1408 ieee transactions on power …bingsen/files_publications/j-16_tpel.pdfmethods to obtain the...

1408 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 31, NO. 2, FEBRUARY 2016

Comparative Evaluation of Direct Torque ControlStrategies for Permanent Magnet

Synchronous MachinesFeng Niu, Student Member, IEEE, Bingsen Wang, Senior Member, IEEE, Andrew S. Babel, Member, IEEE,

Kui Li, and Elias G. Strangas, Member, IEEE

Abstract—This paper presents a comprehensive evaluation ofseveral direct torque control (DTC) strategies for permanent mag-net synchronous machines (PMSMs), namely DTC, model predic-tive DTC, and duty ratio modulated DTC. Moreover, field-orientedcontrol is also included in this study. The aforementioned con-trol strategies are reviewed and their control performances areanalyzed and compared. The comparison is carried out throughsimulation, finite-element analysis, and experimental results of aPMSM fed by a two-level voltage source inverter. With the intentto fully reveal the advantages and disadvantages of each controlstrategy, critical evaluation has been conducted on the basis of sev-eral criteria: Torque ripple, stator flux ripple, switching frequencyof inverter, steady-state control performance, dynamic response,machine losses, parameter sensitivity, algorithm complexity, andstator current total harmonic distortion.

Index Terms—Direct torque control (DTC), duty ratio modu-lation (DRM), model predictive direct torque control (MPDTC),permanent magnet synchronous machine (PMSM).

I. INTRODUCTION

S INCE direct torque control (DTC) was first proposed forinduction machines in the 1980s by Takahashi and Noguchi

[1] and Depenbrock [2], it has become a powerful and widelyadopted control strategy. DTC replaces the decoupling in field-oriented control (FOC) with the bang–bang control, which nat-urally fits the inherently discrete nature of switch-mode powerinverters. Numerous merits of DTC have attracted extensive re-search attention [3]–[8]. The application of DTC to permanentmagnet synchronous machines (PMSMs) was presented in late1990s [9]. Subsequently, DTC has been further applied to othertypes of machines in various applications, such as synchronous

Manuscript received February 14, 2014; revised April 30, 2014, December12, 2014, and February 17, 2015; accepted March 29, 2015. Date of publi-cation April 9, 2015; date of current version September 29, 2015. This workwas supported in part by the University Innovation Team Leader Program ofHebei Province under Grant LJRC003, in part by the National ScholarshipFund of China under Grant 201206700002, and in part by the National KeyBasic Research Program of China (973 project) under Grant 2015CB251000.Recommended for publication by Associate Editor P. Chi-Kwong.

F. Niu and K. Li are with the Province-Ministry Joint Key Laboratory ofElectromagnetic Field and Electrical Apparatus Reliability, Hebei Universityof Technology, Tianjin 300130, China (e-mail: [email protected];[email protected]).

B. Wang, A. S. Babel, and E. G. Strangas are with the Department of Elec-trical and Computer Engineering, Michigan State University, East Lansing, MI48824 USA (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2015.2421321

reluctance machines and doubly fed induction generators [10]–[16]. A DTC scheme for induction machines fed by multilevelinverters is proposed in [10], while a sensorless DTC tailored fora five-phase PMSM is studied in [11]. Recently, a DTC strat-egy for matrix-converter-fed PMSMs was presented in [12],which introduces a enhanced lookup table (LUT) to reducetorque ripple through utilizing the voltage vectors efficiently. Incomparison to FOC strategy, DTC requires explicit torque/fluxregulators instead of current regulators, while the derivation oftorque/flux has a similar complexity to Park transformation ofFOC. DTC does not involve space vector modulation (SVM),but utilizes a switching table that consists of different voltagevectors. In addition, the rotor position sensing that is essentialfor FOC is not necessary for DTC to operate properly even ifspeed control loop is included in the DTC scheme. In spite of thesimplicity, DTC achieves adequate torque control performanceunder both steady-state and dynamic conditions. Additionally,DTC features low sensitivity to the accuracy of machine pa-rameter estimation. On the other hand, it is widely known thatthe conventional DTC has several disadvantages. The prominentone is that the performance of DTC deteriorates at low speeddue to reduced controllability, high torque ripple, and variableswitching frequency. Furthermore, undesirable high samplingfrequency (HSF) is necessary for digital implementation of thecontroller to obtain adequate control performance. The imple-mentation challenge is elevated when HSF is coupled with in-creased computation burden in each control period.

During the past few decades, many researchers have been ad-dressing the challenges associated with conventional DTC [17]–[39]. In [17], a DTC scheme combined with SVM, namely DTC-SVM, is proposed to achieve constant switching frequency,while obtaining the desired torque and stator flux in one controlperiod by synthesizing a suitable voltage vector through SVM.Unlike the conventional switching-table-based DTC, which uti-lizes one of a limited number of voltage vectors with fixedmagnitudes and positions in each control period, DTC-SVMcan synthesize an arbitrary reference voltage vector within itslinear range with multiple vectors in each sampling interval.Methods to obtain the desired voltage vector include deadbeatcontrol [18], stator-flux-oriented control using PI controllers[19], indirect torque control [20], and sliding-mode controller[21] amongst others.

In recent years, the artificial-intelligence-based controllershave expanded in the area of power electronics and electricdrives [22]–[24]. A controller based on an adaptive neurofuzzy

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NIU et al.: COMPARATIVE EVALUATION OF DIRECT TORQUE CONTROL STRATEGIES FOR PERMANENT MAGNET SYNCHRONOUS 1409

system for SVM has been proposed in [22]. It combines artificialneural network and fuzzy logic to achieve decoupled controlof torque and stator flux, and has been proved powerful as itfeatures the advantages of both techniques.

In relatively recent development fronts, model predictive con-trol (MPC) has been attracting research attention due to its im-proved control performance as integrated with DTC [25]–[34].The fundamental principle of MPC is that it predicts a constantnumber of the future machine states, which is called predic-tion horizon denoted by N , using a discrete system model. In[25], a model predictive DTC (MPDTC) scheme based on costfunction is proposed for three-level inverter-fed PMSMs, whichutilizes a prediction horizon greater than 1 to achieve reducedswitching frequency, while the torque and stator flux are keptwithin their respective hysteresis bounds. In [26]–[28], a single-step MPDTC using cost function is presented to evaluate theeffects of each possible voltage vector and the one with mini-mum cost is selected as the optimal voltage vector to be appliedto the machine in the next control period. Recently, a novelmodel predictive torque control with pulse width modulation(PWM) is proposed by M. Preindl et al. as a promising al-ternative compared to the traditional FOC [29]–[30]. The fastgradient method is utilized to obtain the optimal voltage vector,which is then synthesized using PWM or SVM.

Another approach presented by Zhang et al. applies duty ratiomodulation (DRM) to conventional DTC [35]–[36]. The torqueripple has been significantly reduced by adjusting the duty ratioof the active voltage vectors. The key point of this strategy is todetermine the duty ratio. Several different methods have beenproposed to obtain the duty ratio based on different optimizationobjectives [37]–[39].

On the one hand, these modifications have improved the con-trol performance of DTC, and on the other hand, these controlschemes feature increased complexity. At the same time, theseimproved DTC strategies result in varied performance in termsof torque ripple, stator flux ripple, and switching frequency,etc. In practical applications, a particular set of performancecharacteristics of the controllers may be preferred over others.For instance, in high-power applications, reducing the switch-ing frequency of power devices is very likely of top prioritysignificance. The majority of published papers are focused onthe comparison between basic DTC and one modified DTC,or among modified DTC schemes of the same type [40]–[42].Nonetheless, very few have conducted a comparative evaluationover different types of improved DTC schemes. In particular,relatively new methods such as MPDTC for PMSMs have beenexcluded from such study.

In this paper, these basic and improved DTC strategies andFOC are comparatively investigated through simulation, finite-element analysis (FEA) and experiments using various criteria,and a comprehensive conclusion is drawn to summarize theresults. The results provide guidance for users to determinewhich control scheme shall be employed in order to achievethe desired objectives. The rest of this paper is organized asthe following. Section II presents the PMSM model. In SectionIII, the control strategies, i.e., DTC, MPDTC, DDTC, and FOCare reviewed and the basic control performance of each control

scheme is studied through simulation and experimentation. Thecomparative evaluation with various criteria is presented andanalyzed in Section IV. This paper is concluded with a summaryin Section V.

II. MODEL OF PMSMS

For PMSMs, the dynamic model is typically formulated inrotor reference frame (RRF) since sinusoidal quantities in sta-tionary reference frame would become constant in RRF understeady-state condition. The state equations of a PMSM in d,qreference frame are expressed as follows:

us,dq = Rsis,dq +d

dtψs,dq + Fψs,dq (1)

where F =[

0 −ωr

ωr 0

]with ωr being electrical rotor angular

speed, Rs is the stator resistance, ψs,dq = [ψsd ψsq ]T is the vec-

tor of stator flux, and us,dq = [usd usq ]T and is,dq = [isd isq ]T

are the vectors of stator voltage and current, respectively. Thestator flux vector is

ψs,dq = Gis,dq + ψr,dq (2)

where G =[

Ld 00 Lq

]with Ld and Lq being the direct-

axis and quadrature-axis stator inductances, respectively, andψr,dq = [ψf 0]T with ψf being the permanent magnet flux. Theelectromagnetic torque produced by the machine is

Te =32p (ψdiq − ψq id) (3)

where p is the number of pole pairs.

III. CONTROL STRATEGIES

In this section, the DTC-based control strategies are brieflyreviewed to lay foundation for more detailed comparative studyin Section IV. The simulation and experimental results of basiccontrol performance for each control strategy are also presented.

A. DTC

For interior PMSMs, the electromagnetic torque consists oftwo terms. The first term is the excitation torque and the secondone is the reluctance torque, which are shown as

Te = K1 |ψs | |ψr | sin (γ) + K2 |ψs |2 sin (2γ) (4)

where the constants K1 and K2 are determined by machine’sgeometric dimensions and winding configurations; and γ is theangle between stator flux and rotor flux. If the magnitudes ofstator flux and rotor flux stay constant, the torque is uniquelydetermined by γ. The conventional DTC regulates the magni-tude and angle of stator flux by applying appropriate voltagevector to obtain desired torque. The block diagram of DTC usedin this paper is shown in Fig. 1. In order to facilitate the com-parison among different control strategies, speed control loopand MTPA algorithm are utilized in all of the control schemesincluded in this paper.


Fig. 1. Block diagram of DTC.

TABLE IVOLTAGE VECTOR LUT OF DTC

sector

Δψs ΔTe ©1 ©2 ©3 ©4 ©5 ©6

1 1 us 2 us 3 us 4 us 5 us 6 us 1

0 us 0 us 7 us 0 us 7 us 0 us 7

−1 us 6 us 1 us 2 us 3 us 4 us 5

−1 1 us 3 us 4 us 5 us 6 us 1 us 2

0 us 7 us 0 us 7 us 0 us 7 us 0

−1 us 5 us 6 us 1 us 2 us 3 us 4

The desired stator flux ψ∗s and torque T ∗

e are compared withtheir corresponding estimated values using two separate hys-teresis controllers. The flux controller is a two-level comparator,while the torque controller is a three-level comparator. Accord-ing to the stator flux position and the output signals of hysteresiscontrollers, there exists an optimal voltage vector to be appliedto the stator winding, which can minimize the error of torqueand stator flux in each control period. The selection of optimalvoltage vector is implemented with reference to Table I, whichrequires three inputs and provides one output. The three inputsare: desired stator flux variation, desired torque variation, andthe sector w that the actual stator flux located within. The singleoutput is the optimal voltage vector to be applied to the machine.

The control performance of all DTC-based strategies mainlyrelies on accurate estimation of stator flux, which is achievedthrough the utilization of stator voltages and currents. There ex-ist two different families of stator flux estimators that are basedon voltage model and current model, as defined by (5) and (6),respectively. The estimator using voltage model requires fewerparameters than the one based on the current model. However, inpractical implementation, the ideal integrator in (5) cannot workproperly because of the dc drift of current sensors. DC drift inmeasurements of stator currents are inevitable, which are inher-ent in the current sensors and signal conditioning circuits. Theerrors caused by dc drift accumulate during the integration pro-cess, which leads the machine drive system to instability. Themost commonly adopted solution is to utilize a low-pass filter(LPF) instead of the ideal integrator. During normal operatingconditions, the LPF can always perform the task of integration.When the signal is dc, the filter time constant and the gain forcompensation of the LPF become infinite and the integration

Fig. 2. Simulation (blue) and experimental (red): Starting and hysteresisbounds step change response of DTC. Mechanical speed: 50% rated speed(500 r/min); load: 0.5 p.u. (1 N·m); control period Ts = 70 μs. Initial hystere-sis bounds: ΔTe = 0.01 N·m, Δψs = 0.01 Wb, change at 1 s: ΔTe = 0.01N·m, Δψs = 0.001 Wb, and 1.5 s: ΔTe = 0.02 N·m, Δψs = 0.001 Wb. Thegraphs are (from top): mechanical speed; electromagnetic torque; stator flux; d,q-axis current; and switching frequency.

cannot be performed anymore. But errors of magnitude andphase angle would be introduced by the LPF, and the addi-tional measures to compensate the errors make the controllermore complex [43],[44]. In this paper, the estimator based oncurrent model is adopted because of its simple structure. Theflux estimator has been assumed to properly function across thespeed range of interest. Additionally, MTPA algorithm is usedin DTC and the other control schemes to improve the operationefficiency. Two different approaches can be utilized to imple-ment MTPA for PMSMs: One is to solve a set of mathematicalequations online to obtain the optimal d-, q-axes currents, whilethe other one is to search a LUT designed offline to get therequired d-, q-axes currents. In this paper, a LUT containing thed-, q-axes currents for various operating points is employed totrack the MTPA trajectory correctly [45]

ψs,dq =∫

(us,dq − Rsis,dq ) dt (5)

ψs,dq = Gis,dq + ψr,dq . (6)


TABLE IIMAIN PARAMETERS OF MACHINE DRIVE SYSTEM

Electrical Machine

Type IPMSMMaximum current I [A] 10Rated torque Te [N·m] 2Rated speed ωm [r/min] 1000Stator resistance R [Ω] 0.8Inductance (d axis) Ld [mH] 5Inductance (q axis) Lq [mH] 10PM rotor flux ψf [Wb] 0.035Pole pairs p 4

InverterType Two-level VSIDC-link voltage Udc [V] 60Max current I [A] 100

Fig. 3. Block diagram of FCS-MPDTC.

The basic control performance of DTC including rampedstart and step change of hysteresis bounds are illustrated bysimulation and experimental results in Fig. 2, where mechanicalspeed, electromagnetic torque, stator flux, d-, q-axes currents,and switching frequency are included. The main parameters ofPMSM and inverter are listed in Table II. It can be observed thatthe simulation and experimental results agree well with eachother. The machine can track the command speed under 1-N·mload, while torque and stator flux are limited within the hys-teresis bounds. As the hysteresis bounds change, the stator fluxripple shows notable variation accordingly. It is worth mention-ing that the switching frequency changes with the variation ofhysteresis bounds. Additionally, the switching frequency alsovaries according to the machine operating conditions, such asspeed and load torque [46].

B. MPDTC

In general, there are two different types of MPDTC for powerelectronic and drive systems: finite control set MPDTC (FCS-MPDTC) that directly applies the voltage vectors generated byinverters and continuous control set MPDTC (CCS-MPDTC)that utilizes SVM to obtain the desired voltage vector. The de-tails about the two different MPDTCs are presented as followswhile only single-step FCS-MPDTC is considered for the com-parison since the detailed comparison between the two MPDTCstrategies have been conducted in [30].

FCS-MPDTC: The block diagram of FCS-MPDTC is shownin Fig. 3. It is almost the same as the block diagram of DTC, and

Fig. 4. Flowchart of the prediction algorithm for FCS-MPDTC.

the hardware of DTC can be used to implement MPDTC withoutmodifications. The only difference is that the MPDTC modelis employed to replace the hysteresis controllers and voltagevector LUT. The MPDTC model includes prediction algorithmand cost function, which are described in the following.

1) Prediction Model: From (1) and (2), the state-space equa-tion of PMSM can be obtained as

d

dtψs,dq = us,dq − Dψs,dq +

Rs

Ldψr,dq (7)

where D =

[Rs

Ld−ωr

ωrRs

Lq

]. Application of forward Euler ap-

proximation approach yields the following discrete-time modelof PMSM:

ψs,dq (k + 1) = (I − DTs) ψs,dq (k) + Tsus,dq (k)

+RsTs

Ldψr,dq (8)

where I denotes the identity matrix, and Ts is the control period.The prediction of stator flux can be achieved by (8). Further-more, the prediction models of stator current and torque aredescribed by

is,dq (k + 1) = E (ψs,dq (k + 1) − ψr,dq ) (9)

where E =

[ 1Ld

0

0 1Lq

]

Te (k + 1) =32p (ψs,dq (k + 1) ⊗ is,dq (k + 1)) (10)

where ⊗ denotes the cross product of two vectors.2) Prediction Algorithm: The prediction algorithm of

single-step FCS-MPDTC is shown in Fig. 4, where m is the volt-age vector number, and usm is the voltage vector generated bythe two-level VSI, the prediction horizon N = 1. The prediction


algorithm is carried out one control period ahead so that the con-trol delay can be eliminated as much as possible. The optimalvoltage vector is determined during (k − 1)th control period,but it is not applied to the machine until kth sampling instant.

The execution of FCS-MPDTC algorithm proceeds as fol-lows. The machine variables are measured at the beginning of(k − 1)th control period, and the prediction algorithm is alsoexecuted during (k − 1)th control period. The first step is topredict the machine states in kth control period according tothe prediction model and current voltage vector applied to themachine. Then, the possible future machine states within pre-diction horizon N are computed while all admissible voltagevectors are considered. Finally, the prediction results are evalu-ated against a cost function and the voltage vector with lowestcost would be applied to the machine during kth control period.In the next control interval, the same procedure is repeated withupdated measurements.

3) Cost Function: There are various forms of cost function.Geyer et al. [25] proposed a cost function whose main objectiveis to reduce the switching frequency, while torque and stator fluxare limited within the corresponding hysteresis bounds. Anothercost function expressed by (11) combines multiple control cri-teria and corresponding weight coefficients to achieve differentoptimization objectives by adjusting the weight coefficients [26]

cost (m) =

k+n∑i=k+1

⎛⎜⎜⎜⎜⎝

λT (Te (i) − T ∗e )2

+ λF (ψs (i) − ψ∗s)

2

+ λS Ns

⎞⎟⎟⎟⎟⎠

n,m = 1, . . . , 8

(11)where λT , λF , and λS are weight coefficients, and Ns is the to-tal switching instances of the six-phase legs in inverters duringone control period. After the prediction process, all of the futuremachine states of each admissible voltage vector are evaluatedaccording to the cost function in (11). The voltage vector thatminimizes the cost is selected as the optimal one, which is sub-sequently applied to the machine at the beginning of next controlperiod. In this paper, (11) is used as the cost function. Fig. 5shows the basic control performance of FCS-MPDTC aboutramped start and step change of weighting coefficients. The ma-chine starts up to 500 r/min with 1-N·m load, while the currentsand torque increase until they reach the limits. The torque andstator flux are well controlled and feature improved performanceover DTC. It can be observed that the performance of torqueripple, stator flux ripple, d-, q-axes currents, and switching fre-quency vary under different weight coefficients. Similar to theDTC scheme, the switching frequency of inverter is not constantand varies according to the machine operating conditions.

CCS-MPDTC: In contrast to FCS-MPDTC, CCS-MPDTCutilizes voltage modulation (PWM or SVM) to synthesize thedesired voltage vector. This leads to a constant switching fre-quency and decouples control from switching related effects.Additionally, CCS-MPDTC can be operated with relatively low

Fig. 5. Simulation (blue) and experimental (red): starting and weight coef-ficients step change response of FCS-MPDTC. Mechanical speed: 50% ratedspeed (500 r/min); load: 0.5 p.u. (1 N·m); control period Ts = 70 μs. Initialweight coefficients: λT = 1, λF = 1, λS = 0, change at 1 s: λT = 1, λF = 1,λS = 1, and 1.5 s: λT = 1, λF = 1000, λS = 1. The graphs are (from top):mechanical speed; electromagnetic torque; stator flux; d-, q-axis current; andswitching frequency.

sampling frequency, which provides more time for real-timecomputation [29].

At time instant k, CCS-MPDTC solves the constrained finite-time optimal control (CFTOC) problem

minimize(CFTOC) = δyTk+N Pδyk+N

+k+N −1∑i=k+1

δyTi Qδyi + δuT

i Rδui (12)

where yi is the predicted torque according to (8)–(10), δyi =yi − y∗ is the deviation of the predicted yi from the desired valuey∗ at time instant i, δui = ui − ui−1 is the difference betweenthe control input ui at time i and the previous control input ui−1 ,and the matrices P, Q, and R are design variables to define thestage and terminal costs.

The CFTOC problem in (12) is solved during each controlperiod to produce an optimal voltage control sequence over


the prediction horizon N taking into account the current andvoltage limitations while only the first input in the sequence isimplemented. The challenge is that solving the CFTOC problemin (12) is computationally intensive. Since the CFTOC problemis locally convex, the commonly used numerical optimizationtechnics, such as the fast-gradient method described in [29], canbe utilized to solve this problem. The fast gradient is a gradient-based algorithm to solve strictly convex optimization problemsand is a modification of the projected gradient algorithm thatproduces linear convergence. Two additional methods, warmstart and early termination, are used to reduce the computationburden in [29].

C. Duty Ratio Modulated DTC

For DTC and MPDTC, the selected voltage vector is appliedto the machine during the whole control period, which is themain cause of high torque ripple and stator flux ripple. In mostcases, it is not necessary for the voltage vector to be appliedfor the entire control interval to meet the control performancerequirements of stator flux and torque. Therefore, DRM is in-troduced to DTC and leads to an improved DTC algorithm,namely DDTC. Different from DTC-SVM, which utilizes twoactive voltage vectors and one null voltage vector to synthesisarbitrary voltage vector during one sampling interval, DDTConly use one nonzero voltage vector and one zero voltage vectorin each control period. As such, the switching frequency is re-duced significantly, while the control performance deterioratesslightly. The time duration of nonzero voltage vector varies fromzero to the whole control period, which is equivalent to changingthe amplitude of the nonzero voltage vector. Zero voltage vectoris applied for the remaining time to maintain the torque andstator flux. The selection of nonzero voltage vector for DDTC isthe same as DTC, which depends on the desired torque variationand stator flux variation, as shown in Table I. With the aim ofreducing switching frequency, the nonzero voltage vector us1(1 0 0), us3 (0 1 0), us5 (0 0 1) are followed by zero voltagevector us0 (0 0 0), while the other three nonzero voltage vectorsare followed by zero voltage vector us7 (1 1 1). As such, onlyone phase leg changes status during one control period.

For VSI fed PMSMs, the voltage vector is the single control-lable input variable and the torque ripple is usually consideredas the most important criterion of control performance. So, therelationship between the voltage vector and torque variationdominates the duty ratio decision implementation. Accordingto (1), (2), and (3), the torque derivative under different nonzerovoltage vector is

dTe

dt=

3p

2

(1Lq

− 1Ld

)(Im (usψs) − ωr Re

(ψ2

s

))

+3pRs

4

(1L2

d

− 1L2

q

)Im

(ψ2

s

)

− 3p

2Ld

(Rs

LdIm (ψsψr )+ωr Re (ψsψr )−Im (usψr )

)

(13)

Fig. 6. Illustration of DRM.

where us is the nonzero voltage vector. When zero voltagevector is applied to the machine, the torque derivative becomes

dTe

dt=

−3p

2

(1Lq

− 1Ld

)ωr Re

(ψ2

s

)

+3pRs

4

(1L2

d

− 1L2

q

)Im

(ψ2

s

)

− 3p

2Ld

(Rs

LdIm (ψsψr ) + ωr Re (ψsψr )

). (14)

The value of dTe

dt in (14) is negative, which implies that thezero voltage vector continuously decreases the torque. Thereare several different control objectives for DDTC, which lead tovarious duty values [37]–[39]. One of the most commonly usedmethods is to force the actual torque to be equal to the desiredtorque at the end of each control period as illustrated in Fig. 6.

According to the control objective shown in Fig. 6, the ab-solute value of torque error at the end of each control periodis

ET = |T ee + s1dTs + s2 (1 − d) Ts | (15)

where s1 and s2 are torque slopes under nonzero and zero volt-age vector, respectively, T e

e = Te0 − T ∗e is the initial torque er-

ror of each control period, Te0 and T ∗e are the initial actual and

desired torque, respectively, and d is the duty ratio. By lettingET = 0, the duty ratio of nonzero voltage vector can be derivedas

d = − (s2Ts + T ee )

(s1 − s2) Ts. (16)

The duty ratio d should be limited within [0, 1] due to its real-izability. For steady-state operation, the duty ratio d is a constantnumerical value with little variations. But during dynamic pro-cess, the duty ratio would be close to 1, which means that thenonzero voltage vector is applied for the whole control periodin order to reach the desired torque as fast as possible. Fig. 7presents the basic control performance of starting and deceler-ating response of DDTC. The machine starts up to 500 r/minand decelerates to −500 r/min with 1-N·m load. The torque andstator flux show improved performance over DTC. The switch-ing frequency is constant because only one phase leg of VSI is


Fig. 7. Simulation (blue) and experimental (red): starting and deceleratingresponse of DDTC. Load: 0.5 p.u. (1 N·m); control period Ts = 100 μs. Ini-tial mechanical speed command: ωm = 500 r/min, change at 1.3 s: ωm =−500 r/min. The graphs are (from top): mechanical speed; electromagnetictorque; stator flux; d-, q-axis current; and switching frequency.

switched during each control period even though the duty ratiois time varying.

D. FOC

In order to clearly reveal the advantages and disadvantages ofthe aforementioned DTC strategies, the most commonly usedFOC strategy is also included to serve as benchmark. The FOCscheme is implemented in the rotor flux reference frame usingclassical PI regulators. The space vector pulse width modulationwith utilized voltage vectors distributed symmetrically duringeach control period is implemented to generate the desired volt-age vector [47],[48]. Fig. 8 shows the starting and deceleratingcontrol performance of FOC. It is observed that the performanceof torque ripple, stator flux ripple, and d-, q- axes currents aresignificantly improved over the DTC strategies.

IV. COMPARATIVE EVALUATION

In this section, the four control strategies introduced inSection III are comparatively investigated through MAT-LAB/Simulink, FEA, and experimental results of PMSM fed

Fig. 8. Simulation (blue) and experimental (red): starting and deceleratingresponse of FOC. Load: 0.5 p.u. (1 N·m); control period Ts = 100 μs. Ini-tial mechanical speed command: ωm = 500 r/min, change at 0.9 s: ωm =−500 r/min. The graphs are (from top): mechanical speed; electromagnetictorque; stator flux; d-, q-axis current; and switching frequency.

by a two-level VSI. In the experimental setup, NI real-timemodule is employed to implement the control strategies using Clanguage compiled by MATLAB/Simulink real-time workshop.A three-phase IGBT module equipped with isolated firing cir-cuits is used as the inverter. The PWM signals are generated byFPGA embedded in the real-time module and then sent to theinverter through NI PCIE-7852R RIO board, which is also usedto sample the system variables, such as three-phase currents, etc.The load torque is provided by a dc machine fed by a single-phase controller. A 1024-pulse incremental encoder is installedto obtain the mechanical rotor speed of PMSM. An annotatedpicture of the experimental setup is illustrated in Fig. 9.

The comparative study is carried out in the following per-spectives: torque ripple under the same switching frequency;steady-state control performance; stator current; stator flux loci;dynamic response; machine losses; parameter sensitivity; andalgorithm complexity. For DTC, the magnitudes of torque hys-teresis bound and stator flux hysteresis bound are adjusted toobtain the desired torque ripple, stator flux ripple, and switch-ing frequency. For MPDTC, the coefficients λT , λF , and λS can


Fig. 9. Experimental setup of PMSM drive system.

be tuned to achieve different control performance. For DDTCand FOC, the control period is adjusted to get the torque ripple,stator flux ripple, and switching frequency equal to DTC andMPDTC. The switching frequency of inverter is calculated by

fs =NT

6T(17)

where NT is the number of switching instances of inverter dur-ing a fixed period T . Most of the comparison results are obtainedunder the same switching frequency. For DTC and MPDTC, theswitching frequency is not constant. Thus, their average switch-ing frequency are tuned to be equal to the switching frequencyof DDTC and FOC, which makes the comparison reasonable.Considering that the switching instances between two controlperiods are not constant, the switching frequency of DDTC isnot constant either. In order to facilitate the comparison, it isassumed that only one phase of the inverter is switched duringthe transients between two control periods, which results in con-stant switching frequency. The torque and stator flux ripple arecalculated using the following equations:

⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

Trip =

√√√√ 1Nm

Nm∑i=1

(Te (i) − T ∗e )2

ψrip =

√√√√ 1Nm

Nm∑i=1

(ψs (i) − ψ∗s)

2

(18)

where m is the number of samples.

A. Torque Ripple Under Same Switching Frequency

First, torque ripple difference under the same switching fre-quency is investigated and the results are shown in Fig. 10.Table III summarizes the quantitative indices of various controlstrategies. The machine runs without load at 50% and 100%rated speed, respectively.

It can be observed that the torque ripple decreases as theswitching frequency increases at both high and low speeds. Atlow speed (500 r/min), DDTC results in the lowest torque rip-ple, while FOC presents slightly higher torque ripple at lowswitching frequency of 1 kHz, and DTC features the most pro-nounced torque ripple. The torque ripple of MPDTC, DDTC,and FOC are 86%, 59%, and 67% of that of DTC, respec-tively. With switching frequency increasing, the torque rippleof FOC decreases relatively faster than the other three methods,

Fig. 10. Experimental results: Torque ripple difference among the controlstrategies under the same switching frequency. Load: 0 N·m. (a) 500 r/min. (b)1000 r/min.

TABLE IIITORQUE RIPPLE OF DIFFERENT CONTROL STRATEGIES UNDER SAME

SWITCHING FREQUENCY

Trip [N·m] (500/1000 r/min)

fs [kHz] DTC MPDTC DDTC FOC

1 0.162/0.155 0.14/0.131 0.095/0.16 0.108/0.1511.5 0.147/0.142 0.123/0.117 0.083/0.141 0.087/0.1242 0.137/0.136 0.111/0.11 0.07/0.123 0.07/0.1062.5 0.13/0.132 0.101/0.104 0.06/0.109 0.055/0.0913 0.125/0.129 0.094/0.1 0.053/0.1 0.0454/0.08193.5 0.122/0.127 0.089/0.096 0.05/0.095 0.04/0.0784 0.12/0.126 0.085/0.094 0.048/0.093 0.035/0.075

which almost have the same rate of decline. At 4-kHz switchingfrequency, the lowest torque ripple is held by FOC followed byDDTC and MPDTC, while DTC still features the highest torqueripple. The torque ripple of MPDTC, DDTC, and FOC are 71%,40%, and 30% of that of DTC.

With the speed increased to 1000 r/min, the four controlstrategies present different torque ripple variations from that of500 r/min. For DTC and MPDTC, lower torque ripple is obtainedat low switching frequency, while both of them present highertorque ripple under high switching frequency, which means thatthe torque ripples of DTC and MPDTC decrease slower thanthat of 500 r/min with the increasing switching frequency. ForDDTC and FOC, their torque ripples increase with the speedincreasing under various switching frequency. MPDTC achievesthe lowest torque ripple at 1 kHz followed by FOC, DTC, andDDTC, respectively. At 4 kHz, FOC owns the lowest torqueripple, while DTC exhibits the highest torque ripple.

One conclusion to be drawn from the preceding discussionis that MPDTC consistently outperforms DTC because of theoptimized voltage vector selection principle, which is particu-larly true at high switching frequency. On the other hand, FOCconsistently presents better control performances than DTC andMPDTC in terms of torque ripple level because of the adjustableduty ratio of voltage vectors. Additionally, the control period inFOC can be much longer than in DTC and MPDTC. The allowed


Fig. 11. Experimental results: Steady-state torque ripple of different controlstrategies under no load. Mechanical speed: 1000 r/min; switching frequency:3 kHz. The graphs are for (from top): DTC; MPDTC; DDTC; and FOC.

lower sampling frequency in FOC is advantageous for experi-mental implementation. DDTC also exhibits lower torque ripplethan that of the other two DTCs at low speed, but the controlperformance deteriorates at high speed, which is mainly causedby the deviation of stator resistance and inductance used in thecontroller from actual values.

B. Steady-State Control Performance

In this section, the steady-state control performance of eachcontrol strategy, without and with load, are presented in Figs. 11and 12, respectively. Table IV summarizes the quantitative in-dex of torque ripple and stator flux ripple for different methodsunder various speeds. All of the experimental results for thefour control methods are collected under the same switchingfrequency, which is approximately 3 kHz. When the machineruns at 1000 r/min with no load, DTC and MPDTC generatealmost identical stator flux ripple, while the stator flux ripples

Fig. 12. Experimental results: Steady-state torque ripple of different controlstrategies under 1-N·m load. Mechanical speed: 1000 r/min; switching fre-quency: 3 kHz. The graphs are for (from top): DTC; MPDTC; DDTC; andFOC.

TABLE IVSTATOR FLUX RIPPLE AND TORQUE RIPPLE OF THE CONTROL STRATEGIES

UNDER DIFFERENT SPEED AND LOAD

Load Speed Methods

[N·m] [r/min] DTC MPDTC DDTC FOC

ψ rip 0 500 0.0035 0.004 0.0013 0.00091000 0.0038 0.0043 0.0024 0.0018

1 500 0.005 0.0055 0.0034 0.00261000 0.0056 0.0054 0.0042 0.004

Trip 0 500 0.125 0.094 0.053 0.04541000 0.129 0.1 0.1 0.0819

1 500 0.159 0.141 0.105 0.08731000 0.143 0.14 0.122 0.1


of DDTC and FOC are reduced significantly compared to thoseof DTC and MPDTC. For DTC, DDTC, and FOC, the stator fluxripple are 88%, 56%, and 42% of that of MPDTC, respectively.For the torque ripple, MPDTC and DDTC have the same perfor-mance that exceeds DTC, while FOC achieves the lowest value.The torque ripples of MPDTC, DDTC, and FOC are 78%, 78%,and 64% of that of DTC, respectively.

With the machine load being increased to 1 N·m at1000 r/min, the stator flux ripples increase to 147%, 126%,175%, and 222% as compared to no-load condition for DTC,MPDTC, DDTC, and FOC, respectively. The torque ripple alsoincreases for all the four strategies as compared to that under noload, the torque ripple increase by 11%, 40%, 22%, and 22%for DTC, MPDTC, DDTC, and FOC, respectively.

Figs. 11 and 12 also illustrate the zoomed torque responsefor the four different control strategies. For DTC and MPDTC,the sharp torque ripples are mainly caused by the changing ofvoltage vectors. For FOC, the smooth torque ripple is causedby cogging effects introduced by concentrating windings. Ad-ditionally, it can be observed from Table IV that almost bothstator flux ripple and torque ripple increase along with the ma-chine speed except for several cases, i.e., the torque ripples ofboth DTC and MPDTC decrease when the mechanical speedincreases under 1-N·m load. It is worth noting that the mag-nitudes of hysteresis bounds of DTC and the coefficients λT ,λF , and λS of MPDTC can be tuned to trade stator flux ripple,torque ripple, and switching frequency of the desired controlperformance.

C. Stator Flux Loci

The steady-state stator flux loci at 500 and 1000 r/min un-der 3 kHz switching frequency for the four control strategiesare shown in Fig. 13, and Table IV presents the quantitativeindex of stator flux ripple. It is seen that, at low speed, DTCand MPDTC feature almost identical stator flux ripple underno-load operation, but the stator flux locus of MPDTC moreclosely follows the circular shape than DTC. DDTC and FOCpresent much better stator flux locus in shape and smoothnessthan DTC and MPDTC. With the speed increased to 1000 r/min,the stator flux ripples also increase to various extent for all thefour control strategies. It can be seen that the stator flux loci ofDTC and MPDTC have not changed significantly in both shapeand smoothness compared with that at 500 r/min, while DDTCand FOC show notable deterioration in the performance of locussmoothness and stator flux ripple. During the experimental ver-ification, it is found that with the machine load increasing, theperformance of stator flux locus for all the four control strategiesdeteriorates obviously in both shape and smoothness, which isnot pictorially presented here due to the page limitation, but thequantitative results are provided in Table IV.

D. Stator Current

The high-order harmonics in stator current affects the ma-chine losses indirectly, and the total harmonic distortion (THD)calculated using (19) is the widely adopted merit figure of

Fig. 13. Experimental results: Stator flux loci of different control strategies.Load: 0 N·m; switching frequency: 3 kHz. (a) 500 r/min. (b) 1000 r/min.

spectrum performance

THD =

√I2rms − I2

1,rmsI21,rms

(19)

where I2rms is the root-mean-square (RMS) value of stator cur-

rent, and I21,rms is the RMS value of fundamental in stator

current. The stator current and the corresponding THD for


different control strategies are shown in Fig. 14. The machineoperates at steady state under 3-kHz switching frequency withmechanical speed being 1000 r/min and the load being 1 N·m.

It can be observed that the four control strategies featurevarious stator current ripples and THD under the same switchingfrequency. DTC results in the most distorted current waveformand highest THD. The deteriorated performance of stator currentand THD for DTC is mainly caused by the large stator fluxripple, which can be regulated by adjusting the magnitudes ofhysteresis bounds. The current waveform of MPDTC is lessdistorted than that of DTC, while the THD is also lower thanDTC. It is apparent that the dominant harmonics of MPDTCis around 3 kHz. Similar to DTC, the stator current and THDperformance of MPDTC can also be improved through tuningthe coefficients of cost function. It is a tradeoff among statorflux ripple, torque ripple, and switching frequency that need tobe balanced according to application requirements. For DDTCand FOC, the stator current and THD performance are superiorto that of DTC and MPDTC, especially FOC, which presentsvery few high-frequency harmonics. The low-order harmonicsin current waveforms of DDTC and FOC is mainly caused bythe anisotropy of IPMSM.

E. Dynamic Response

In addition to the study of steady-state control performance,the dynamic response is further investigated here. Fig. 15 illus-trates the response to step change of reference torque for thefour control strategies. It takes less than 1 ms for the torque toreach the commanded value for DTC, MPDTC, and DDTC, andthere is no significant difference among them except the torqueripples under steady state. It can be stated that the quick dynamicresponse of DTC is maintained in MPDTC and DDTC, while thesteady-state control performance is improved. For FOC, thereare two PI controllers for d-, q-axes currents, respectively, andthe response to step change of torque greatly depends on the tun-ing of the gains for PI controllers. As shown in Fig. 15, “FOC-1”exhibits quick torque response as same as the DTC schemes, butan undesired overshoot is also introduced. The torque overshoothas been eliminated in “FOC-2” with lengthened response time,which verify that the DTC possess quicker dynamic responsethan FOC.

Figs. 16 and 17 present the acceleration response withoutload from −1000 to 1000 r/min for DTC, MPDTC, DDTC, andFOC, respectively. From top to bottom, the curves in each ofFigs. 16 and 17 are mechanical rotor speed, torque, stator flux,d-, q-axes currents, and the current of phase A. It is seen thatthe machine speed increases to the commanded speed only in afew hundred milliseconds with small overshoot for all the fourcontrol strategies. During the dynamic process, the torque ripple,stator flux ripple, and current waveform smoothness of differentcontrol methods show varied performances, among which FOCexhibits superior performance than the other three strategies.It is worth mentioning that the dynamic responses of differentcontrol methods depend on the tuning of PI controller gains, i.e.,proportional gain and integral gain. If quick response of speedor torque is desired for the dynamic process, oscillations wouldalso be introduced at the same time.

Fig. 14. Experimental results: Stator current and THD of different controlstrategies. Mechanical speed: 1000 r/min; load: 1 N·m; switching frequency:3 kHz. (a) DTC. (b) MPDTC. (c) DDTC. (d) FOC.


Fig. 15. Experimental results: Torque step change response from 0 to 2 N·mof different control strategies.

F. Machine Losses

For machine drive systems, the power losses mainly includeinverter loss and machine loss. The inverter loss is partly relatedto the switching frequency of the switching devices embedded ininverters, such as IGBTs. The machine losses usually refer to thecopper loss and iron loss, which are difficult to measure in prac-tical experiments. In this paper, in order to achieve the objectiveof comprehensive comparison for the four control strategies, themachine is modeled using FEA with Flux2-D software packagebased on the geometric structure of the IPMSM employed in theexperimental setup, as shown in Fig. 18.

The three-phase current data obtained from experimental re-sults are applied to the FEA model to calculate the iron loss andcopper loss, and the results are presented in Fig. 19. The statorcurrent data are collected at 3-kHz switching frequency.

For iron loss, the four control strategies exhibit almost thesame performance under different operating conditions. At lowspeed (500 r/min), lower iron loss is obtained when no load isadded for all of the control methods. The iron loss increasesslightly with 1-N·m load applied to the machine. At higherspeed (1000 r/min), the iron loss increases to almost twice ofthat at low speed for both with and without load operation.This is mainly caused by the increased rotating frequency ofalternating magnetic field in the machine.

For copper loss, the various control strategies present morenotable variations than that of iron loss. Under no-load opera-tion, the copper loss increases sightly with the machine speedaccelerating. When the machine runs under 1-N·m load, the cop-per loss shows an increase for all of the control methods. It isworth noting that the copper loss of FOC is consistently lowerthan that of the DTCs, especially when the machine operateswith load.

G. Parameter Sensitivity

The parameter sensitivity is of substantial significance inpractical implementations for all control strategies. For DTC-based control methods, the stator flux estimator is affectedseverely by the variations of machine parameters. With statorflux estimator using voltage model in (5), stator resistance isrequired to estimate the stator flux and torque. At high speed,the stator resistance can be ignored because the voltage dropacross it is negligible as compared to the voltage drop across the

Fig. 16. Experimental results: Acceleration response from −1000 to1000 r/min for DTC and MPDTC. Hysteresis bounds: ΔTe = 0.01 N·m,Δψs = 0.001 Wb; load: 0 N·m. (a) DTC. (b) MPDTC.


Fig. 17. Experimental results: Acceleration response from −1000 to1000 r/min for DDTC and FOC. Load: 0 N·m. (a) DDTC. (b) FOC.

Fig. 18. FEA model of the IPMSM.

Fig. 19. FEA and experimental: Iron losses and copper losses of machine fordifferent control strategies. (a) Iron losses. (b) Copper losses.

inductance. However, the variation of stator resistance results insignificant error in the estimated stator flux at low speed. Dueto the variations in temperature and operating speed, stator re-sistance can vary considerably. The machine drive system maybecome unstable if the stator resistance used in (5) is bigger thanthe actual value. On the other hand, the actual stator flux andtorque deviate from the desired values if the estimated statorresistance is less than the actual value. With the stator flux esti-mator based on the current model in (6), the accuracy of statorflux estimation significantly depends on the variations of statorinductance. Iron saturation reduces air gap flux density causingIPMSMs to demonstrate stator inductance that varies as a func-tion of operation point. Usually, the stator inductance decreaseswith increasing stator current. As such, the online estimationof stator resistance or inductance is often required to achieveadequate performance [49]–[51].

Due to the nonlinear nature of the control strategies, it is noteasy to conduct the comparison of parameter sensitivity basedon closed-form analytical solutions. Hence, the performance ofthe control strategies with deliberately introduced estimation er-ror in the machine parameters is evaluated through experiments.Fig. 20 shows the stator flux ripple and torque ripple of differ-ent control strategies with the values of stator resistance and


Fig. 20. Experimental results: Parameter variation response of different con-trol strategies with machine parameters used by the controllers exceeding theactual values by 100% at 2.5 s. Mechanical speed: 1000 r/min; load: 0 N·m;switching frequency: 3 kHz. (a) DTC. (b) MPDTC. (c) DDTC. (d) FOC.

inductance used by the controllers exceeding the actual valuesby 100%.

Among the four control strategies using current model-basedestimator, DTC only involves stator inductance to achieve thestator flux and torque estimation, while MPDTC and DDTCare affected by the accuracy of both stator resistance and

inductance to realize the prediction and duty ratio calculation.The conventional FOC utilizes none of the machine parametersfor its control strategy, but in order to conduct comparison withthe other three methods, the estimated stator inductance is usedto calculate the actual stator flux and torque for FOC.

The experimental results suggest that, for all control meth-ods, the control performance deterioration of stator flux rippleis significant when the machine parameters vary because thestator inductance is utilized to estimate the stator flux for all ofthe control strategies. On the other hand, the torque ripple ofDTC almost stays independent from the variation of machineparameters. In contrast, the torque ripples of both MPDTC andDDTC show higher sensitivity to stator inductance estimationerror. During experimentation, it is found that the torque rippleof FOC is affected slightly by the mismatched machine parame-ters. Such an observation is due to the fact that the determinationof proportional and integral gains of the current regulators is re-lated to the values of stator resistance and inductance. Therefore,the machine parameter variation indirectly affects the controlperformance of FOC, even though the control strategy directlyemploys neither of them.

H. Algorithm Complexity

In practical applications, algorithm complexity is an unavoid-able issue because of the limited hardware capacity, i.e., theoperating frequency of DSP or microcontrollers. The controlstrategy becomes unfeasible if the amount of time for neces-sary calculations in each control period exceeds the limits of thehardware. One possible approach is to increase the control pe-riod to accommodate the computation burden, which leads to thedeterioration of control performance. The preferred approach tosolving this problem is to simplify the control algorithm withoutaugmenting the calculation capability of microprocessor.

Among the four control methods, DTC demands the leastamount of computation. The main part of its computation is toestimate the stator flux and torque. On the other end, MPDTCis the most complicated because of its complex prediction algo-rithm. The computational complexity of single-step MPDTC isproportional to the number of admissible voltage vectors, whichis determined by the inverter topology, i.e., a multilevel inverterhas more admissible voltage vectors than a two-level inverter.The algorithm complexity of multistep MPDTC is related tothe prediction horizon, which can be adjusted according to therequirements in certain applications. Long prediction horizongreatly boosts the control performance of MPDTC, such as re-duced switching frequency and torque ripple. In the meantime,large prediction horizon also leads to substantial increasing ofcalculation burden even if extrapolation is always used for mul-tistep MPDTC. Several approaches to reducing the amount ofcomputation for MPDTC have been proposed, such as reducedfinite control set MPDTC and branch and bound algorithm forMPDTC [33], [34]. But further simplification is still necessaryfor MPDTC to be implemented in broader range of applications.The computation complexities of DDTC and FOC are essen-tially equivalent. Their main tasks are almost the same, whichinvolve calculating the duty ratio of different voltage vectors.


TABLE VSUMMARY OF COMPARISON RESULTS

Comparison indices DTC MPDTC DDTC FOC

torque ripple undersame switching frequency high middle middle lowstator flux ripple high high middle lowstator current THD high middle middle lowdynamic response fast fast fast slowmachine losses high high high lowparameter sensitivity low high high lowalgorithm complexity low high middle middlerequired control period short short middle long

I. Summary of the Comparative Evaluation

In Table V, the main comparison results of the four controlstrategies are summarized.

A grade or description has been given to each of the evaluationcriteria based on the obtained experimental results. It should benoted that the evaluation does not convey an absolute meaning.The experimental results may vary if the control strategies areused for different kinds of machine with various power ratings,but the basic advantages and disadvantages should be the samefor each control method.

V. CONCLUSION

Four control strategies that include three DTC-based methodsand FOC for PMSMs have been critically evaluated against sev-eral control performance metrics, i.e., torque ripple, switchingfrequency, stator flux ripple, steady-state and dynamic response,parameter sensitivity, and algorithm complexity. The compar-ative study clearly reveals the advantages and disadvantagesassociated with each control scheme, and the results providevaluable guidance to select the most suitable control scheme fora specific application.

Generally speaking, DTC features the simplest structureamong the control strategies, and its switching frequency islow, which collectively indicates that it is suitable for high-power applications. But HSF is required to obtain adequatelylow torque ripple. MPDTC can achieve lower switching fre-quency and torque ripple than DTC under the same samplingfrequency, but its algorithm complexity is substantially elevatedwhile it is also relatively sensitive to parameter changes. Hence,it can be employed for high accuracy control in high poweroccasions. FOC has simple structure which makes it easy tobe implemented in practical applications. Moreover, the switch-ing frequency of FOC is inherently constant. But the switchingfrequency of FOC is higher than the other three methods un-der the same sampling frequency, which means it is suitablefor low-power applications. DDTC delivers acceptable controlperformance as a compromised approach between FOC andDTC, which suggests DDTC be employed in a broad range ofapplications.

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Feng Niu (S’13) was born in Hebei, China, in 1986.He received the B.S degree in electrical engineeringand automation from the Hebei University of Tech-nology, Tianjin, China, in 2009, where he is currentlyworking toward the Ph.D. degree in electrical engi-neering at the School of Electrical Engineering.

From September 2012 to September 2014, he wasa Visiting Researcher in the Electrical Machines andDrives Laboratory at Michigan State University, EastLansing, MI, USA. His research interests include ma-chine control, power converter control, and intelligent

electric apparatus.

Bingsen Wang (S’01–M’06–SM’08) is a native ofChina. He received the M.S. degrees from ShanghaiJiaotong University, Shanghai, China, and the Uni-versity of Kentucky, Lexington, KY, USA, in 1997and 2002, and the Ph.D. degree from the Universityof Wisconsin-Madison, Madison, WI, USA, in 2006,all in electrical engineering.

From 1997 to 2000, he was with Carrier Air Con-ditioning Equipment Company as an Electrical Engi-neer at Shanghai. He was also with the General Elec-tric (GE) Global Research Center in New York as a

Power Electronics Engineer. While being with GE, he was involved in variousresearch activities in power electronics, mainly focused in the high-power area.From 2008 to 2009, he was on the Faculty of the Department of Electrical En-gineering, Arizona State University. Since 2010, he has been a Faculty Memberwith the Department of Electrical and Computer Engineering, Michigan StateUniversity, East Lansing, MI, USA. He has authored and coauthored 35 techni-cal articles in refereed journals and peer-reviewed conference proceedings. Hiscurrent research interests include reliability and dynamic modeling/control ofpower electronic systems, power conversion topologies, in particular multilevelconverters and matrix converters, application of power electronics to renewableenergy systems, power conditioning, flexible ac transmission systems, and elec-tric drives.

Dr. Wang holds one Chinese patent and one US patent with two patents pend-ing. He received the Prize Paper Award from the Industrial Power ConverterCommittee of the IEEE Industry Application Society in 2005. He has been anAssociate Editor of the IEEE POWER ELECTRONICS LETTERS since 2009.


Andrew S. Babel (S’12–M’15) received the B.S. andM.S. degrees in electrical engineering in 2009 and2012 and the Ph.D. degree under Prof. E. G. Strangaswith the Electrical Machines and Drives Laboratory,all from Michigan State University, East Lansing, MI,USA

From March through September 2013, he wasa Visiting Researcher at the Technical University ofGraz, Graz, Austria, on the Marshall Plan FoundationScholarship. His research interests include conditionmonitoring, machine design, and the control of elec-

trical machines and power electronics.

Kui Li was born in Hebei, China, in 1965. He re-ceived the B.S. and M.S. degrees from the HebeiUniversity of Technolog, Tianjin, China, in 1987 and1992, respectively, and the Ph.D degree from FuzhouUniversity, Fuzhou, China, in 1996, all in electricalengineering.

He is currently a Professor with the School of Elec-trical Engineering, Hebei University of Technology.He (co)authored more than 100 technical articles andtwo monographs. His research interests include reli-ability and intellectualization of electrical apparatus,

fault diagnosis, and life prediction of electrical apparatus.

Elias G. Strangas (M’80) received the Dipl.Eng. de-gree in electrical engineering from the National Tech-nical University of Greece, Athens, Greece, in 1975,and the Ph.D. degree from the University of Pitts-burgh, Pittsburgh, PA, USA, in 1980.

He was with Schneider Electric, Athens, from1981 to 1983 and with the University of Missouri-Rolla, from 1983 to 1986. Since 1986, he has beenwith the Department of Electrical and Computer En-gineering, Michigan State University, East Lansing,MI, USA, where he heads the Electrical Machines

and Drives Laboratory. His research interests include the design and controlof electrical machines and drives, finite-element methods for electromagnetics,and fault prognosis and mitigation of electrical drive systems.

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