pulsating torque minimization techniques for permanent magnet ac motor drives-a review

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO. 2, APRIL 1996 321

Pulsating Torque Minimization Techniques for Permanent Magnet AC Motor Drives-A Review

Thomas M. Jahns, Fellow, IEEE, and Wen L. Soong, Member, IEEE

(Invited Paper)

Abstruct- Permanent magnet ac (PMAC) motor drives are finding expanded use in high-performance applications where torque smoothness is essential. This paper reviews a wide range of motor- and controller-based design techniques that have been described in the literature for minimizing the generation of cogging and ripple torques in both sinusoidal and trapezoidal PMAC motor drives. Sinusoidal PMAC drives generally show the greatest potential for pulsating torque minimization using well- known motor design techniques such as skewing and fractional slot pitch windings. In contrast, trapezoidal PMAC drives pose more difficult tradeoffs in both the motor and controller design which may require compromises in drive simplicity and cost to improve torque smoothness. Controller-based techniques for minimizing pulsating torque typically involve the use of active cancellation algorithms which depend on either accurate tuning or adaptive control schemes for effectiveness. In the end, successful suppression of pulsating torque ultimately relies on an orchestrated systems approach to all aspects of the PMAC machine and controller design which often requires a carefully selected combination of minimization techniques.

I. INTRODUCTION ORQUE smoothness is an essential requirement in a wide T range of high-performance motion control applications.

For example, the quality of the surface finish achievable with metal-working machine tools is directly dependent on the smoothness of the instantaneous torque delivered to the rotary tool-piece. Similarly, the performance specifications of servo motors imbedded in equipment ranging from robots to satellite trackers require minimization of all sources of pulsating torque. Even mass-produced consumer products such as electric-assisted power steering demand high levels of torque smoothness to meet user expectations.

A. Review of PMAC Motor Drive Types Permanent magnet ac (PMAC) synchronous motors are

appealing candidates for many high-performance applications such as those identified above because of their attractive characteristics in such key categories as power density, torque- to-inertia ratio, and electrical efficiency. There are two major classes of PMAC motor drives which can be charac- terized by the shapes of their respective back-EMF waveforms-sinusoidal and trapezoidal. Under idealized conditions, each of these two types of PMAC drives is capable of

Manuscript received July 11, 1995; revised November 30, 199.5. The authors are with the GE Corporate Research and Development,

Publisher Item Identifier S 0278-0046(96)02364-7. Schenectady, NY 12301 USA.

delivering perfectly smooth instantaneous torque waveforms. Only a few of the key relevant characteristics of these two types of PMAC motor drives will be briefly reviewed here, with interested readers referred to other sources [l], [2] for more comprehensive treatments.

Sinusoidal PMAC Drives: Sinusoidal PMAC motor drives share many of the basic characteristics of other classic types of polyphase ac machine drives. In particular, both the machine back-EMF and the current excitation waveforms are perfectly sinusoidal for ideally smooth torque generation, as sketched in Fig. l(a). Sinusoidal back-EMF waveforms require that the machine’s stator windings be sinusoidally distributed around the airgap and/or the radial magnetic flux density (B) amplitude generated by the rotor magnets vary sinusoidally along the airgap. Rotors for sinusoidal PMAC machines can be designed using either surface-mounted or buried (interior) magnet configurations, as sketched in Fig. 2.

Sinusoidal phase currents are typically developed using a current-regulated inverter that requires individual phase current sensors and a high-resolution rotor position sensor to maintain accurate synchronization of the excitation waveforms with the rotor angular position at every time instant. Any source of nonideal properties which causes either the phase

0278-0046/96$0.5.00 0 1996 IEEE

322 EEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO. 2, APRIL 1996

Fig. 2. Cross-sectional views of two major types of PMAC motor construction. (a) Surface-mounted magnets. (b) Buned (intenor) magnets. Solid black areas identify magnet positions.

currents or the back-EMF waveforms to diverge from their purely sinusoidal shapes will typically give rise to undesired pulsating torque components.

Trapezoidal PMAC Drives: Trapezoidal PMAC motor drives, also known as brushless dc drives, exhibit some notable distinctions from their sinusoidal counterparts. The machines are designed to develop trapezoidal back-EMF waveforms as sketched in Fig. l(b), with crest widths that should be as wide as possible (at least 120' elec. for three- phase machines) in order to meet the textbook conditions for smooth torque generation. Meeting this requirement tends to drive trapezoidal PMAC machines to use surface-magnet rotors and concentrated stator windings, in contrast to the distributed windings preferred in sinusoidal PMAC machines described above.

Excitation waveforms for three-phase trapezoidal PMAC machines take the form of quasisquare-wave (six-step) current waveforms with two 60" elec. intervals of zero-current excitation per cycle (see Fig. l(b)). The nature of the excitation waveforms for trapezoidal PMAC machines permits some important system simplifications compared to sinusoidal PMAC machines. In particular, the resolution requirements for the rotor position sensor are much lower with trapezoidal machines since only six commutation instants per electrical cycle must be sensed. In addition, the baseline trapezoidal PMAC machine drive only requires a single current sensor in the inverter dc link. Unfortunately, these simplifications leave the trapezoidal PMAC drives vulnerable to some mechanisms of pulsating torque generation which do not afflict their sinusoidal counterparts, as discussed in more detail in Section 111-c.

Pulsating Torque Definitions: Any source of divergence from ideal conditions in either the motor or associated power converter in a PMAC motor drive typically gives rise to undesired torque pulsations. However, there are various specific sources for these harmonic torque components, and the following terms have been adopted for use in this paper:

Cogging Torque-Pulsating torque components generated by the interaction of the rotor magnetic flux and angular variations in the stator magnetic reluctance. By definition, no stator excitation is involved in cogging torque production. Ripple Torque-Pulsating torque components generated by the interaction of stator current magnetomotive forces

( d s ) and rotor electromagnetic properties, which can take two forms: a) Mutual or Alignment Torque-resulting from the

interaction of the current mmf's with the rotor magnet flux distribution. This is the dominant torque production mechanism in most PMAC machines.

b) Reluctance Torque-resulting from the interaction of the current mmf's with the angular variation in the rotor magnetic reluctance. Surface-magnet PMAC machines generate almost no reluctance torque.

3) Pulsating Torque-the sum of the cogging and ripple ,

torque components.

B. Pulsating Torque Minimization Overview Given the importance of torque smoothness in many PMAC

motor drive applications, a wide variety of techniques have been proposed during the past fifteen years for minimizing the generation of pulsating torque components. Broadly speaking, these techniques fall into two major categories. The first major class consists of techniques for adjusting the PMAC machine design to cause it to more closely approach its ideal characteristics for achieving smooth torque production, whether the machine be trapezoidal or sinusoidal in nature. Accordingly, these technique tend to address the fundamental eIectromagnetic sources of the pulsating torque and adjust the design in such a way to drive it toward the ideal. These motor-based techniques are reviewed in Section I1 of this paper.

The second major class of techniques for minimizing pulsating torque are based on active control schemes which modify the excitation to correct for any of the nonideal characteristics of the machine or its associated power inverter. Many of these techniques involve active cancellation of the pulsating torque components which would otherwise be generated using the classic sinusoidal or square-wave current excitation waveforms. The effectiveness of these techniques relies on preknowledge of the individual machine's design parameters or the use of self-tuning mechanisms to adapt to the machine's torque production characteristics. Section I11 is devoted to reviewing a wide range of these reported control-based techniques.

11. MOTOR DESIGN TECHNIQUES FOR PULSATING TORQUE MINIMIZATION

The most effective means to minimize pulsating torque in sinusoidal and trapezoidal PMAC drives is by proper motor design. Methods such as skewing and fractional slot- pitch windings have been traditionally used for this purpose. This section examines these and other design techniques for minimizing pulsating torque available to the motor designer. It is assumed that the motor drive is operating at low speed and that ideal sinusoidal or rectangular converter waveforms are available. The effects of controller imperfections on the pulsating torque as well as its application to minimize motor imperfections are examined in Section 111.

A. Motor Types and Designs There is inherently a trade-off in PMAC machine design

between obtaining maximum average torque, minimum cog-

JAHNS AND SOONG. PULSATING TORQUE MINIMIZATION TECHNIQUES POK I'hKMANhN I MACTNCI AL MUIUK UKIVGS-A KGVIDW JLJ

ging torque and minimum ripple torque. For sinusoidal PMAC machines, both cogging and ripple torques can be minimized with some reduction in the average torque. For trapezoidal PMAC machines it is difficult to obtain both low cogging torque and low ripple torque simultaneously due to their conflicting requirements in this type of machine.

Some of the techniques to minimize the effect of pulsating torque such as using dummy slots do not attempt to eliminate it but rather increase its frequency, decrease its amplitude and so make it less objectionable. For applications where accurate speed control of inertial loads is required, both these effects help reduce the resultant speed fluctuations.

Another important issue when examining techniques for reducing pulsating torque is the sensitivity to manufacturing tolerances. Techniques which require high accuracy of as- sembly, magnetization, magnet placement or dimensions may prove to be impractical for low-cost high volume production.

B. Skewing One of the most popular techniques to reduce pulsating

torque is to skew the stator lamination stack or rotor magnetization [3]-[8]. Skewing reduces the variation of reluctance seen by the rotor magnets and hence the cogging torque. The cogging torque varies approximately linearly from its peak with an unskewed rotor and stator to ideally zero with one slot pitch skewing. In practice, even with a full slot pitch skew, end-effects and rotor eccentricities result in a nonzero residual cogging torque of the order of one percent of rated torque.

Skewing also has the effect of improving the stator windings distribution and substantially reduces higher order back-EMF harmonics hence producing more sinusoidal back-EMF waveforms [4]. In sinusoidal PMAC machines this reduces the ripple torque; however for trapezoidal PMAC machines this smoothes the trapezoidal back-EMF waveform and hence may slightly increase the ripple torque [7].

Skewing is a simple, effective, and widely used technique but it does have its drawbacks. It results in some loss in average torque, a more complex stator construction and an increase in leakage inductance and stray losses. The reduction in average torque is generally a few percent for motors with a moderate number of slots per pole per phase. However for machines with low slot numbers, skewing by a full slot pitch can result in substantial average torque loss and other techniques must be used.

C. Stator Electrical Winding Types Winding Distribution: For sinusoidal PMAC machines the

stator winding is designed to reduce the back-EMF harmonics while maximizing the fundamental component to obtain the largest average torque. Using short-pitched windings is a well-known technique to reduce the high-order harmonics with some loss of average torque [9]. Fractional-slot pitch windings are applicable to machines with a low number of slots per pole per phase [ 101, [ 111 which are not amenable to skewing. As the number of slots is not integrally related to the number of poles, the cogging torque is of high frequency and low amplitude. Fractional-slot pitch windings also have good harmonic rejection but do show a significant reduction of the fundamental and thus a reduction of average torque.

For trapezoidal PMAC machines, concentrated full-pitched windings are desired in order to increase the width of the trapezoidal back-EMF plateau region (see Fig. l(b)). Ideally to produce smooth torque, the difference between the magnet arc and the stator winding phase band width must be equal or greater to 120" electrical [12]. Thus 180" magnet arcs are required with nonoverlapping phase belts of 60" electrical. Even under these circumstances a perfectly smooth torque cannot be obtained due to fringing.

Increasing the Number of Phases: Increasing the number of phases in a PMAC drive reduces the ripple torque in a similar fashion to increasing the number of commutator segments in dc commutator motors [13]. The main drawback is the consequent increase in the complexity of the drive electronics and wiring. Five and seven-phase trapezoidal PMAC machines [l], [11], [14] have been investigated and shown to give moderate values of torque ripple (of the order of 5 to 10%). For sinusoidal PMAC motors the use of high numbers of phases increases the ripple torque frequency and reduces its amplitude [9]. Odd phase numbers are preferred as they have similar ripple frequency and amplitude characteristics as an even phase number winding of twice the phase number.

Airgap Windings: An airgap winding eliminates the stator teeth and hence cogging torque [l], [15] at the loss of some average torque and efficiency. This approach has become practical with the availability of high energy rare-earth magnets. Motors with airgap windings generally have lower back- EMF harmonics due to the more uniform distribution of the stator windings and the more sinusoidal airgap flux density waveform in the wide airgap. This reduces the harmonic content of the back-EMF and hence decreases the ripple torque of sinusoidal machines. Airgap winding PMAC machines have found application in miniature axial-flux disk drive motors [ 11 and high-speed machine tools. They have also been proposed for direct drive robotics applications [ 151.

D. Rotor Magnetic Design

Airgap Flux Distribution: For minimum ripple torque the airgap flux density waveform of sinusoidal PMAC machines should be a sinewave while that for trapezoidal PMAC machines should be rectangular. Fig. 3 illustrates some of the rotor magnet configurations used to approximate these ideal flux distributions.

The most common types are arc-shaped magnets with parallel (Fig. 3(d)) and radial (Fig. 3(e)) magnetization. Parallel magnetization is most easily obtained in isotropic magnets though radial magnetization can be produced using anisotropic magnets [ 81. With two-pole motors, parallel magnetization produces a sinusoidal airgap flux distribution while radial magnetization produces a near-ideal rectangular distribution. The two flux distributions become more similar as the number of poles increase.

More rectangular flux distributions can be obtained by interleaving a higher energy magnet segment at the pole tips (Fig. 3(f)) to counteract the effects of leakage [16].

A more sinusoidal flux distribution can be obtained by using a thin magnetic retaining can on the rotor as shown in (Fig. 3(b)) to increase the magnet leakage at the pole tips [17].

324 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO. 2, APRIL 1996

More Sinusoidal More Trapezoidal Fig. 3. (c) Tapered. (d) Parallel. (e) Radial. (f) Interleaved.

Alternate means for obtaining sinewave and rectangular airgap flux distributions illustrated with four-pole motors. (a) Blocked. (b) Magnetic can.

This also serves to retain the magnets and decrease the effective magnetic airgap counteracting some of the loss of torque due to the extra magnet leakage flux. Other techniques include tapering the magnet poles and/or airgap using breadloaf style magnets (Fig. 3(c)) and constructing the magnet poles out of blocks with varying magnetization directions (Fig. 3(a)) [9].

Magnet Pole Arc Width and Positioning: Ripple torque is minimized in trapezoidal PMAC machines by choosing the pole arc to be as large as possible [12], however for sinusoidal PMAC machines a value of approximately 150" minimizes the 6th harmonic ripple torque [9].

Cogging torque can be minimized by an appropriate selection of the magnet arc. This is because the cogging torque is produced by the interaction of the ends of the magnet poles and the stator teeth [6]. The overall cogging torque is the sum of the forces at each of the magnet pole tips. Finite-element analysis has shown [4], [6], [18] that choosing the magnet arc as approximately ( k + 0.14) slot pitches where k is an integer, cancels the first harmonic of the ripple torque.

Another means for reducing cogging torque is by shifting one pair of magnet poles with respect to the other [4], [6], [l8]. As the cogging torque is produced by the magnet ends, shifting one set of magnets by 1/4 slot pitch for example should cancel out the second harmonic of ripple torque. Using finite-element analysis [6] it has been shown that cogging torque of a fraction of one percent of rated torque should be achievable using a combination of magnet arc selection and pole shifting. These techniques show promising results though experimental validation and the analysis of the possible sensitivity to manufacturing tolerances is required.

Stepped Skewing of Magnet Blocks: If a skewed rotor magnetization is not practical then this can be approximated by an arrangement of magnets skewed axially in discrete steps [4]. This approach cancels all cogging torque harmonics except for multiples of the number of blocks. The effect on the back- EMF voltage fundamental and harmonic components are the same as for continuously skewing magnetization except for harmonics which are multiples of the number of blocks.

Practical Implementation: An extensive comparison of the relative merits of skewing the rotor magnets in blocks, alter- nately shifting poles, choosing magnet arcs and using different magnet arcs for different poles are examined in [4]. It is concluded that where possible for sinusoidal PMAC machines the use a full pitch skew on the stator and the use of 150" magnet arcs will lead to low cogging torque and good rejection

of the 5th and 7th back-EMF harmonics. If skewing of the stator is not desirable then appropriately choosing the rotor magnet arc and using pole-shifting may result in low pulsating torque.

E. Stator Magnetic Design Dummy Slots and Dummy Teeth: Skewing by one full slot

pitch in motors with low numbers of slots per pole per phase can lead to excessive reduction of the fundamental and high levels of leakage. An extreme example is for 2-pole motors with 3 slots. For such motors the use of dummy slots has been proposed [19], [20]. Fig. 4(a) shows a developed view of a conventional stator tooth design and Fig. 4(b) shows the addition of shallow auxiliary or dummy slots which magnetically mimic the actual slot openings. In the example shown the dummy slots increase the cogging torque frequency by a factor of three and reduce its amplitude correspondingly. Dummy teeth can also be utilized as shown in Fig. 4(c). Note that skewing the rotor by one dummy slot pitch would further reduce the cogging torque.

Other Techniques: Cogging torque is produced by the rotor magnets interacting with the stator slotting. This can be reduced by decreasing the stator slot openings [5] , using magnetic slot wedges or adjusting the slot opening [21] in a similar fashion to adjusting the magnet arc. The first two techniques however increase the leakage and reduce the average torque. A limitation on the smallest stator slot opening is caused by the requirement to insert the stator winding during manufacture. Distributing the stator slots in an irregular fashion may also allow the minimization of the cogging torque in a similar fashion to magnet shifting [22].

F. Summary of Motor Design Techniques

A broad range of alternative techniques have been discussed for minimizing the pulsating torque in PMAC motor drives. For sinusoidal PMAC drives, the traditional use of one slot pitch skewing of either the stator or the rotor magnetization and 150" magnet arcs will generally yield good results. For motors with a low slot numbers, fractional slot pitch windings and dummy slots are alternatives which should be considered. Other techniques include selection of the magnet arc and pole shifting.

For trapezoidal PMAC machines, full-pitched concentrated windings with magnet arcs as large as possible is recom-

JAHNS AND SOONG: PULSATING TORQUE MINIMIZATION TECHNIQUES FOR PERMANENT MAGNET AC MOTOR DRIVES-A REVIEW 325

(C)

Fig. 4. Concept of dummy slots and dummy teeth for cogging torque minimization. (a) Conventional configuration. (b) Dummy slots. (c) Dummy slots and teeth.

mended. Skewing can be used to reduce the cogging torque'at the cost of an increase in the ripple torque. Techniques such as using high numbers of phases, dummy slots and magnet arc shifting should also be considered.

111. CONTROL TECHNIQUES FOR PULSATING TORQUE MINIMIZATION

Despite the wide range of machine design techniques that are available for reducing cogging and ripple torque components, there are many occasions when they are not either sufficient or appropriate to achieve the required minimization of these parasitic torques during motor operation. For example, some special motion control applications such as antenna trackers may actually require that cogging torque be designed into the basic machine to provide detent load torque when the motor is de-energized, yet demand smooth torque production during tracking operation [23].

Fortunately, a second major approach has been developed for neutralizing these undesired pulsating torque components by actively controlling the excitation current waveforms to generate smooth output torque using various cancellation techniques. As reviewed in the following subsections, a variety of different techniques have been reported during the past fifteen years to address each of the major sources of pulsating torque in brushless PM machines- cogging, ripple, and commutation torques.

Current Reference Cunent-Regulated inverter Waveform Generator

Torque PMAC

Te' Machine

Current Feedback

Fig. 5 . Simplified block diagram of programmed current waveform control scheme for pulsating torque attentuation.

A. Programmed Current Wuvefom Control Introduction: One of the most popular approaches for ac-

tively controlling the cogging and ripple torques in a PMAC motor is to use programmed excitation waveforms for the phase currents to cancel the pulsating torque components. A simplified control block diagram which applies to many of these related techniques is shown in Fig. 5. As shown in this figure for a baseline 3-phase machine, the individual phase current command waveforms are programmed as predetermined functions of the torque command and angular position to generate the desired average torque while canceling the pulsating torque components.

This approach assumes that sufficient information is available a priori about the cogging and/or ripple torque characteristics of the specific PM machine to derive the necessary excitation current waveforms to achieve the desired cancellation. The resulting sensitivity of this approach to imperfect knowledge and variations in the motor parameters is one of the factors which must be considered when adopting this scheme, as discussed in more detail later in this section.

The impact of the preprogrammed current approach on sinusoidal PMAC motor drives is relatively modest since the baseline sinusoidal drive already requires that each of the phase currents be individually controlled as a function of torque command and rotor angle. In contrast, the impact of this scheme on the baseline trapezoidal PMAC motor drive is far more significant. The rudimentary rotor position sensors (often Hall sensors) which deliver the required commutation instant information six times per electrical cycle must now be replaced by an encoder or resolver to provide the necessary increased resolution in the rotor position feedback. Further- more, the single current sensor located in the dc current link of the baseline trapezoidal drive typically requires replacement by multiple current sensors to sense each of the individual phase currents. As a result, the net costkomplexity penalties associated with adopting the preprogrammed current approach require more careful consideration for a trapezoidal PMAC machine drive than for its sinusoidal counterpart.

Selected Hurmonic Injection Techniques: A significant variety of preprogrammed current algorithms have been proposed since the early 1980's for minimizing both cogging and ripple torque. One of the earliest of these techniques [24] that was proposed for trapezoidal PMAC drives calls for adjusting the crest width of the square- or trapezoidal-wave current excitation waveforms in order to minimize the pulsating torque. Unfortunately, delivery of the resulting optimized waveforms

326 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO 2, APRIL 1996

complicates the power electronics by requiring individual H- bridge inverters for each of the machine phases.

Subsequently, the majority of proposed algorithms have been based on shaping the individual phase current waveforms by injecting selected harmonic components to perform the desired pulsating torque cancellation. For example, one of the earliest schemes for three-phase PMAC machines [25] was designed to minimize the sixth and twelfth harmonic ripple torque components since these are typically the dominant components in the pulsating torque waveform. Predetermined values of fifth and seventh harmonic currents derived from measurements of the back-EMF waveform harmonic spectrum are added to the basic sinusoidal current commands in order to perform this cancellation.

One of the appealing features of the resulting “optimized” current waveforms for torque ripple elimination in surface- magnet (nonsalient) PMAC machines is that all of the harmonic current components scale in direct proportion to the fundamental due to the linearity of the machine’s basic torque equation. As a result, only the amplitudes of the phase current waveforms change as the torque command varies and not their waveshapes. This linearity characteristic simplifies the hardware implementations of such algorithms by making it possible to use familiar circuit techniques such as lookup tables to store the current waveshape data [26].

These selected current harmonic injection algorithms have evolved significantly during the past decade into more sophis- ticated forms. Whereas only four of the pulsating torque harmonics are cancelled using closed-form solutions as proposed by Pirou et al. [27], iterative calculations are employed by Favre et al. [ 131 to determine the necessary current harmonics to cancel several additional pulsating torque components. During the course of this latter work, the important observation is made that the current waveshapes for cancelling all pulsating torque components up to a given harmonic order 6n (where n is an integer) are not uniquely defined unless additional constraints are introduced.

More recent work [26], [28], [29] has generalized the harmonic injection approach by employing numerical op- timization techniques to calculate current waveshapes for eliminating all ripple and cogging torque components up to an arbitrarily high harmonic order. Recognizing the lack of solution uniqueness hoted above, an additional constraint of minimum ohmic winding losses (i.e., minimum i2R) is introduced in an attempt to maximize motor efficiency. Efforts are also made in these works to incorporate the current waveform constraints imposed by the associated inverters due to finite source voltage (limiting maximum dz ld t ’ s ) and wye motor connections (eliminating triplen current harmonics).

Back-EMF Inversion: An important alternative approach to calculating the optimized current waveforms for eliminating ripple torque comes from recognizing that the instantaneous torque contributed by each machine phase is proportional to the product of back-EMF and phase current. As a result, the optimized current can be derived as being proportional to the reciprocal of the back-EMF under the appropriate conditions. This approach makes it possible to avoid the need for performing any harmonic analyses of the flux or back-EMF waveforms.

Application of this technique to sinusoidal PMAC machines can be simplified by first transforming all of the key variables into the d-q synchronously rotating reference frame which has the benefit of automatically eliminating the fundamental frequency component from the back-EMF inversion process [30]. An alternate approach in the stationary reference frame [31] uses a special formulation of the reference current equations which is conveniently compatible with this inversion technique, using back-EMF waveforms which have been calculated by means of finite element analysis.

Application Considerations: Since all of these current harmonic injection techniques are based on open-loop cancellation concepts, the effectiveness of these algorithms in practical applications, including sensitivity to motor parameter variations, is a justifiable concern. Unfortunately, experimental verification of the proposed harmonic injection techniques is generally weak, and motor parameter sensitivity of these algorithms has received little attention in the literature to date. The limited empirical data which has been published suggests that it is difficult to reduce the PMAC machine’s pulsating torque amplitude below 1 % of the rated torque using these feedforward techniques, even with careful tuning in a laboratory environment [13], [23], [30], [32].

In addition to motor parameter sensitivities, major sources of residual pulsating torque when using these harmonic injection algorithms include machme and inverter imperfections such as unbalanced phase winding impedances, phase alignment errors, and mismatched current measurement gains [23], [33]. Each of these error sources contributes a pulsating torque component at twice the electrical frequency (2we) which is not compensated by the open-loop harmonic injection control algorithms. As a result, the residual 2w, pulsating torque component tends to be quite apparent in the measured instantaneous torque waveforms when using any of these open-loop techniques [13, 301.

B. Estimators and Observers

In view of the inherent limitations of feedforward control techniques described in the preceding section, some investigators have explored alternative approaches applying feedback control techniques to achieve the desired pulsating torque minimization. Various estimation and observer techniques for torque and flux have been proposed to generate the necessary feedback signals for suppressing the cogging and ripple torque components.

A block diagram illustrating the general class of torque estimator algorithms is provided in Fig. 6. Unfortunately, well-known difficulties associated with accurate estimation of instantaneous torque make it difficult to completely escape the negative effects of motor parameter variations and changes in motor operating point. For example, the developers of one torque estimation algorithm [34] point out that their estimator does not work well at low speeds where pulsating torque elimination is typically the most important. Another proposed torque estimation algorithm [35] operates well down to zero speed, but depends on advance knowledge of the machine’s harmonic torque coefficients which are subject to motor parameter variations. The authors in this latter case suggest an approach for updating the coefficient values


Voltage- or Current-Regulated

Inverter . iLor vA‘

ig or VB

L . *

Torque Command

PMAC ic or vc Machine

Position Sensor

Fig. 6. pulsating torque attenuation.

Simplified block diagram of torque estimator control scheme for

using an on-line recursive least-squares estimator [36], but the technique is computationally intensive and has not yet been reduced to practice.

Other published estimatiodobserver approaches incorporate the current harmonic injection technique discussed in the preceding section. One such approach [37] adopts a real-time harmonic flux estimator to calculate the sixth-harmonic current that must be injected to cancel the sixth- and twelfth-harmonic pulsating torque components rather than depending on stored coefficients. Unfortunately, the flux estimation algorithm still depends on pre-knowledge of the motor resistances and inductances, and no clear evidence is provided to quantify the extent of the remaining parameter sensitivities.

An alternative approach [38], [39] uses a Gopinath observer to estimate the machine torque in combination with a Fourier decomposition to determine the compensating current components that must be added to the baseline current commands to cancel the pulsating torque. Application of this observer algorithm requires speed and current feedback, in addition to pre-knowledge of the machine’s torque constant, KT, which may be sensitive to changes in motor temperature.

C. Commutation Torque Minimization

Introduction: Trapezoidal PMAC machine drives are subject to an additional source of ripple torque commonly known as commutation torque that does not afflict sinusoidal PMAC drives. The term commutation is used to identify this component because of its analogy with the torque ripple in dc motors caused by the transfer of armature current between adjacent commutator bars. More specifically, commutation torque in trapezoidal PMAC drives takes the form of torque spikes or dips which are generated at each discrete time instant when any of the square-wave current excitation waveforms change levels. This ripple torque is caused by the combination of nonzero phase inductances and finite inverter bus voltage which prevents the phase current excitation waveforms from changing levels instantaneously (i.e., d i / d t # ca), thereby invalidating one of the key simplifying assumptions used to describe the idealized operation of such drives.

In fact, it is the simplicity of the basic trapezoidal PMAC motor drive inverter control scheme that is responsible for causing the commutation torque ripple to develop. As sketched in Fig. 7, the basic trapezoidal PMAC drive inverter uses a

Inverter 0A 0B 0c

0 I T T T T T I +

Trapezoidal ( PMAC ) Machine

Fig. 7. Basic trapezoidal PMAC motor drive configuration. Arrow shows circulating current path immediately following phase A turn-off event.

single current sensor in the dc link to regulate the current flowing through two motor phases in series during each of the six sequential segments per electrical cycle [ 2 ] . This current regulation scheme works well except during the “commutation” intervals when the inverter link current is being shifted between adjacent motor phases. Current temporarily flows in all three motor phases simultaneously during these intervals until the current in the off-going phase decays to zero. The single current sensor present in the inverter dc link cannot simultaneously regulate all three phase currents during these transition intervals, and this temporary loss of complete current control gives rise to commutation torque ripple during each current transfer interval.

Fig. 8 shows an example of the three phase current waveforms along with the instantaneous torque waveform during low-speed operation when the phase current is being trans- ferred from phase A to phase B. A current spike temporarily develops in the phase C current waveform which the dc link current sensor cannot distinguish since it measures the sum of currents in phases C and A (the off-going phase) during this interval. As reported by various investigators [40], [41], the amplitudes of the resulting current and torque spikes can be quite significant during low-speed motoring and high- speed regenerative operation, reaching peak values nearly double the average link current and torque during regeneration. In a complementary fashion, significant commutation torque and current dips are developed during high-speed motoring operation, causing premature decays in the average motor torque at elevated speeds.

Attenuation Techniques Without Extra Current Sensors: Recognizing that the use of a single current sensor is one of the attractive features of trapezoidal PMAC motor drives from the standpoints of simplicity and cost reduction, several investigators have attacked the problem of attenuating commutation torque ripple without adding any new current sensors.

For example, Murai et al. [42] introduced two different techniques for reducing the effects of commutation torque dips at elevated motor speeds. Since torque dips are caused

325 EEE TRANSACTIONS ON INDUSTF3AL ELECTRONICS, VOL. 43, NO. 2, APRIL 1996

+‘O

0

-10

the origin of commutation torque ripples lies in the temporary loss of motor current regulation when using a single dc link current sensor, the introduction of independent current sensors in the motor phases provides a powerful approach for eliminating this torque ripple component. Unfortunately, this approach also eliminates one of the important sources of cost advantage for the trapezoidal PMAC motor drive over other types of ac motor drives. Part of the cost premium can be avoided by recognizing that only two sensors are necessary to extract all three phase currents in a wye-connected machine,

Te

iA

+ I I 1 but these two sensors must be galvanically isolated from each

iC I I I iC other, and, typically, from the rest of the controller hardware

I t -

I

I I

I

T I tumsoff, I T3turnson I

as well. Carlson et al. [40] demonstrate how the introduction of

direct phase current sensing can be used to eliminate commutation torque spikes during low-speed operation. The availability

by delays in building up current in the next on-going phase before the current in the off-going phase has decayed to zero, both techniques attempt to remedy this delay by giving the on-going phase a head start in its current build-up. To this end, the “overlapping” technique introduced by Murai turns on each new on-going phase an adjustable advance time before removing excitation from the off-going phase, replacing the torque dip with a compensating torque spikeldip combination.

The second torque dip attenuation technique described by Murai [42] introduces PWM excitation pulses during the intervals when each motor phase would normally be unexcited. This has the effect of allowing current to flow simultaneously in all three motor phases, allowing current to gradually build up in each sequential on-going motor phase during high- speed operation. While effective in reducing the speed ripple caused by commutation torque dips, both of these attenuation techniques suffer from the fact that they are open-loop in nature, requiring customized tuning for each set of machine parameters.

A related open-loop technique for attenuating commutation torque spikes during low-speed operation has been described by Cros et al. [43]. Recognizing that the commutation torque ideally disappears whenever the summed back-Em’s of two motor phases equals one-half the inverter bus voltage [40], the authors propose a PWM technique which temporarily suppresses the effective excitation voltage amplitude during commutation intervals in order to meet this voltage condi- tion. Although technically sound, this technique has limited usefulness in practice due to motor parameter sensitivities, as recognized by the authors themselves.

In contrast, Schulting et a1 [41] describe an alternate approach for attenuating commutation torque spikes at low operating speeds by introducing an auxiliary chopper control function which is only active during the commutation intervals. This chopper technique has the advantage of eliminating torque spikes using a single dc link current sensor without requiring special tuning for changes in motor parameters. However, this particular technique is not effective for attenuating commutation torque dips during high-speed operation.

along with the resulting torque spike. Elimination of commutation torque dips during high-speed

operation is somewhat more difficult to achieve, even with direct phase current sensing. Cros et al. [43] describe a promising approach which uses a special current regulation scheme at high speeds, causing current to flow in all three motor phases simultaneously. Unlike the open-loop PWM scheme [42] described above for use with a single dc link current sensor, this alternative closed-loop control technique takes advantage of complete phase current feedback information to eliminate the commutation torque dips without falling victim to motor parameter sensitivities.

D. Speed Loop Disturbance Rejection While all of the techniques described in the preceding

subsections seek to attenuate the pulsating torque by adjusting the current excitation waveforms to compensate the undesired torque components, an alternative approach relies on a surrounding closed-loop speed regulator to accomplish this attenuation. That is, the speed loop acts to attenuate any speed variations caused by the motor pulsating torque in the same way it responds to reject any other source of speed disturbance.

Assuming the availability of a high-quality rotor speed feedback signal, the effectiveness of this disturbance rejection technique is nevertheless limited to low motor speeds where the frequency of the pulsating torque falls within the bandwidth of the speed loop [12]. Since the dominant frequency component of the pulsating torque typically occurs at 6 times the fundamental frequency, the upper speed threshold for effectiveness of this technique is given by

where w, is the rotor speed in radls (mech.), wbw is the speed loop bandwidth in rads (elec.), and y is the number of machine pole pairs. The effectiveness of this approach for minimizing speed disturbances actually increases as the rotor speed is lowered below the speed threshold value given above, making this technique quite useful for applications where low-speed torque smoothness is most critical.


E. High-speed Current Regulator Saturation Since the back-EMF of any PMAC machine increases

linearly with speed, the current regulators saturate and lose their ability to perform their regulating function when the motor back-EMF approaches the inverter dc link voltage. The inverter reverts to its basic voltage-source operation under these conditions, exciting the PMAC machine with some variation of square-wave voltage excitation depending on the nature of the motor drive. In particular, the current regulators in sinusoidal PMAC drives saturate naturally to classic six- step voltage excitation in which each inverter switch is on for 180 elec. degrees per cycle. In contrast, trapezoidal PMAC current regulators saturate naturally into a different mode of quasisquare-wave voltage excitation in which each switch is on for only 120 elec. degrees per cycle, leaving one motor phase effectively open-circuited at each time instant.

These differences in saturated-regulator excitation modes are very important to the extended high-speed operating characteristics of PMAC machine drives. In particular, the torque- speed operating envelope of the trapezoidal PMAC motor drive tends to drop off quite abruptly at high speed due to the impact of 120’ excitation [ 121. Although the 120’-excitation torque-speed envelope can be expanded to higher speeds by advancing the excitation angle to achieve flux weakening, the resulting increase in pulsating torque is quite dramatic. In contrast, the torque-speed envelope associated with 180’ excitation is considerably more appealing, with a much smaller ratio of pulsating-to-average torque as the excitation angle is advanced at high operating speeds.

Recognizing this advantage of 180’ excitation over its 120’ counterpart during saturated-regulator operation, some investigators have proposed techniques for smoothly transitioning trapezoidal PMAC drives into the preferred 180” excitation mode at high operating speeds [44], [45]. In particular, the technique proposed by Fratta et al. [44] which gradually advances the turn-on angle at high rotor speeds while keeping the turn-off angle fixed provides an effective means for expanding

I the drive’s torque-speed envelope while keeping the pulsating torque amplitude within acceptable limits.

IV. CONCLUSIONS

This paper has reviewed the broad range of motor-based and control-based techniques which have been presented during the past fifteen years for minimizing the production of pulsating torque in PMAC machine drives. The following key observations can be drawn from this survey.

It is generally preferable to eliminate pulsating torque by improving the machine design whenever possible rather than depending on control-based techniques to cancel the undesired harmonic torque components. Sinusoidal PMAC machines are generally better suited than their trapezoidal counterparts for applications where torque smoothness is most critical. Sinusoidal PMAC machines lend themselves well to established ac machine design techniques such as slot skewing and fractional slot pitch windings for minimizing pulsating torque production.

In contrast, minimization of pulsating torque in trapezoidal PMAC machines often entails knotty tradeoffs between cogging torque and ripple torque production. Control-based techniques for minimizing pulsating torque generally involve use of active cancellation techniques which depend on accurate knowledge of machine parameters provided by either careful tuning or adaptive control. Trapezoidal PMAC drives are subject to commutation torque spikes and dips which often require additional sensors to correct, thereby eliminating some of the cost and simplicity advantages they otherwise enjoy over their sinusoidal counterparts.

In conclusion, the achievement of smooth torque production in PMAC machine drives is a demanding objective that requires painstaking attention to every aspect of machine and controller design. Despite the expanding number of techniques that have been reported to date for minimizing pulsating torque production, no universally effective solution has yet appeared for all applications. This is testimony to both the creativity of workers in this specialized field and to the difficulty of the underlying problem. There is every reason to believe that the search will continue.

REFERENCES

[l] J. R. Hendershot and T. J. E. Miller, “Design of brushless permanent- magnet motors,” Magna Physics and Oxford Science Publications, 1994.

[2] T. Jahns, “Motion control with permanent-magnet AC machines,” in IEEE Proc., vol. 82, no. 8, Aug. 1994, pp. 1241-1252.

[3] K. J. Binns, F. B. Chaaban, and A. A. K. Hameed, “Major design parameters of a solid canned motor with skewed magnets,” in IEE Proc., vol. 140, no. 3, May 1993, pp. 161-165.

[4] R. Carlson, A. Tavares, J. Bastos, and M. Lajoie-Mazenc, “Torque ripple attenuation in permanent magnet synchronous motors,” in Rec. IEEE Ind. Appl. Soc. Annu. Meet., 1989, pp. 57-62.

[5] M. Jug, B. Hribemik, A. Hamler, M. Trlep, and B. Kreca, “Investigation of reluctance torque of brushless DC motor,” in Proc. Int. Con$ Elec. Machines, 1990, pp. 132-137.

[6] T. Li and G. Slemon, “Reduction of cogging torque in permanent magnet motors,” IEEE Trans. Mugn., vol. 24, no. 6, pp. 2901-2903, Nov. 1988.

[7] J. De La Ree and N. Boules, “Torque production in permanent-magnet synchronous motors,” IEEE Trans. Ind. Applicat., vol. 25, no. 1, pp. 107-112, Jan./Feb. 1989.

[8] T. Sebastian and V. Gangla, “Analysis of induced EMF and torque waveforms in a brushless permanent magnet machine,” in Rec. IEEE Ind. Applicat. Soc. Annu. Meet., 1994, pp. 240-246.

[9] B. Nogarede and M. Lajoie-Mazenc, “Torque ripple minimization methods in sinusoidal fed synchronous permanent magnet machines,” in Proc. IEE Con$ Elec. Machines & Drives, Sept. 1991, pp. 41-45.

[lo] E. C. Andresen, J. Xie, and C. Topfer, “A shearing-wave generator for operation in deep bore holes,” IEEE Trans. Ind. Applicat., vol. 28, no. 2, pp. 434-440, Mar./Apr. 1992.

[ 111 C. Chan, J. Jiang, G. Chen, X. Wang, and K. Chau, “A novel polyphase multipole square-wave permanent magnet motor drive for electric ve- hicles,” IEEE Trans. Ind. Applicat., vol. 30, no. 5, pp. 1258-1266, Sept./Oct. 1994.

[ 121 T. Jahns, “Torque production in permanent-magnet synchronous motor dries with rectangular current excitation,” IEEE Trans. Ind. Applicat., vol. 20, no. 4, pp. 803-813, July/Aug. 1984.

1131 E. Favre, L. Cardoletti, and M. Jufer, “Permanent-magnet synchronous motors: a comprehensive approach to cogging torque suppression,”lEEE Trans. Ind. Applicat., vol. 29, no. 6, pp. 1141-1 149, Nov./Dec. 1993.

[14] H. R. Bolton and N. M. Mallinson, “Investigation into a class of brushless DC motor with quasisquare voltages and currents,” in IEE Proc., pt. B, vol. 133, no. 2, Mar. 1986, pp. 103-111.

[15] A. Kaddouri and H. Le-Huy, “Analysis and design of a slotless NdFeB permanent-magnet synchronous motor for direct drive,” in Rec. IEEE Ind. Applicat. Soc. Annu. Meet., 1992, pp. 271-278.

330 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO. 2, APRIL 1996

[16] G. H. Jang and D. K. Lieu, “Vibration reduction in electric machine by magnet interlacing,” IEEE Trans. Mag., vol. 28, no. 5, pp. 30263026, Sept. 1992.

[17] A. Miraoui, L. De Fang, and J. M. Kauffmann, “Performance analysis of permanent magnet brushless DC motor,” in Proc. IEE Con$ Elec. Machines & Drives, Oxford, Sept. 1993, pp. 371-375.

[18] T. Ishikawa and G. Slemon, “A method of reducing ripple torque in permanent magnet motors without skewing,” IEEE Trans. Mag., vol. 29, no. 2, pp. 2028-2031, Mar. 1993.

1191 M. Goto and K. Kobayashi, “An analysis of the cogging torque of a DC motor and a new technique of reducing the cogging torque,” Elec. Eng. Jpn., vol. 103, no. 5, pp. 113-120, 1983.

[20] K. Kobayashi and M. Goto, “A brushless DC motor of a new structure with reduced torque fluctuations,” Elec. Eng. Jpn., vol. 105, no. 3, pp. 104-112, 1985.

[21] B. Ackermann, J. Janssen, R. Sottek, and R. Van Steen, “New technique for reducing cogging torque in a class of bnkhless DC motors,” in IEE Proc., pt. B, vol. 139, no. 4, Jul. 1992, pp. 315-320.

[22] Z. Q. Zhu and D. Howe, “Analytical prediction of cogging torque in radial-field permanent magnet brushless motors,” IEEE Trans. Mag., vol. 28, no. 2, pp. 1371-1374, Mar. 1992.

[23] E. Favre, L. Cardoletti, E. von Siebenthal, and M. Jnfer, “Speed control of a constant torque brushless motor,” in Proc. Int. Con$ Elec. Machines, Manchester, U.K, Sept. 1992, pp. 828-832.

[24] H. Bolton and R. Ashen, “Influence of motor design and feed-current waveform on torque ripple in brushless dc drives,” in IEE Proc., vol. 131, pt. B, no. 3, May 1984, pp. 82-90.

[25] H. Le-Huy, R. Perret, and R. Feuillet, “Minimization of torque ripple in brushless DC motor drives,” IEEE Trans. Ind. Applicat., vol. 22, no. 4, pp. 748-755, July/Aug. 1986.

1261 J. Hung and Z. Ding, “Design of current to reduce torque ripple in brushless permanent magnet motors,” in IEE Proc., vol. 140, no. 4, July 1993, pp. 260-266.

[27] F. Piriou, A. Razek, R. Perret, and H. Le-Huy, “Torque characteristics of brushless DC motors with imposed current waveform,” Rec. IEEE Ind. Applicat. Soc. Annu. Meet., Denver, Sept. 1986, pp. 176-181.

[28] D. Hanselman, “Minimum torque ripple, maximum efficiency excitation of brushless permanent magnet motors,” IEEE Trans. Ind. Electron., vol. 41, no. 3, pp. 292-300, June 1994.

[29] C. Marchand and A. Razek, “Optimal torque operation of digitally controlled permanent magnet synchronous motor drives,” in IEE Proc.- B, vol. 140, no. 3, May 1993, pp. 232-240.

[30] B. ‘Brnusbach, G. Henneberger, and T. Klepsch, “Compensation of torque ripple,” in Proc. IEE Con$ Elec. Machines & Drives, Oxford, Sept. 1993, pp. 588-593.

[31] C. Clenet, Y. Lefevre, N. Sadowski, S. Astier, and M. Lajoie-Mazenc, “Compensation of permanent magnet motors torque ripple by means of current supply waveshapes control determined by finite element method,” IEEE Trans. Magn., vol. 29, no. 2, pp. 2019-2023, Mar. 1993.

[32] F. Colamartino, C. Marchand, and A. Razek, “Estimation and minimization of electromagnetic torque ripple in a buried permanent magnet synchronous motor,” in Proc. Int. Con$ Elec. Machines, Paris, 1994,

[33] D. Hanselman, J. Hung, and M. Keshura, “Torque ripple analysis in brushless permanent magnet motor drives,” in Proc. Int. Con$ Elec. Machines, Manchester, U.K., Sept. 1992, pp. 823-827.

[34] F. Colamartino, C. Marchand, and A. Razek, “Considerations of non- sinusoidal field distribution in a permanent magnet synchronous motor control,” in Proc. IEE Con$ Power Electron., Var.-Spd. Drives, Oct.

[35] T . 3 . Low, K.-J. Tseng,T.-H. Lee, K.-W. Lim, a n d K . 3 . Lock, “Strategy for the instantaneous torque control of permanent-magnet brushless DC drives,” in IEE Proc., vol. 137, pt. B, no. 6, Nov. 1990, pp. 355-363.

[36] T . 3 . Low, T.-H. Lee, K.-J. Tseng, and K.-S. Lock, “Servo performance of a BLDC drive with instantaneous torque control,” IEEE Trans. Ind. Applicat., vol. 28, no. 2, pp. 455462, Mar./Apr. 1992.

[371 K. Y. Cho, J. D. Bae, S. K. Chung, and M. J. Youn, “Torque harmonics minimization in permanent magnet synchronous motor with hack EMF estimation,” in IEE Proc. Elec. Power Applicat., vol. 141, no. 6, 1994,

pp. 715-719.

1994, pp. 508-513.

pp. 323-330.

[38] N. Matsui, T. Makino, and H. Satoh, “Auto-compensation of torque ripple of DD Motor by torque observer,” Rec. IEEE Ind. Applicat. Soc. Annu. Meet., Dearbom, MI, Sept. 1991, pp. 305-311.

1391 N. Matsui, “Autonomous torque ripple compensation of DD motor by torque observer,” in Proc. IEEE Asia-Pacijic Workshop, Advances in Motion Contr., 1993, pp. 19-24.

[40] R. Carlson, M. Lajoie-Mazenc, and J. dos S. Fagundes, “Analysis of torque ripple due to phase commutation in brushless DC machines,” in Rec. IEEE Ind. Applicat. Soc. Annu. Meet., Seattle, Oct. 1990, pp. 287-292.

[41] L. Schlting and H-C Skudelny, “A control method for permanent magnet synchronous motors with trapezoidal electromotive force,” in Proc. Eur. Con$ Power Electron.. Applicat. (EPE), Florence, 1991, vol. 4, pp. 117-122.

[42] Y. Mnrai, Y. Kawase, K. Ohashi, K. Nagatake, and K. Okuyama, “Torque ripple improvements for brnshless DC miniature motors,” IEEE Trans. Ind. Applicat., vol. 25, no. 3, pp. 441-450, May/June 1989.

[43] J. Cros, J. Vinassa, S. Clenet, S. Astier, and M. Lajoie-Mazenc, “A novel current control strategy in trapezoidal EMF actuators to minimize torque ripples due to phase commutations,” in Proc. Eur. Con$ Power Electron., Applicat. (EPE), Brighton, 1993, pp. 266-271.

[44] A. Fratta, A. Vagati, and F. Villata, “Extending the voltage saturated performance of a DC brushless drive,” in Proc: Eur. Con5 Power Electron., Applicaf. (EPE), Florence, 1991, vol. 4, pp. 134-138.

(451 G. Schaefer, “Field weakening of brushless permanent magnet servo- motors with rectangular current,” in Proc. Eur. Con$ Power Electron., Applicat. (EPE), Florence, 1991, vol. 3, pp. 429434.

Thomas M. Jahns (M’78-SM’91-F’93) received the S.B. and S.M. degrees in 1974 and the Ph.D. degree in 1978 from the Massachusetts Institute of Technology, Cambridge, MA, all in electrical engineering.

He joined GE Corporate Research and Develop- ment, Schenectady, NY, in 1983, where he has pur- sued new adjustable-speed motor drive technology in the Control Systems & Electronic Technologies Laboratory. His technical efforts have included development of high-performance permanent magnet

motor servo drives and high-power resonant converters for machine tools and aerospace applications. In 1986 he was appointed Manager of the Power Controls Program, leading efforts to develop advanced permanent magnet and switched reluctance motor drives for a variety of industrial, commercial, and aerospace applicatiofls. In his present position as Project Manager, he is Ieading R&D activities which have included low-cost permanent magnet motor drives for commercial/residential applications and high-power induction motor drives for industrial process applications.

Dr. Jahns has been an active member of the IEEE-IAS Industrial Drives Committee since 1978, including two years of service as Committee Chair during 1988-89. He is presently serving as President of the Power Electronics 1

Society and as an At-Large Member of the IAS Executive Board.

Wen L. Soong (S’89-M’9O-S’9O-M’93) was born in Kuala Lumpur, Malaysia, and received the B.Eng, degree from Adelaide University, Australia, in 1989, and the Ph.D degree from Glasgow Unlverslty, Scotland, in 1993.

He is an electncal engineer in the Power Controls Program at General Electric Corporate Research and Development in Scheuectady, NY His research interests include PM and reluctance motor design and modeling and magnetic bearmg design and control

pulsating torque minimization techniques for permanent magnet ac motor drives-a review

Documents