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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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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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MENGONI et al.: COMPARISON OF FOUR ROBUST CONTROL SCHEMES FOR FIELD-WEAKENING OPERATION OF INDUCTION MOTORS 311
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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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.