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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 1, JANUARY 2012 307

A Comparison of Four Robust Control Schemes forField-Weakening Operation of Induction Motors

Michele Mengoni, Luca Zarri, Member, IEEE, Angelo Tani, Giovanni Serra, Senior Member, IEEE,and Domenico Casadei, Senior Member, IEEE

AbstractFour sensorless control schemes for the operation ofinduction motors in the field-weakening region are compared andassessed in terms of performance and complexity. These four con-trol schemes fully utilize the maximum available voltage and cur-rent and can produce the maximum possible torque in the entirefield-weakening region. For comparison, the four control schemesare implemented on the same experimental platform, i.e., the sameDSP board, power inverter, and motor drive. In this way, it is possi-ble to assess not only the performance of each solution, but also itsrequirements in terms of computational time, tuning complexity,parameter knowledge, and stability of operation.

Index TermsAC motor drives, torque control, traction motordrives, variable speed drives, velocity control.

I. INTRODUCTION

POWER electronics has deeply changed the use of induction

motors in automotive or automation applications, giving

them the capability of fast torque response and, consequently, a

full control of the drive speed.

When the induction motors are used for applications at high

speed, it is desirable to retain the maximum torque capability

in the field-weakening region. Several papers about this issue

were presented [1][4]. According to these field-weakening al-gorithms, the optimal flux value of the motor should be updated

by means of lookup tables or explicit expressions containing the

motor parameters and quantities, such as the motor speed, the

motor currents, the dc-link voltage, and the requested torque.

However, the performance of these algorithms is strictly related

to the accuracy by which the parameters are known. A further

problem is represented by the variable value of the leakage

and magnetizing inductances, to which the rotor-flux-oriented

scheme is particularly sensitive [5]. In addition, the drive perfor-

mance in the high-speed range may depend on the correct deter-

mination of the base speed, which is the function of the actual

dc-link voltage and the overload capability. As a consequence,

new methods for compensating the parameter variations and

Manuscript received December 17, 2010; revised February 24, 2011 andApril 22, 2011; accepted May 1, 2011. Date of current version December 16,2011. Recommended for publication by Associate Editor R. M. Kennel.

The authors are with the Department of Electrical Engineering, Universityof Bologna, 40136 Bologna, Italy (e-mail: [email protected]; [email protected]; [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.2011.2156810

the uncertainties of the models have been investigated. Among

these, some adaptive schemes have been proposed in order to

provide a suitable estimation of the varying parameters [6][9].

These methods provide good drive performance to the detri-

ment of the complexity of the control scheme and the regulator

tuning.

For the aforementioned reasons, the stator-flux-oriented

drive, more insensitive to parameter variations than the rotor-

flux-oriented one, has received increasing attention for field-

weakening applications [10][13]. The stator-flux-oriented con-

trol is usually appreciated for its simplicity and is often proposedfor low-cost applications.

An alternative method for robust field weakening is to de-

termine the optimal flux level using closed-loop schemes that

analyze the motor behavior, rather than lookup tables or explicit

expressions containing the motor parameters.

During the last ten years, several important contributions

toward robust field-weakening strategies have been proposed

in [14] and [15] for stator-flux-oriented induction motor drives

and in [16][20] for rotor-flux-oriented induction motor drives.

According to these papers, the flux level is adjusted on the ba-

sis of the supply voltage requested by the regulators, and the

maximum torque capability is exploited by means of a suitablecontrol strategy.

Some comparisons among different control schemes can be

found in [21] and [22]. In particular, the aim of this paper is

to extend the analysis carried out in [22] by assessing four

speed control schemes for the sensorless operation of induction

motors in the field-weakening region in terms of performance

and complexity.

These four control schemes fully utilize the available inverter

voltage and the maximum inverter current for steady-state torque

production at any speed and, thus, provide the maximum pos-

sible torque in the entire field-weakening region. In addition,

all these control algorithms are robust, i.e., they are insensitive

to changes of the machine parameters and to variations of the

dc-link voltage.

The four control schemes are different in terms of number and

type of regulators, complexity of implementation, and transient

behavior.

It is rather difficult to compare their performances, since they

are often proposed in the literature with reference to different

hardware architectures.

For these reasons, for the comparison presented in this paper,

these schemes have been implemented on the same experimen-

tal platform, i.e., the same DSP, power inverter, and induction

motor, and use the same basic functions, such as the voltage

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308 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 1, JANUARY 2012

Fig. 1. Block diagram of control Scheme A.

modulator. In this way, it is possible to assess not only the

performance of each solution, but also its requirements in

terms of computational burden, calibration complexity, param-

eter knowledge, and operating stability.

II. OPERATINGPRINCIPLES OF THEROBUST

FIELD-WEAKENINGCONTROLSCHEMES

In the high-speed range, the performance of an induction mo-

tor is limited by the maximum inverter voltageVs, m ax , related

to the dc-link voltage, and the inverter/machine current rating,

represented by the maximum stator current Is, m ax .

Due to these limits, the motor operation can be divided into

three speed ranges, namely the low-speed range (Region I),

the constant-power speed range (Region II), and the decreasing

power speed range (Region III).

The current limit determines the maximum torque that can

be generated in Regions I and II. In particular, in Region I, the

maximum torque corresponds to the maximum current and to

the rated flux level, whereas in Regions II and III, it is necessary

to reduce the flux magnitude to keep the back electromotive

force (EMF) approximately constant.When the motor operates in Region III, the maximum torque

is delivered to the load when the angle between the stator and

rotor flux vectors is45[20]. One comes to this conclusion byinspecting the following equation, which expresses the motor

torque when the stator voltage magnitude equals Vs, ma x [20]:

T= 34p M2

L2sLr

Vs,m axr

2sin2 (1)

where 2pis the number of poles; Ls ,Lr , and Mare the motor

self and mutual inductances;r is the angular speed of the rotorflux vector with respect to a stationary reference frame; is

the angle between the stator and rotor flux vectors; and is the

leakage coefficient defined as follows:

= 1 M2

LsLr. (2)

From (1), it is clear that, for any value ofr , the maximumtorque is produced when the angle between the stator and rotor

flux vectors is 45, i.e.,= 45. This fundamental relationshipis used by the four control schemes compared in this paper to

achieve the maximum torque operation in Region III.There are different ways to express the condition =45.

An equivalent formulation considers the input voltage vector

instead of the stator flux vector. Since the input voltage vector

leads the stator flux vector by nearly 90, the condition of max-imum torque satisfies when the angle between the input voltage

vector and the rotor flux vector is 9045, namely 135 formotor operation or 45 for generator operation.

III. DESCRIPTION OF THECONTROLSCHEMES

In this paper, four sensorless robust field-weakening con-

trol schemes for induction motors are compared. The first one

(Scheme A) is the control scheme of a stator-flux-orienteddrive, and its basic principle was presented in [15]. The sec-

ond one (Scheme B), the third one (Scheme C), and the fourth

one (Scheme D) are the control schemes of rotor-flux-oriented

drives, and their basic principles were presented in [16], [19],

and [20], respectively.

These control schemes were selected because they are rather

recent and are based on the common principle of analyzing the

motor voltage to adjust the flux level.

A. Control Scheme A

The block diagram of Scheme A is shown in Fig. 1. For

a better understanding of the figure, some symbols should be

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MENGONI et al.: COMPARISON OF FOUR ROBUST CONTROL SCHEMES FOR FIELD-WEAKENING OPERATION OF INDUCTION MOTORS 309

clarified. The signals starting from a little circle (O) are user

set points, such as speed reference m, re f, or the maximumabsolute ratings, such asVs, m ax and Is, m ax . The signals starting

from a little triangle () come from somewhere else in thecontrol scheme, although the wirings are not shown to keep the

scheme as simple as possible.

The control scheme of Fig. 1 is implemented in a reference

frame that is synchronous with the stator flux vector. The main

control variables are the stator flux magnitude s and the q-component of the stator currentisq.

In Fig. 1, the speed is adjusted by the PI regulator (a), which

generates the request of torque-producing current isq ,re q . The

current reference is tracked on its turn by the PI regulator (d).

Due to the action of the saturation block (g), isq ,re f is limited

in such a way that the stator current magnitude cannot exceed

Is,m ax in Regions I and II. In this case, the maximum value for

isq ,re fdepends on the currentisd used for the generation of the

flux. The greater isisd , the lower isisq ,ma x . In Region III, the PI

regulator (e) further decreases isq ,ma x until the angle between

the stator and rotor flux vectors is 45, i.e., the maximum torquecondition is satisfied.

The stator flux command is generated by the PI regulator (b)

on the basis of the voltage request. If this request is greater than

the available voltage, the field-weakening algorithm reduces the

flux; otherwise, the flux is increased, but not beyond its rated

value.

Finally, the switch (s) can create a temporary voltage margin

to enable a fast reaction of the current controller, in order to

improve the transient behavior. If the requested voltage is greater

than the available voltage, i.e., the flux is being decreased, the

switch (s) is closed and the angle s of the reference frame

is modified by adding a small quantity s proportional tothe speed error. As a consequence, this small rotation of thereference frame, applied to the stator voltage, has the effect of

improving the torque production to the detriment of the flux,

especially, at the beginning of the speed transient [15].

Although this last algorithm has the aim of improving the

behavior of the motor during the speed transients in the field-

weakening speed range, actually, it is not essential for the field-

weakening operation. Hence, for the sake of simplicity, the ef-

fects related to the switch (s) have not been considered in this

paper.

It is worth noting that this control scheme does not control

thed-component of the stator current directly. For this reason, if

the response of PI (b) is very fast, thed-component of the motormay reach a very high peak during the magnetization transient.

It is possible to come to this conclusion by expressing isd as

follows:

isd = 1

Ls

s M

Lrrd

(3)

whererd is thed-component of the rotor flux vector.Equation (3) shows that thed-component of the stator current

is limited by the rotor flux. Before the motor startup, the rotor

flux magnitude is zero, and this explains why a sudden stator

flux request may cause a very high magnetizing current.

To prevent this occurrence, a widely used remedy is to in-

crease the stator flux set point slowly up to the rated value

during the motor startup. Although this solution is very com-

mon, it is not the best one, because the optimal slope of the

ramp depends on the motor parameters, and it is not completely

integrated in the normal control scheme.

The solution proposed in Fig. 1, not presented in [15], is to

insert a variable upper bound on the stator flux in block (f). This

bound should be s, rated during the steady-state operation ofthe machine, but during the magnetizing transients, re fshouldnot overcome the limit values, lim given by

s, lim =M

Lrrd+ LsIs,m ax . (4)

Under the assumption that the rotor flux varies more slowly than

the other quantities, ifs is lower thans, lim , then the currentisd is lower than Is, m ax whatever fast the response of PI (b) is

and, in particular, during the magnetization transient.

Although (4) requires the knowledge of the leakage induc-

tanceLs , the estimation of the rotor flux is not necessary. Infact, it is possible to find an alternative formulation ofs, lim bysolving (3) forrd and substituting its expression in (4). It turnsout that

s, lim =s+ Ls(Is,m axisd ) . (5)In conclusion, the upper bound of the limitation block (f) shown

in Fig. 1 is calculated as follows:

s,ma x = min {s, rated, s, lim } (6)wheres, rated is the rated flux, and s, lim is given by (5).

B. Control Scheme B

The block diagram of the control Scheme B is shown in Fig. 2.

The control scheme is implemented in a reference frame that

moves synchronously with the rotor flux vector.

The motor currents, which are the main control variables, are

adjusted by the PI regulators (c) and (d). The d-component of

the stator current is used to regulate the rotor flux, whereas the

q-component is used to vary the motor torque.

To adjust the field level, this scheme uses the same method as

in Scheme A, namely the reference value for isd is set by the PI

regulator (b) on the basis of the voltage request. If the voltage

request is greater than the available voltage, the flux level isreduced; otherwise, it is increased up to the rated value.

The speed is controlled by the regulator (a), which generates

the reference value forisq. The limitation block (g) ensures that

the constraint on the maximum stator current is met in Regions

I and II and, also, ensures the exploitation of the maximum

torque capability in Region III. In fact, the upper and lower

bounds of the limitation block (g), respectively, are +isq ,m axandisq ,m ax , i.e., the output signal of the limitation block (h).The signal isq ,m ax is equal to

I2s,ma xi2sd ,re f in Regions I and

II, whereas in Region III, it decreases until the absolute value of

thevsd is equal to(Vs,ma x/

2). As explained in Section II, this

condition means that, under the assumption that the maximum

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Fig. 2. Block diagram of control Scheme B.

Fig. 3. Block diagram of control Scheme C.

voltage is applied to the motor, the phase angle of the voltage

vector in the rotor-flux-oriented reference frame is 9045.C. Control Scheme C

The block diagram of the control Scheme C is shown in Fig. 3.

This control scheme is implemented in a reference frame that

is synchronous with the rotor flux vector. As can be seen, this

control scheme is very similar to Scheme B. The motor currents

are adjusted by the PI regulators (c) and (d). The d-component

of the stator current is used to regulate the rotor flux, whereas

theq-component is used to control the motor torque.

To adjust the field level, the reference value of isd is set

by the PI regulator (b) on the basis of the voltage request. If

the voltage request is greater than the available voltage, the

flux level is reduced; otherwise, it is increased up to the ratedvalue.

The speed is controlled by the regulator (a) that generates

the reference value for isq. The limitation blocks (f) and (g)

ensure that the constraint on the stator current is satisfied in

Regions I and II and, also, the exploitation of the maxi-

mum torque capability in Region III. However, unlike control

Schemes A and B, these conditions are obtained without using

additional regulators, but only with algebraic relationships.

In fact, the signal isq ,ma x , which is used to generate the up-

per and the lower bounds of limitation block (g), is equal toI2s,ma xi2sd in Regions I and II, whereas, in Region III, when

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Fig. 4. Block diagram of control Scheme D.

the condition=45 is verified, it is equal to

isq =sdLs

. (7)

Equation (7) means that sq is equal tosd , i.e., the phaseangle of the stator flux vector is45in a rotor reference frame.

Although this solution is very simple, it has the counterpart

of requiring the knowledge of the d-component of the stator

flux vector and of the parameter Ls . Both of these are oftennecessary in the flux observer for the determination of the rotor-

field-oriented reference frame. Therefore, their knowledge isnot usually an additional burden.

D. Control Scheme D

The block diagram of the control Scheme D is shown in Fig. 4.

In this rotor-flux-oriented control scheme, the main control vari-

ables are the components of the stator flux vector instead of the

stator current components.

To understand the control principle, it is useful to recall the

main motor equations written in terms of stator flux components

in a rotor-flux-oriented reference frame [20]:

LrRr

drdt

+r = MLs

sd (8)

T = 3

2p

M

LsLrrsq. (9)

As can be seen, (8) and (9) are quitesimilar to the corresponding

equations of the traditional field-oriented control based on dqstator current components. In fact, the rotor flux depends only

onsd , whereas the motor torque is proportional tosq.According to (9), the torque demand is transformed by the

speed regulator (a) in the request of the q-component of the

stator flux.

The limitation block (b), which works as in Scheme C, en-

sures the respect of the constraint on the maximum current in

Region II and the maximum torque capability in Region III. To

satisfy the condition =45,sqhas to be equal tosd ,whereas the overcoming of the maximum current is prevented

by ensuring that the absolute value ofsq , re fis lower than thequantitysq ,available.

The stator flux regulator behaves as a proportional controller,

with some additional terms compensating the stator back EMF

and the voltage drop caused by the stator resistance. The equa-

tions of the stator flux regulator can be expressed as follows:

vsd ,re q =Rsisdrsq+ sd ,re fsdd

(10)

vsq ,re q =Rsisq+rsd +sq ,re fsq

q(11)

where 1/d and 1/qare the gains of the controller, andr is theangular frequency of the rotor flux vector. It is worth noting that

it is possible to selectdequal to q, but it could be convenient toadopt two different time constants to the advantage of flexibility

in the tuning of the regulators.

The rotor flux is controlled by adjusting the d-component

of the stator flux. However, the basic principle that regu-lates the flux-weakening request is quite different from that of

Schemes A, B, and C. It is widely known that, if the motor op-

erates at constant speed, fast torque responses can be achieved

only if the control scheme keeps the flux level constant during

the torque transients. In particular, the flux level should always

be set to the value required to generate the maximum achiev-

able torque at any operating speed. In this way, any demand

of torque variations within the admissible values is achieved

without changingsd but onlysq.For a given value of the d-component of the stator flux, and

consequently of the rotor flux, the maximum torque is achieved

whensq , re f =sq ,ma x .

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Taking this equation into account, the voltage required to

generate the maximum torque can be determined from (10) and

(11) as follows:

vsd ,max req =Rs isdr,ma x(signsq)sq ,m ax+sd ,re fsd

d

(12)

vsq ,max req =Rs isq ,m ax + r,m axsd +sq ,re fsq

q(13)

whereisq ,m ax is defined as follows:

isq ,m ax =sq ,m axLs

. (14)

Here,r,ma x is the angular frequency of the rotor flux corre-sponding to the maximum torque, which is expressed by

r,m ax =r + (signsq) RrLr

sq ,ma x |sq|sd

. (15)

It is worth noting that in practical applications, it is possible toapproximater,m ax with r , and therefore, the knowledge ofthe rotor parameters is not necessary.

In Scheme D, the flux request sd , re q is reduced only ifthe maximum torque that could be generated at a given speed

requires a voltage greater thanVs, m ax . In other words, the flux

level is alwaysset to the value required to generate the maximum

achievable torque at any speed.

Theuse of flux components as control variables is very similar

to that of the traditional vector control based on the regulation

of the stator currents. However, a little attention should be paid

during the start-up transient, because the stator flux reference

cannot change too quickly, in order to avoid overcurrents. The

analysis of the overcurrent problem is very similar to the one

of Scheme A, and therefore, it can be solved in the same way.

In other words, the upper bound of the saturation block (f) in

Fig. 4 is varied according to the following quantity:

sd ,m ax = min {sd ,rated, sd ,lim } (16)wheresd , ratedis the rated flux, and sd , lim is given as

sd ,lim =Ls(Is,m axisd ) +sd . (17)As can be seen, (17) requires the knowledge of the leakage

inductanceLs , which is already used by the control scheme.

IV. TUNING OF THECONTROLSCHEMES

As far as the tuning of the regulators is concerned, the four

schemes present different complexities.

In total, Scheme A requires five PI regulators (two PI regu-

lators are used for the flux and the current control, one for the

speed control, and the other two for the robust field-weakening

algorithm), and if a fast torque response is requested, it is op-

portune to tune also the two constant gains shown in the block

(m).

Scheme B requires five PI regulators (two PI regulators are

used for the current control, one for the speed control, and the

other two for the robust field-weakening algorithm).

Scheme C requires four PI regulators (two PI regulators are

used for the current control, one for the speed control, and

another one for the robust field-weakening algorithm).

Finally, Scheme D requires two PI regulators (the first one

for the speed control and the second one for the robust field-

weakening control), and two gain constants for the flux regula-

tors (10) and (11).

It is quite obvious that if the tuning of a control scheme is not

satisfactory, the comparison among the four control schemes

may be distorted. However, the concept of optimal tuning is

very evanescent without the right context, i.e., without specify-

ing the quality indices and the target application.

In this paper, under the assumption of considering general

purpose electric drives, the goal is to obtain the fastest speed

and torque responses with small or absent overshoot. The well-

known cascade tuning is adopted, i.e., thefirst control loops to be

tuned are the inner ones and, then, the outer ones. Consequently,

the inner loops have the highest bandwidth, whereas the outer

loops have lower cutoff frequencies. It is worth noting that other

methods for the tuning of the regulators could lead to better driveperformance. For example, the simultaneous tuning of all the

regulators of a certain scheme could produce a better response

than that obtained by tuning one regulator after the other, but

requires a greater computational effort.

Since cascade tuning is well known and is adopted also for

on-site applications, it has been assumed as the most suitable

choice.

The criteria used for the tuning of the regulators during the ex-

perimental tests are rather traditional and are beyond the scope

of this paper. However, some comments can be useful to under-

stand the difficulties that have to be overcome.

For the regulators of the inner loops, i.e., regulators (c) and(d) in Schemes A, B, and C, and the stator flux regulators in

Scheme D, some simple design rules can be used, generally,

based on zero-pole cancellations.

The tuning of the other regulators, instead, is more difficult,

because the drive dynamics depends on the motor inertia and

on the field-weakening algorithm itself. So, the tuning of these

regulators has been initially faced by means of numerical sim-

ulations, and then, it has been refined during the experimental

tests by using a trial-and-error procedure.

To conclude, it is worth noting that a proper tuning of the

speed regulators tends to reduce the differences among the con-

trol schemes, because the outer speed loop compensates for the

nonideal behavior of the inner control loops.

V. EXPERIMENTALRESULTS

A complete drive system has been realized to verify the per-

formances of the control schemes. The experimental setup con-

sists of an insulated gate bipolar transistor inverter and a 4-kW,

4-pole squirrel cage induction motor. The parameters of the

electric motor are given in Table I. The electric drive used for

the experimental tests is a didactic product developed for aca-

demic research. For a correct operation of the motor at the

rated speed, the dc-link voltage should be 270 V. However, for

safety reasons, the dc-link of the inverter is limited below 135 V.

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TABLE IMOTORPARAMETERS

TABLE IIREGULATORPARAMETERS

Consequently, the base speed (around 700 r/min) is about half

the rated speed of the motor (1480 r/min).

The control algorithms, written in C code, are implemented

on a DSP TMS320C28. The sampling period (coinciding with

the switching period) is 100s. The parameters of the regulatorsare given in Table II.

It is important to note that the performance of each control

scheme depends on many factors that are not directly related to

the field-weakening control scheme, such as the use of fixed-

point or floating-point math, the compensation for the inverter

dead times, or just the skill of the programmer.

Therefore, the results stated in this section should be consid-

ered as a particular case, which depends on the adopted hardware

architecture.

A. Comparison of the Steady-State and the Transient Behavior

From the analysis of the experimental tests, it is possible tonote that the four control schemes have practically the same

performance in terms of speed response and field-weakening

speed range. Each of them has reached a maximum speed that

is about seven times the base speed. The maximum speed is

practically imposed by the friction torque of the drive bench.

However, each control scheme has shown its own advantages

and disadvantages that are presented hereafter.

Figs. 58 show the behavior of the four control schemes

after a speed step command up to 700% of the base speed.

Since the completion of transients takes too long, the end of

the transients is not shown. Higher speeds cannot be reached

due to the inherent friction torque of the test bench. Each figure

Fig.5. Behaviorof SchemeA duringa speed stepchangefrom0% to700% ofthe basespeed (500ms/div). Fromtop to bottom:angularspeed (2000 r/min/div),stator flux (0.25 Wb/div), q-component of the stator current (20 A/div), andphase current (20 A/div).

Fig.6. Behaviorof SchemeB duringa speed stepchangefrom0% to700% ofthe basespeed (500ms/div). Fromtop to bottom:angularspeed (2000 r/min/div),d-component of the stator current (20 A/div),q-component of the stator current(20 A/div), and phase current (20 A/div).

shows the speed response (at the top) and the corresponding

phase current waveform (at the bottom).

The two intermediate traces of each figure show the wave-forms of the main control variables of each control scheme,

i.e., the stator flux and the current isqfor Scheme A, the stator

current components for Schemes B and C, and the stator flux

components for Scheme D.

In Figs. 58, the extension of Regions II and III is also repre-

sented.

Finally, in Fig. 9, we compare thespectral content of themotor

currents for the four control schemes under a typical operating

condition. The motor torque is 80% of the rated torque, and

the motor speed is 90% of the base speed. As can be seen, the

harmonic content of the currents resulting from Schemes A and

D appears to be higher than that of Schemes B and C.

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Fig.7. Behaviorof SchemeC duringa speed stepchangefrom0% to700% ofthe basespeed (500ms/div). Fromtop to bottom:angularspeed (2000 r/min/div),d-component of the stator current (20 A/div),q-component of the stator current(20 A/div), and phase current (20 A/div).

Fig.8. Behaviorof SchemeD duringa speed stepchangefrom0% to700% ofthe basespeed (500ms/div). Fromtop to bottom:angularspeed (2000 r/min/div),d-component of the stator flux (0.25 Wb/div), q-component of the stator flux(0.25 Wb/div), and phase current (20 A/div).

The main comments that can be made about the performance

of the four schemes are the following.

1) The speed responses of all schemes are very similar, but

Scheme A requires a very fine tuning to avoid small oscil-

lations in Region III.2) The best quality of the motor current is obtained by

Schemes B and C, since the stator current components

are the main control variables. The current quality is pre-

served, also, during the transition from Region I to Region

II and from Region II to Region III.

3) The best flux quality is obtained by Scheme D, since the

stator flux components are the main control variables.

B. Tuning of the Regulators and Robustness

As expected, the tuning of Scheme D is simpler than that of

the other ones, whereas the tuning of Scheme A turns out to be

more complex, particularly of the flux regulators (b) and (c) of

Fig. 9. Experimental results. Spectra of the phase current for the four controlschemes when the motor speed is 90% of the base speed and the motor torqueis 80% of the rated torque. The spectra are normalized with respects to thefundamental component of the current.

Fig. 1, in order to avoid flux and torque oscillations during the

transition from Region II to Region III.

As far as the robustness against parameter uncertainties is

concerned, the performance of the four control schemes is af-

fected mainly by the mismatching of the leakage inductance Lsand of the stator resistanceRs . The parameterLs is importantfor the orientation of the reference frame in Schemes B, C, and

D, which are rotor-flux-oriented controls, whereas Scheme A,

which is a stator-flux-oriented control, is sensitive mainly toRs .

A mismatching onRs could reduce the torque in Scheme D,

since the flux regulators (10) and (11) do not include an integral

term and present a feed-forward compensation of the voltage

drop on the stator resistance.

A mismatching on Ls causes a reduction of the maxi-mum torque that can be delivered by all control schemes in

Region III, since it is related with the angle between the rotorand stator flux vectors, as shown in (1).

In this paper, all the control schemes share the same stator

and rotor flux observer, i.e., a full-state nonlinear identity ob-server. To some extent, this choice could appear questionable,

because Scheme A is a stator-flux-oriented control scheme, and

therefore, it may use some more specific and more performing

flux observers. Nowadays, advanced adaptive observers, which

ensure good behavior even in the case of unknown parameters,

are available [23], [24].

However,under the assumption that the parameters are known

with sufficientaccuracy, it is possible to compare thefour control

schemes without considering the performance of the observer.

On the other side, in the case of mismatching in the parameters

of the observer, the field orientation is not perfect. Since it is

not possible to ascribe the worsening of the performance to thecharacteristics of the schemes, the variation of the parameters is

not further considered.

C. Stability of the Control System

In Figs. 1013, we show the behavior of the four control

schemes during a sequence of speed step changes from the base

speed to 2000 r/min (about 300% of the base speed). As can be

seen, the behavior of the four control schemes is comparable.

However, in Figs. 1417, we show the waveform of some

inner variables, such as theflux level, andreveal that thebehavior

of Schemes A, B, and C is quite different from that of Scheme D.

While the flux level of Scheme D tends to decrease as expected,

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Fig. 10. Behavior of Scheme A during a sequence of speed steps from 0%to 300% of the base speed (500 ms/div). From top to bottom: reference angu-lar speed (2000 r/min/div), angular speed (2000 r/min/div), estimated torque(20 Nm/div), and phase current (20 A/div).

Fig. 11. Behavior of Scheme B during a sequence of speed steps from 0%to 300% of the base speed (500 ms/div). From top to bottom: reference angu-lar speed (2000 r/min/div), angular speed (2000 r/min/div), estimated torque(20 Nm/div), and phase current (20 A/div).

Fig. 12. Behavior of Scheme C during a sequence of speed steps from 0%to 300% of the base speed (500 ms/div). From top to bottom: reference angu-lar speed (2000 r/min/div), angular speed (2000 r/min/div), estimated torque(20 N

m/div), and phase current (20 A/div).

Fig. 13. Behavior of Scheme D during a sequence of speed steps from 0%to 300% of the base speed (500 ms/div). From top to bottom: reference angu-lar speed (2000 r/min/div), angular speed (2000 r/min/div), estimated torque(20 Nm/div), and phase current (20 A/div).

Fig. 14. Behavior of Scheme A during some speed steps from 0% to 300%of the base speed (500 ms/div). From top to bottom: actual angular speed(2000 r/min/div), stator flux magnitude (0.25 Wb/div), q-component of thestator current (20 A/div), and phase current (20 A/div).

the flux level of Schemes A, B, and C presents a short undershot

after each speed step.

The reason is that these control schemes are based on an oper-

ating principle other than that of Scheme D. In fact, as explained

in Section III, Scheme D keeps the rotor flux almost constant

during the torque transient, in order to achieve the fastest torque

response, whereas the other control schemes adjust the flux level

after any torque variation.

These flux oscillations are undesired and could destabilize

the control scheme at high speed. However, the problem of the

stability of the control schemes is very complex and is beyond

the scope of this paper. The reason is that it is strictly dependent

on the characteristics of the electric drives, such as motor size,

the motor parameters, and the total inertia.

The amplitude of the flux undershoot shown in Figs. 1416

is sensitive to the tuning of the regulators, the motor inertia, the

amplitude, and the fastness of the torque step. If the undershoot

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Fig. 15. Behavior of Scheme B during some speed steps from 0% to300% of the base speed (500 ms/div). From top to bottom: angular speed(2000 r/min/div), d- and q-components of the stator flux (0.25 Wb/div), andphase current (20 A/div).

Fig. 16. Behavior of Scheme C during some speed steps from 0% to300% of the base speed (500 ms/div). From top to bottom: angular speed(2000 r/min/div), d- and q-components of the stator flux (0.25 Wb/div), andphase current (20 A/div).

is remarkable, the flux level can go down to zero, and this

prevents the motor from working correctly.

To better explain what kind of stability problems one can

encounter, it is opportune to examine Figs. 1821, which were

obtained by increasing, excessively, the gain of the voltage reg-

ulators that control the flux level. In particular, Scheme B looses

completely the field orientation after a large undershoot of the

flux level and stops, whereas Schemes A and C show an unsat-

isfactory behavior.

It is possible to avoid the flux undershoot by reducing the

gain of the voltage regulators, but in this case another stability

problem can be encountered. When this gain is too low, the

motor drive is not able to enter into the field-weakening region

because the reduction of the flux level is not quick enough.

For example, in Fig. 22, we show the behavior of Scheme B

under these operating conditions, but similar results can also be

obtained for the other schemes.

Fig. 17. Behavior of Scheme D during some speed steps from 0% to300% of the base speed (500 ms/div). From top to bottom: angular speed(2000 r/min/div), d- and q-components of the stator flux (0.25 Wb/div), andphase current (20 A/div).

Fig. 18. Behavior of Scheme A with detuned regulators during some speedsteps from 0% to 150% of the base speed (500 ms/div). From top to bot-tom: actual angular speed (500 r/min/div), stator flux magnitude (0.25 Wb/div),q-component of the stator current (20 A/div), and phase current (20 A/div).

Fig. 19. Behavior of Scheme B with detuned regulators during some speedsteps from 0% to 150% of the base speed (500 ms/div). From top to bot-tom: angular speed (500 r/min/div), d- and q-components of the stator current(10 A/div), and phase current (20 A/div).

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Fig. 20. Behavior of Scheme C with detuned regulators during some speedsteps from 0% to 150% of the base speed (500 ms/div). From top to bot-tom: angular speed (500 r/min/div), d- andq-components of the stator current(10 A/div), and phase current (20 A/div).

Fig. 21. Behavior of Scheme D with detuned regulators during some speedstepsfrom0% to150%of thebasespeed (500 ms/div).Fromtopto bottom: angu-lar speed (500 r/min/div),d- andq-components of the stator flux (0.25 Wb/div),and phase current (20 A/div).

Fig. 22. Behavior of Scheme B with detuned regulators (low gain) during aspeed step change from 0% to 700% of the base speed (500 ms/div). From topto bottom: angular speed (500 r/min/div), d-component of the stator current(20 A/div), q-component of the stator current (20 A/div), and phase current(20 A/div).

Fig. 23. Behavior of Scheme A above the base speed after a step in the loadtorque (1 s/div). From top to bottom: angular speed (500 r/min/div), stator flux(0.25 Wb/div),q-component of the stator current (10 A/div), and phase current(20 A/div).

In fact, in theflux-weakening region, thestator flux magnitudecan be related to the motor angular speed by means of the

following approximated relationship:

Vma x=rs . (18)The absolute value of the time derivative of the stator flux is as

follows: dsdt = Vma x2r

drdt . (19)

To achieve a correct motor operation, the voltage controller

should ensure a rate of change of the stator flux not lower than

(19), and this cannot be achieved if the regulator gain is too low.In other words, if the gain of the voltage regulators has to be kept

low enough to ensure the stability at high speed, the simplest

remedy to allow the motor to enter into the field-weakening

region is to reduce the motor acceleration, thus, limiting the

performance of the speed loop.

Another possible remedy to avoid the flux undershoot at high

speed is to adopt regulators more complex than simple PI regu-

lators. It is well known that PI regulators are suitable to control

low-order systems, but in Schemes A, B, and C, the inner loops,

which control the motor torque, and the outer loop, which con-

trols the flux reference, may be coupled to some extent, thus,

leading to higher order systems. In this case, control methods

based on state feedback may lead to better results. Scheme D ap-

pears less sensitive to this kind of problems because the voltage

loop is inherently independent of the torque request.

Finally, the capability of the control scheme to face a variation

of the load torque at high speed has been assessed. In Figs. 23

26, we show the behavior of the control scheme after a load

torque change.

Due to the characteristics of the brake system, the time con-

stant of this torque change is about 300 ms. Although all the

schemes exhibit a good behavior under these test conditions, it

is worth noting that Schemes A, B, and C modify the flux level

after the variation of the load torque, whereas Scheme D keeps it

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Fig. 24. Behavior of Scheme B above the base speed after a step variation inthe load torque (1 s/div). From top to bottom: angular speed (2000 r/min/div),d-component of the stator current (10 A/div),q-component of the stator current(10 A/div), and phase current (20 A/div).

Fig. 25. Behavior of Scheme C above the base speed after a step in theload torque (1 s/div). From top to bottom: angular speed (500 r/min/div),d-component of the stator current (10 A/div),q-component of the stator current(10 A/div), and phase current (20 A/div).

Fig. 26. Behavior of Scheme D above the base speed after a step in theload torque (1 s/div). From top to bottom: angular speed (500 r/min/div),d-component of the stator flux (0.25 Wb/div), q-component of the stator flux(0.25 Wb/div), and phase current (20 A/div).

Fig. 27. Behavior of Scheme A during the start-up magnetization transient(200 ms/div). From top to bottom: angular speed (500 r/min/div), stator flux(0.25 Wb/div),q-component of the stator current (10 A/div), and phase current(20 A/div).

Fig. 28. Behavior of Scheme B during the start-up magnetization transient(200 ms/div). From top to bottom: angular speed (500 r/min/div),d-componentof the stator current (10 A/div), q-component of the stator current (10 A/div),and phase current (20 A/div).

unchanged, in accordance to the fact that the steady-state value

of the speed does not vary.

D. Startup Magnetizing Transient

The problem of the start-up currents may rise when the drive

is turned ON. If the magnetization transient is not specifically

managed, the control system tries to establish the rated flux level

as quickly as possible. If the currents are directly controlled, the

risk of overcurrents is averted. On the contrary, if the main con-

trol variables are fluxes,there is not a direct control of the current

amplitudes, and it is necessary to adopt some countermeasures

to avoid overcurrents in Schemes A and D.

In Figs. 2730, we show the behavior of the four control

schemes during the magnetization transient. As can be seen, the

behavior is acceptable for all of them. Schemes A and D inject

into the motor a dc current and show the shortest magnetiza-

tion transients, but require an additional section of the control

scheme.

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Fig. 29. Behavior of Scheme C during the start-up magnetization transient(200 ms/div). From top to bottom: angular speed (500 r/min/div),d-componentof the stator current (10 A/div), q-component of the stator current (10 A/div),and phase current (20 A/div).

Fig. 30. Behavior of Scheme D during the start-up magnetization transient(200 ms/div). From top to bottom: angular speed (500 r/min/div),d-componentof the stator flux (0.25 Wb/div), q-component of the stator flux (0.25 Wb/div),and phase current (20 A/div).

Schemes B and C are not as fast as the previous ones, but

overcurrents are inherently avoided.

E. Comparative Table

In Table III, the main results of the comparison of the fourcontrol schemes are given.

The properties that are compared in Table III are the easiness

of tuning of the regulators, the quality of the motor currents, the

torque dynamic, the independence of the motor parameters, and

the stability of the control system at high speed.

A grade has been given to each of them based on the results

obtained in the experimental tests. This grade is qualitative and

varies from + (lowest performance) to +++ (best perfor-mance). It is important to point out that this grade has not an

absolute meaning, but it refers only to the comparison of the se-

lected control schemes, implemented on the same experimental

platform, available in laboratory.

TABLE IIICOMPARISON OF THEFOURCONTROLSCHEMES

VI. CONCLUSION

Four control schemes that feature a robust field-weakening

algorithm have been compared. Although the performance is

very much alike, each control scheme presents some advantages

and some disadvantages regarding the complexity of tuning, the

quality of the load currents, the robustness against the parame-

ter uncertainties, and the operation stability, as summarized in

Table III.

The results cannot be generalized, since they depend on the

specific DSP, inverter, and motor used to carry out the exper-

imental tests. Nevertheless, they suggest some practical rules

that can be useful to select which control scheme is the most

suitable for an application.

The control Scheme A should be preferred when the robust-

ness to variations of the motor parameters could be crucial forthe drive performance. Control Schemes B and C should be pre-

ferred for a specific application when the quality of the motor

currents plays a key role, or just because theindustrial know-how

is mainly related to traditional field-oriented control schemes.

Finally, control Scheme D is preferable when the application

requires a fast torque response in the field-weakening region or

the tuning of the regulators has to be as simple as possible.

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[5] H. Grotstollen andJ. Wiesing, Torque capabilityand control of a saturatedinduction motor over a wide range of flux weakening, IEEE Trans. Ind.Electron., vol. 42, no. 4, pp. 374381, Aug. 1995.

[6] R. J. Kerkman, T. M. Rowan, and D. Leggate, Indirect field-orientedcontrol of an inductionmotor in the field-weakening region, IEEE Trans.

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[11] D. Casadei, G. Serra, A. Tani, and L. Zarri, A Robust method for flux-weakening operation of DTC induction motor drive with on-line estima-tion of the break-down torque, inProc. Eur. Conf. Power Electron. Appl.,Dresden, Germany, Sep. 1114, 2005, pp. 110.

[12] R. Bojoi, P. Guglielmi, and G. Pellegrino, Sensorless stator field-orientedcontrol for low cost induction motor drives with wide field-weakeningrange, in Proc. Ind. Appl. Soc., Edmonton, Canada, Oct. 59, 2008,pp. 17.

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[23] M. Hinkkanen, L. Harnefors, and J. Luomi, Reduced-order flux ob-servers with stator-resistance adaptation for speed-sensorless induction

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Michele Mengoni was born in Forl, Italy, in1981. He received the M.Sc. and Ph.D. degrees(Hons.) in electrical engineering from the Univer-sity of Bologna, Bologna, Italy, in 2006 and 2010,respectively.

He is currently a Fellow Researcher at the De-partment of Electrical Engineering, University ofBologna. His research interests include sensorlesscontrol of induction motors, multiphase drives, andac/ac matrix converters.

Luca Zarri (M06) was born in Bologna, Italy, in1972. He received the M.Sc. degree (Hons.) in elec-trical engineering and the Ph.D. degree from the Uni-versity of Bologna, Bologna, Italy, in 1998 and 2007,respectively.

He worked as a Freelance Software Program-mer from 1989 to 1992 and as a Plant Designerwith an engineering company from 1998 to 2002.In 2003, he became a Laboratory Engineer with theDepartment of Electrical Engineering, University ofBologna, where he has been an Assistant Professor

since 2005. He is the author or coauthor of more than 70 scientific papers. Hisresearch interests include the modulation strategies of innovative converters andthe robust control of electric drives.

Dr. Zarri is a member of the IEEE Industry Applications, IEEE Power Elec-tronics, and IEEE Industrial Electronics Societies.

Angelo Taniwas born in Faenza, Italy, in 1963. Hereceived the M.Sc. degree (Hons.) in electrical en-gineering from the University of Bologna, Bologna,Italy, in 1988.

He joined the Department of Electrical Engineer-

ing, University of Bologna, in 1990, where he is cur-rently an Associate Professor. His scientific work isrelated to electricalmachines, motor drivesand powerelectronics. He has authored more than 100 paperspublished in technical journals and conference pro-ceedings. His current research interests include mul-

tiphase motor drives, ac/ac matrix converters, and field-weakening strategies forinduction motor drives.

Giovanni Serra(SM04) received the M.Sc. degree(Hons.) in electrical engineering from the Universityof Bologna, Bologna, Italy, in 1975.

He joined the Department of Electrical Engineer-ing, University of Bologna,first as a recipientof a fel-

lowship of the National Research Council, and then,he became a Research Associate and, in 1987, anAssociate Professor. He is currently a Full Professorof electrical machines in the Department of Elec-trical Engineering. He has authored more than 150papers published in technical journals and confer-

ence proceedings. His research interests include electrical machines, electricaldrives, and power electronic converters. His current activities include multi-phase drives, direct torque control of ac machines, linear motors, and ac/acmatrix converters.

Dr. Serra is a member of the IEEE Industry Applications and IEEE Di-electrics and Electrical Insulation Societies and the Italian Electrotechnical andElectronic Association.

Domenico Casadei(SM04) received the M.Sc. de-gree (Hons.) in electrical engineering from the Uni-versity of Bologna, Bologna, Italy, in 1974.

He joined the Department of Electrical Engineer-ing, University of Bologna, in 1975, as ResearchAssistant Professor. He is currently a Full Profes-sor of electrical drives. His scientific work is relatedto electrical machines and drives and power elec-tronics. He is author and coauthor of more than 200scientific papers, published in technical journals andconference proceedings. His current research inter-

ests include vector control of ac drives and diagnosis of electrical machines.He has been involved in several research projects with the industry in the sameresearch areas.

Dr. Casadei is a senior member of the IEEE Industrial Electronics Society, amember of the IEEE Power Electronics Society, and a member of the European

Power Electronics Society.

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