approach,” IEEE Trans. Ind. Applicat., vol. 34, pp. 1123–1130, Sept./Oct. 1998.
Vladan Petrovic´ (M’03) was born in Novi Sad, Yugoslavia, in 1972. He received the Dipl. Ing. degree in electrical engineering from the University of Novi Sad, Novi Sad, Yugoslavia, in 1996, and the M.S. and Ph.D. degrees in electrical engineering from Northeastern University, Boston, MA, in 1998 and 2001, respectively. His M.S. thesis was on torque ripple modeling and minimization, and his Ph.D. dissertation was on position estimation in PM synchronous motors, both advised by Prof. A. M. Stankovic. At Northeastern University, he also worked on nonlinear control of electric motor drives. His research interests are in control theory and digital signal processing applications to motor drives and power electronics. He is currently a DSP Engineer with Aware, Inc., Bedford, MA.
Aleksandar M. Stankovic´ (S’88–M’93–SM’02) received the Dipl. Ing. and M.S. degrees from the University of Belgrade, Belgrade, Yugoslavia, in 1982 and 1986, respectively, and the Ph.D. degree from Massachusetts Institute of Technology, Cambridge, in 1993, all in electrical engineering. Since 1993, he has been with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, where he is currently a Professor. He spent the 1999–2000 school year on sabbatical at the United Technologies Research Center. His research interests are in modeling, analysis, estimation and control of power electronic converters, electric drives, and power systems. Dr. Stankovic´ is active in the IEEE Industry Applications, IEEE Circuits and Systems, IEEE Power Electronics, IEEE Power Engineering, IEEE Control Systems, and IEEE Industrial Electronics Societies. He serves as an Associate Editor of the IEEE TRANSACTIONS ON POWER SYSTEMS, and he served the IEEE TRANSACTIONS ON CONTROL SYSTEM TECHNOLOGY in the same capacity from 1997 to 2002.
Vladimir Blasko (M’89–SM’97) received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the University of Zagreb, Zagreb, Croatia, in 1976, 1982, and 1986, respectively. From 1976 to 1988, he was with the Electrotechnical Institute Rade Koncar, Zagreb, Croatia, in the Power Electronics and Automatic Control Department. From 1989 to 1992, he was with the Research and Development Center of the Otis Elevator Company, Farmington, CT. From 1992 to 2000, he was with the Standard Drives Division of Rockwell Automation—Allen Bradley Company, Mequon, WI. He is currently with Otis Elevator Company, Farmington, CT. His work has been in the area of research, development, and design of high-power transistor choppers, drives for electrical vehicles, standard industrial and high-performance regenerative ac drives and low-harmonics regenerative three-phase converters. His primary areas of interest are ac drives, intelligent power management, power electronics, and applied modern control theory and technology. Dr. Blasko received the Prof. Dr. Vratislav Bednjanic Award for his Ph.D. dissertation in 1987. During the academic year 1988–1989, he was at the University of Wisconsin, Madison, as a recipient of an IREX scholarship.
