Predictive Torque Control

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VARGASet al.: PREDICTIVE TORQUE CONTROL OF AN INDUCTION MACHINE FED BY A MATRIX CONVERTER 1427

Fig. 1. Power circuit of the system.

andy {a,b,c}, as shown in Fig. 1. Considering that the loadshould not be in an open circuit, due to its inductive nature, and

that phases of the source should not be short circuited, switching

functions should fulfil, at all times, the following equation:

Suy + Svy + Swy = 1 y {a,b,c} (2)

whereSxy = 0 represents switchxy open andSxy = 1repre-sents switchxy closed. This restriction allows the topology tohave 27 valid switching states and implies the requirement for

a commutation strategy in the switching process [8]. These 27

switching states can be classified into three groups according

to the kind of output voltage and input current vector that each

switching state generates, which are as follows.

1) All three output phases are connected to the same input

phase. Space vectors from this group of switching states

have zero amplitude.2) Two output phases connected to a common input phase,

and the third output phase connected to a different input

phase. This group generates stationary space vectors with

varying amplitude and fixed direction.

3) Each output phase is connected to a different input phase.

Space vectors have a constant amplitude, but its angle

varies at the supply angular frequency.

The trajectories of the output voltage space vectors, assuming

balanced three-phase input voltages of 230Vrm s per phase, areshown in Fig. 2. Vectors from group 1) can be identified by the

symbol, while groups 2) and 3) are represented byand ,

respectively.Most control techniques (including most space vector mod-

ulation (SVM) based methods and direct torque control (DTC)

strategies [4], [6], [10]) use only zero and stationary vectors.

The method proposed in this paper considers all valid switch-

ing states, including the rotating vectors that have the benefit of

producing lower common-mode voltage.

III. PREDICTIVETORQUECONTROL

Predictive torque control (PTC) consists of choosing, at fixed

sampling intervals, one of the 27 feasible switching states of

the MC. A diagram of the PTC strategy is shown in Fig. 3. The

selection of the switching state for the following time interval

Fig. 2. Output voltage space vectors generated by the MC.

Fig. 3. Block diagram of the control strategy.

is performed using a quality function minimization technique.

The quality function grepresents the evaluation criteria in orderto select the best switching state for the next sampling interval.

For the computation ofg, the input current vector is , the electrictorqueTe , and the stator fluxs on the next sampling intervalare predicted, assuming the application of each valid switching

state, by means of a mathematical model of the input filter and

IM. These predicted values are indicated by the superscript pand are compared with their reference values denoted by the

superscript withing. A propotionalintegral (PI) controlleris used to generate the reference torque Te to the predictive al-gorithm. It also compensates deviations of the prediction model

caused by possible variations of the parameters of the IM.

A. Evaluation Criterion: Quality Functiong

The quality function represents the evaluation criteria used to

decide which switching state is the best to apply. The function

is composed of the absolute error of the predicted torque, the


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1428 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 6, JUNE 2010

absolute error of the predicted flux magnitude, and the absolute

error of the predicted reactive input power, resulting in

g= T|Te T

pe|+ |

s

ps |+ Q |Q

in Q

pin | (3)

where T, , and Q are weighting factors that handle the re-

lationship between reactive input power, torque, and flux condi-

tions. The units of each weighting factor are defined to maintaing as a magnitude without a physic interpretation. In this sense,Tis measured in Newtonmeter inverse, in webers inverse,and Q in voltampere inverse.

In practice, only two of these factors are required to adjust

the method. The third can be kept constant. The reason is that

the weighting factors must handle the relative importance of the

errors in g and this task can be accomplished simply by changingtwo ratio magnitudes. For example, Tcan be set as constant,

using and Q to change the values of the weighting ratios

/T andQ/T. Through the development of this study, thevalue of T is kept constant at T = 1(Nm)

1 . The values

of

and

Q are modified to evaluate the performance of themethod and find the optimum set of factors.

The quality functiong must be calculated for each of the 27feasible switching states. The state that generates the optimum

value, in this case a minimum, will be chosen and applied during

the next sampling period. The states that generate the higher

predictions of torque error, flux error, and reactive input power

error will be penalized with higher values ofg , and thus, willnot be selected. In this sense, the technique assigns costs to the

objectives reflected ing, weighted by T, Q , and , and thenchooses the switching state that presents the lowest cost.

B. Models Used to Obtain Predictions1) MC Model: The equation that relates load or output volt-

ages with input voltages of the MC can be expressed as vavbvc

=

Sua Sva SwaSub Sv b SwbSuc Svc Swc

T

veuvevvew

. (4)

Output voltages applied to the load can then be considered as de-

pendant variables of the switching functions, reflected in matrix

T, and the input voltages. The relation between input currentsand output or load currents is expressed as

ieuieview

=

Sua Sub SucSva Svb SvcSwa Swb Swc

TT

iaibic

. (5)

Input currents depend on output currents and the switching state

of the MC, due to the inductive nature of the load.

2) Load Model: In this section, a mathematical discrete-

time model is derived to predict the behavior of the system

under a given switching state, based on well-known [19][23],

[33][35] dynamic equations for an IM. The stator and rotor

voltage equations in fixed stator coordinates for a squirrel-cage

IM can be presented as

vo =Rs io+dsdt

(6)

vr =Rr ir+drdt

jpr = 0 (7)

where Rs and Rr are the stator and rotor resistances, s and rare the stator and rotor fluxes, is the mechanical rotor speed,andp is the number of pole pairs of the IM. The stator and rotorfluxes are related to the stator and rotor currents by

s =Lsio+ Lm ir (8)

r =Lm io+ Lr ir (9)

where Ls , Lr , and Lm are the self- and mutual inductances.Finally, the electric torque produced by the machine can be

obtained by

Te = 3

2p

LmLrLs L2m

Im{rs}

= 32p L

m

LrLs L2m(rs rs ) (10)

where r is the complex conjugate of vector r , and the sub-scriptsandrepresent real and imaginary components of theassociated vector.

Equations (6) and (7) can be rewritten, solving the stator and

rotor currents in terms of the stator and rotor fluxes from (8) and

(9), as

dsdt

= RsLrLsLr L2m

s + RsLmLsLr L2m

r + vo (11)

drdt =

RrLmLsLr L2m s

RrLsLsLr L2m r jpr . (12)

The next step is to define a discrete-time model based on these

continuous-time equations. Using a forward Euler approxima-

tion [19], the following discrete equations are computed from

(11) and (12) as

ps (k+ 1) =

1

TsRsLrLsLr L2m

s(k)

+ TsRsLmLsLr L2m

r(k) + Tsvo(k) (13)

pr (k+ 1) = TsRrLm

LsLr L2m

s(k)

+

1

TsRrLsLsLr L2m

r(k)jpTs(k)r(k)

(14)

whereTs is the sampling period. An alternative approach is tocompute the state-space representation of (11) and (12), and

apply a discretization process similar to the one presented for

the input filter in the next section [31][33]. This approach must

deal with the fact that in (14) changes in time, causing thestate-space representation to be a linear time-varying system.

Although under certain assumptions, this method produces a

more accurate representation [33], the time-varying nature of the


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system implies more computational requirements. This forces

the control platform to use a higher sampling time, which could

produce a deterioration in the performance of the drive [24].

Equations (10), (13), and (14) are used by the proposed

method to predict the stator flux and the electric torque pro-

duced by the IM during the next sampling interval if a certain

voltage vector vo(k)is applied from the MC.3) Input Filter Model: The input filters dynamic can be

described by the following continuous-time equations [27], [31]

as

vs =Rfis+ Lfdisdt

+ ve (15)

is = ie+ Cfdvedt

(16)

whereLfandRfare the inductance and resistance from the lineand filter, and Cfis the filter capacitance. This continuous-timesystem can be rewritten as

x(t) = 0

1

Cf

1

Lf

RfLf

A c

x(t) + 0

1

Cf

1

Lf 0

Bc

u(t) (17)

with

x(t) =

ve

is

and u(t) =

vs

ie

. (18)

A discrete state-space model can be derived when a zero-order

hold input is applied to a continuous-time system described in

state space form as (17). Considering a sampling period, Ts , the

discrete-time system derived from (17) is

x(k+ 1) = Aqx(k) + Bqu(k) (19)

with

Aq =eAc Ts and Bq =

Ts0

eAc(Ts)Bcd. (20)

Discrete-time variables will match continuous-time variables at

the sampling instants [31]. To predict the grids current, it is

possible to solveis(k+ 1) from (19) as

ips (k+ 1) = Aq(2, 1)ve(k) + Aq(2, 2)is(k)

+B

q(2, 1)vs

(k) +B

q(2, 2)ie

(k) (21)where (m,n)is the(m,n)element of matrix . To analyzethe resulting effect on the reactive input power, it is necessary to

consider the instantaneous power theory [36]. The instantaneous

reactive input power can be predicted, based on predictions of

the input current, as

Qp(k+ 1) =Im{vs(k+ 1)ips (k+ 1)}

=vs(k+ 1)ips (k+ 1) vs (k+ 1)i

ps(k+ 1).

(22)

Line voltages are low-frequency signals. Based on this, the

method considers vs(k+ 1) vs(k).

Fig. 4. Time diagram of the calculations performed during the sampling in-terval between timek andk + 1.

C. Time Frame for the Calculations

Equations (10), (13), (14), and (22) are used to obtain pre-

dictions of torque, flux, and reactive power for each of the 27

valid switching combinations. The cost of a switching state is

evaluated applying these predictions in (3). Nevertheless, it is

important to evaluate the predictions at the appropriate sam-

pling instant, taking into consideration the computational re-

quirements of a real implementation of the method. An expla-

nation of the tasks that the control processor must perform is

presented in Fig. 4. The switching state that was selected at the

preceding sampling interval will be applied between time (k)and(k+ 1) (shadowed sampling interval in Fig. 4). The algo-rithm begins by acquiring measurementsof the systemvariables.

Then, the model is used to update, at time(k+ 1), the variablesthat will be required for the prediction. This process implies

a one-step-forward estimation using the equations described in

Section III-B, considering that the switching state that was pre-

viously selected at thepreceding sampling interval is held during

the present interval (k) to (k+ 1). Consequently, this processimplies just one application or use of the prediction model, i.e.,

only for the previously selected switching state, as indicated in

Fig. 4 asactualization at time (k+ 1). This step, previous to the

exhaustive search algorithm based on predictions, is usually notexplained when presenting similar MPC strategies. However,

this delay affects the performance of the control technique and

has been considered in previous reports [17], [28], [29].

After updating the variables at time (k+ 1), it is possibleto start with the predictive algorithm to analyze the effect that

every feasible switching state would produce if applied during

the next sampling interval. It is important to notice that this

process, presented in Fig 4 as predictions for each switching

state, is also computed within the shadowed sampling interval

(k)to(k+ 1). It implies calculating predictions for each of the27 switching states, in order to evaluate these predictions by

means ofg and select the best state for the period (k+ 1) to(k+ 2). The effect of the switching state under evaluation, tobe applied at time (k+ 1), must be assessed at time (k+ 2),since this is when its effects will be noticeable in the system.

A flow diagram of the steps required to implement the strategy

on a digital control platform is presented in Fig. 5. It is worth

noting that the prediction equation used from time (k+ 1) to(k+ 2) are the same as equations used from time (k)to(k+ 1)(see Section III-B) shifting one-step forward in time.

D. Adjusting the Weighting Factors

The PTC method presented in this paper uses three weight-

ing factors that the designer must adjust: Tor torque control


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Fig. 5. Flow diagram of the implemented code on the control platform.

parameter, or flux control parameter, and Q or reactive in-

put power control parameter. These weighting factors handle

the cost assigned to each specific objective within the quality

function g. As mentioned, only two of these factors are requiredto adjust the method, the third can be kept constant. In this sense,

the value ofTis set constant at T = 1 (Nm)1 .

The proposed control technique can be classified as finite-

state model predictive control (FS-MPC). FS-MPC has emerged

as a promising control tool for power converters and drives [24].

One of the major advantages is the possibility to control several

system variables with a single control law, by including them

with appropriate weighting factors, as PTC does with torque,

flux, and reactive input power (it would be possible to add

further variables in order to improve theperformance of the drive

in specific topics). However, these coefficients are determined

empirically. The design problem is to select appropriate values

for these weighting factors. The topic has been treated in [24]

and [37] and the reported method implies testing feasible values

until reaching to an appropriate result. The method exposed in

these publications gives guidelines to starting the search processand sets boundaries for the exploration. In the specific case of

PTC, an appropriate starting point for the search process is to

consider the three objectives with an equal relative importance.

This implies considering the nominal values (indicated by a

subscript N) of the variables that are being balanced in theequation. In this sense

T TN = sN = Q (isNvsN) =K (23)

whereKis an arbitrary constant. As an example, for K= 73and considering the parameters of the experimental setup (see

Table I), the result is T = 1 (Nm)1 , = 72 Wb

1 , and

Q = 0.02 (VA)1

. The value ofK was chosen in order to

TABLE 1PARAMETERS OF THEMC SETUP ANDCONTROLMETHOD

obtain the required value ofT = 1 (Nm)1 . Note that this is

only a suggested starting point for a search process over and

Q for finding the optimum values [37].

A series of 6161 simulations were carried out in order to

analyze the performance of the method under a wide range of

parameter values and to define the optimum set of weighting

factors. This exhaustive search process was performed setting

T = 1(Nm)1 and sweeping Q in 101 equidistant values

between 0 and 0.025(VA)1 , and in 61 equidistant intervals

between1and 301 Wb1

. Each value ofQ is tested with eachvalue of , resulting in the total of 6161 simulations.

The total harmonic distortion (THD) of the input current is ,and the standard deviation of the flux and torque signals were

considered as merit functions, defined to evaluate the perfor-

mance of the system working under each set of parameters. The

following definition for the standard deviation of a data vector

xwas considered:

x =

1n 1

ni= 1

(xi x)2 wherex= 1

n

ni= 1

xi (24)

and n is the number of elements in the sample. The result of the

exhaustive search process, in terms of the standard deviation ofthe flux and torque, and the THD of the input current, is shown

in Fig. 6. In the graphics, a logarithmic function is applied to

the merit functions, to help in the visualization of the plotted

information. The darker areas represent the regions where the

merit functions reach low values, indicating a good performance

of the system in terms of the specific objective (flux, torque, and

input current, respectively). These regions are highlighted in the

images by a white scattered line, defined as acceptable regions

on each case.

It is possible to observe, based on Fig. 6 (left), that there is

a minimum acceptable value of , and that for greater values

of , higher values ofQ are admissible. From Fig. 6 (center),


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Fig. 8. Experimental setup. (Upper) Converter. (Lower right) Machine.(Lower left) interface circuits.

solely on experimental results, as a solid basis to demonstrate

the effectiveness of the method.

A. Setup Description and Implementation Issues

An11kW,4-pole IM is connected to an MC with 50 A peakoutput current capability running at 400 V grid voltage. The MCconsists of an arrangement of 18 insulated-gate bipolar transis-

tors (IGBTs) (IXDN 55N120D1) in common emitter configu-

ration, and additional filter and protection components. Control

of the commutation and overcurrent protection is provided by

an field programmable gate array (FPGA) circuit, following acurrent-controlled four-step commutation scheme. The dc load

machine is fed from a line-commutated thyristor rectifier with an

appropriate armature current control to apply torque within the

range from50 to 50 Nm, whereas the IM control system con-tains a speed controller, according to Fig. 3. The experimental

setup converter, IM, and necessary interface boards are shown

in Fig. 8. A powerful dSPACE 1103 rapid prototyping platform

is used to implement the predictive control strategy. Its 1 GHzclock frequency allows for a sampling time of 14.5 s for thepredictive torque and reactive input power control. The super-

imposed speed control loop is handled at 290 s sampling time,using a standard PI controller. The predictive torque and reactive

power control algorithm is implemented in C code, followingthe two-step approach previously explained to compensate the

calculation delay. Field weakening is easily achieved by reduc-

ing the flux reference value for a speed rage over 1330 r/min. A

complete list of parameters of the system and control strategy

are included in Table I.

A key aspect of the experimental implementation of the con-

trol method is the flux observer (see Fig. 3). Since the proposed

method is based on the calculation of the actual flux in the IM,

this estimation has to be as accurate and reliable as possible.

Equations (13) and (14) are used to predict the future behav-

ior of the IM, but there might be differences in the result of

the calculation and the real value, depending on the knowledge

Fig. 9. Block diagram of theelectrical part of an IM (discrete-time equations).

of the machines parameters. To reduce the error, a simple P

(proportional) controller is applied in the predictive formulas,

specifically in the stator voltage equation, to implement the flux

observer. In this flux observer, the P controller corrects the pre-

dicted value based on the measurement of the stator current. By

correcting the calculated stator current, both the stator and rotor

flux estimations are corrected to be closer to their actual values.

The procedure is explained in the following paragraph and is

based on the previously presented IM model.

As stated in Section III-B.2, (13) and (14) are discrete-time

versions of the stator and rotor voltage equations, respectively,

reached after solving the stator and rotor currents in terms of thestator and rotor fluxes. It is possible to express (13) to explicitly

show the stator current as

s(k+ 1) =s(k) TsRs

LrLsLr L2m

s(k) Lm

LsLr L2mr(k)

io(k )

+ Tsvo(k).

(25)

By means of (13) and (14), it is possible to build an equivalentblock diagram for the electrical part of the IM, as shown in

Fig. 9, with = 1/LsLr L2m . As presented in the figure, (13)and (14) allow access to the stator and rotor flux from a one-

step prediction. Note that this model includes both the stator

and rotor voltage equations. If the machines parameters were

exactly known, no more effort would be necessary to match the

observed to the real values, and these equations could be used as

they are for the flux observer. Since there is always a mismatch

in the parametersas well as variations caused by temperature,

etc.the flux observing equations can be improved by adding

an additional input based on measurements to correct the result

considering the real behavior of the machine.


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Fig. 15. Input and output electric variables in steady state without reactiveinput power control, Q = 0 (VA)

1 : output current and voltage, input current(voltages phase in dotted line), and reactive input power.

Fig. 16. Input and output electric variables in steady state including reactiveinput power control, Q = 0.003 (VA)

1 (optimum set of weighting factors):

output current and voltage, input current (voltages phase in dotted line), andreactive input power.

Figs. 15 and 16 for two reasons: the low-pass filtering nature of

the load and the fact that the predictive method considers the

instantaneous (updated) value of the input voltages, considering

this variation in the strategy.

In Figs. 17 and 18, the harmonic content of the input current

and output voltage for Q = 0 (VA)1 and Q = 0.003 (VA)

1

are shown. Figs. 17 and 18 represent the spectrum analysis of

variables shown in Figs. 15 and 16 in the time domain, respec-

tively. It is possible to observe a drastic reduction on the inputcurrents distortion by including the strategy to control reactive

power. The THD ofiu was reduced from 75.1%to 17.6%, alsoadding the correct phase to synchronize it with the input voltage,

as shown in Fig. 16. A high amount of energy can be seen at

the input filters resonance frequency fr = 1/2LfCf near

2 kHz. The method effectively avoids exciting this resonance in

order to reduce the total distortion in Fig. 18.

The output voltage presents, in both cases, a spread spec-

trum, with significant energy in a wide range of frequencies.

This is an attribute of many nonlinear or nonmodulated control

methods. For the presented predictive approach, a concentrated

spectrum can be reached by applying the strategy described

Fig. 17. Spectrum analysis without the strategy to control reactive power,Q = 0 ( VA)

1 . (Top) Input currentiu . (Bottom) Output voltageva b .

Fig. 18. Spectrum analysis including the strategy to control reactive power,Q = 0.003 (VA)1 (optimum set of weighting factors). (Top) Input current

iu . (Bottom) Output voltageva b .

in [28]. The MCs switched output pattern and the methods

fixed time period for the switching states transitions is notice-

able by a higher amplitude harmonic at the sampling frequency

fs = 1/Ts = 69kHz. Nevertheless, the average switching fre-quency per IGBTfsfis considerably lower. The highest reach-able value isfsf =fs/6 = 11.5 kHz, assuming the maximumnumber of transitions as each Ts[27], [31]. In practice, the mea-

sured average switching frequency per IGBT was fsf = 6kHz.A last test of the performance of the drive is shown in Fig. 19,

applying a step change on the reference torque using the op-

timum set of weighting factors. The IM starts from standstill,

delivering only magnetizing current from the MC. No torque is

applied from the drive. At timet = 94ms, the reference torqueTe is modified externally (the speed controller is bypassed) fromzero to maximum torque. It is possible to observe in Fig. 19 how

the machines torque reaches its reference value in around1ms,the motors current is fast forced to a sinusoidal waveform, and

the speed increases with a rate proportional to Te . The torquemeasurement is obtained based on the result delivered by the

flux observer and (10).


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Fig. 19. Behavior of the system under a step change on the reference torque (0to80 Nm): speed, output current, and electric and reference torque.

V. CONCLUSION

The proposed control method for an MC-based IM drive has

been shown to give excellent performance, effectively control-

ling both the machine and the input current. The method has afast torque response, unity PF with low reactive power deliv-

ered to the mains, and low torque and flux ripple. PTC consid-

ers a fictional cost assigned to specific objectives, balanced by

weighting factors. These factors are determined by analyzing

the performance of the system for different values.

The presented control approach represents a basic frame in

which other features can be added [24][31], for example, to

improve the efficiency of the drive [32]. The objectives of this

paper areto introducethe methodand itstheoreticalbackground,

analyzing, in depth, the most relevant issues related to its im-

plementation and showing its excellent performance based on

experimental results. An assessment with conventional control

and modulation methods was not included in the scope of this

paper and is a topic that will be faced in the next step of this

research.

PTC takes advantage of the discrete nature of the MCs

switching states and the control processor. The method also

utilizes the rotating vectors, usually discarded by MC modula-

tion techniques. The high sampling frequency required should

not be a problem nowadays, opening interesting possibilities

with a conceptually different approach to optimization in the

control of power converters and drives.

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Rene Vargas (S05M09) received the Engineerand M.Sc. degrees in electronics engineering, in2005, and the Ph.D. degree for his work on predic-tive control applied to matrix converters, in 2009,from the Universidad Tecnica Federico Santa Mara(UTFSM), Valparaso, Chile.

For a total period of eight months within20062008, he was with the Institute of Power Elec-tronics and Electrical Drives, University of Stuttgart,Germany. In 2009, he was a Research Assistant atthe Power Electronics Research Group, UTFSM. In

2010, he joined ABB Switzerland, R&D Traction Converters, as DevelopmentEngineer. He has authored or coauthored over 20 papers in leading internationalconferences and journals, mainly on the topic of new control techniques applied

to power conversion and drives.

Ulrich Ammann(M06) received the Dipl.-Ing. de-gree in electrical engineering in 2002 from the Uni-versity of Stuttgart, Stuttgart, Germany, where heis currently working toward the Ph.D. degree indiscrete-time modulation schemes, including predic-tive techniques.

In 2002, he joined the Institute of Power Electron-ics and Electrical Drives, University of Stuttgart, asa Research Assistant. His current research interestsinclude electric drives, high-power current sources,and automotive power electronics.

Boris Hudoffsky received the Dipl.-Ing. (F.H.) de-gree in mechanical engineering and automationin 2001 from the University of Applied ScienceFurtwangen, Furtwangen, Germany, and the Dipl.-Ing. degree in electrical engineering in 2007 from theUniversity of Stuttgart, Stuttgart, Germany, where heis currently working toward the Ph.D. degree in cur-rent measurement at the Institute of Power Electron-ics and Electrical Drives.

Since 2001, he has been with TR Electronic

GmbH, Trossingen, Germany for three years.

Jose Rodriguez (M81SM94) received the Engi-neer degree in electrical engineering from the Uni-versidad Tecnica Federico Santa Mara (UTFSM),Valparaso, Chile, in 1977, and the Dr.-Ing. de-gree in electrical engineering from the University ofErlangen, Erlangen, Germany, in 1985.

Since 1977, he has been a Professor with theUTFSM, where he was the Director of the Electron-ics Engineering Department from 2001 to 2004, theVice Rector of academic affairs from 2004 to 2005,and has been a Rector since 2005. During his sabbat-

ical leave in 1996, he was with Siemens Corporation, Santiago, Chile, where

he was responsible for the mining division. He has extensive consulting experi-ence in the mining industry, particularly in the application of large drives, suchas cycloconverter-fed synchronous motors for semiautogenous grinding mills,high-power conveyors, controlled ac drives for shovels, and power quality is-sues. He wasthe Director of more than 40 R&Dprojectsin thefield of industrialelectronics. He has coauthored more than 250 journal and conference papers,and has contributed one book chapter. His research group has been recognizedas one of the two centers of excellence in engineering in Chile in 2005 and2006. His current research interests include multilevel inverters, new convertertopologies, and adjustable-speed drives.

Prof. Rodriguez is an active Associate Editor of the IEEE Power Electronicsand the IEEE Industrial Electronics Societies since 2002. He was the GuestEditor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICSin five op-portunities [Special Sections on Matrix Converters (2002), Multilevel Inverters(2002), Modern Rectifiers (2005), High-Power Drives (2007), and PredictiveControl of Power Electronic Drives (2008)].

Patrick Wheeler (M00) receivedthe B.Eng. (Hons.)degree and the Ph.D. degree in electrical engineeringfrom the University of Bristol, Bristol, U.K., in 1990and 1994, respectively.

Since 1993, he has been with the University ofNottingham, Nottingham, U.K., where he was a Re-search Assistant in the Department of Electrical andElectronic Engineering, a Lecturer in the Power Elec-tronics, Machines and Control Group during 1996,and has been a Full Professor in the same researchgroup since January 2008. He has authored or coau-

thored more than 200 papers in leading international conferences and jour-nals. His research interests include power conversion and more electric aircraft

technology.

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Predictive Torque Control