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Feedforward Flux-Weakening Control of Surface-Mounted Permanent-

Magnet Synchronous Motors Accounting for Resistive Voltage Drop

Article  in  IEEE Transactions on Industrial Electronics · February 2010

DOI: 10.1109/TIE.2009.2034281 · Source: IEEE Xplore

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 Feed-forward Flux-Weakening Control
of Surface Mounted Permanent Magnet Synchronous
Motors Accounting for Resistive Voltage Drop
Marco Tursini, Member, IEEE, Enzo Chiricozzi, and Roberto Petrella, Member, IEEE

Abstract – This paper deals with the flux-weakening control of

surface mounted permanent magnet synchronous motors, taking I. INTRODUCTION
into account the influence of the resistive voltage drop in the
stator windings, whose effect is usually neglected in similar Surface mounted Permanent Magnet (SPM) synchronous
studies. First, the motor equations exploiting the optimal torque- motors represent the preferred solution among the electrical
speed limits in the flux-weakening region are evaluated and actuators for high performance applications. In the common
discussed. Then, the influence of the resistive voltage drop is stator/rotor assessment, these motors are excited through
pointed out, highlighting its effect on the the set-up of the flux-
weakening strategy. Hence, a simplified approach to flux-
permanent magnets positioned on the surface of a cylindrical
weakening motor control is presented, useful for the practical iron-laminated rotor body, whilst the stator locates the three-
implementation in micro-controlled drives. Finally, experimental phase windings. Due to the absence of rotor windings and
results are shown, using a position-tracking application as a test related losses, SPM motors are referred to as “cool and light”
case. rotor motors, definition which outlines their basic features such
Index Terms – AC motor drives, permanent magnet motors, as high efficiency, high torque/weight ratio, and reduced
industrial automation, motion control, position control, flux- cooling requirements.
weakening control, resistive voltage drop. Owing to the opposing effect of the magnets induced voltage
(back-EMF), operation above the base (rated) speed, i.e. at
NOMENCLATURE voltage limit, requires the introduction of a flux-weakening
d-q Rotating reference frame current component which produces additional non-negligible
vd, vq d-q stator voltage components voltage drops. As a result, SPM motors designed to achieve
high torque/power capability at rated speed have a limited flux-
id, iq d-q stator current components weakening operating region, whereas the ones designed for
ψd, ψq d-q stator flux-linkage components increased flux-weakening operation have a lower rated torque/
ψm Stator flux linkage amplitude due to the magnet power [1].
n Rotor speed Motors employed in industrial automation are usually
me Electromagnetic torque designed to work below the rated speed, i.e. in the constant
rs, x Stator phase resistance and synchronous inductance torque region. In such a case a simple rotor-flux-oriented
vb, ib Base stator voltage and current vector control strategy is arranged, where the “direct” (d-axis)
idA, iqA Coordinates of the voltage limit circle centre (Cv) magnets-aligned current component is set to zero, whilst the
in the d-q current plane “quadrature” (q-axis) torque-producing current component
P1, P1’ Intersections between the voltage and the current increases according to the torque requirements.
limit circles in the motoring/braking region On the contrary, motors employed in specific applications,
in the d-q current plane such as traction, can require a wide constant-power operating
id1, iq1 Coordinates of point P1 region by means of flux weakening [2], [3]. In this case the
vector control strategy becomes much more sophisticated, with
id1’, iq1’ Coordinates of point P1’
the d and q currents both varied according to the speed and
P2 Intersection between the voltage limit and the d torque requirements [4], [5]. A great number of proposals can
current axis in the d-q current plane be found in literature, usually classified as “feed-back” or
id2,0 Coordinate of point P2 “feed-forward” flux-weakening solutions.
Feed-forward solutions ([6]–[9]) employ analytically or
Manuscript received March 1, 2009. Accepted for publication September experimentally evaluated control characteristics, which are
15, 2009.
Copyright © 2009 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be E. Chiricozzi is with the Department of Electrical and Information
obtained from the IEEE by sending a request to pubs-permissions@ieee.org. Engineering, University of L’Aquila, I-67040 Monteluco di Roio, L’Aquila,
M. Tursini is with the Department of Electrical and Information Italy (e-mail: enzo.chiricozzi@univaq.it).
Engineering, University of L’Aquila, I-67040 Monteluco di Roio, L’Aquila, R. Petrella is with the Department of Electrical, Management and
Italy (phone: +39-0862-434456; fax: +39-0862-434403; e-mail: Mechanical Engineering, University of Udine, I-33100 Udine, Italy (e-mail:
marco.tursini@univaq.it). roberto.petrella@uniud.it).
computed to exploit the maximum motor performance in the accounting for the resistive voltage drop significantly increases
(assumed) feeding voltage and current limits. Therefore, the q- the complexity of the equations for the optimal d-q current
axis current command is determined from the torque profiles, leading to approximate solutions [22].
command, while the demagnetizing d current is obtained by This paper deals with the flux-weakening control of SPM
flux-weakening characteristics as a function of the operating synchronous motors using a feed-forward approach which
speed [6], [7]; moreover, decoupling compensation improves accounts for resistive voltage drop [23]. The control strategy is
the response of the current control loops [8]. obtained on analytical basis starting from the voltage and flux
Feed-forward methods are strongly dependent on motor motor equations. The effect of the resistive voltage drop in the
parameters and/or operating conditions, but they guarantee stator windings is taken into account. Possible discrepancies
good stability and transient responses. Experimentally related to its neglecting in the set-up of optimal flux-
evaluated flux-weakening characteristics have been recently weakening strategy are pointed out, with particular emphasis to
employed in sensorless applications [9]. the actual exploitation of the motor torque-speed capability.
In feed-back approaches ([10]–[13]), instead, the motor Finally, a simplified approach to flux-weakening control of
voltage and/or speed are measured and the demagnetizing SPM motors is presented, useful for practical implementation
current is adjusted in order to track the voltage limit at in micro-controller based drives. Experimental results obtained
increasing speed. Depending on the authors, the demagnetizing using a position-tracking application as test case confirm the
current is set proportionally to the filtered q current error in feasibility of the method.
[10]; it is computed through a proportional-integral (PI) Compared to the Authors’ recently published paper [23], the
regulator fed by the voltage-vector error (difference between studies here proposed include further details on the influence
the inverter maximum and the output voltage of the current of the resistive drops, the complete presentation of the feed-
controller) in [11]; it is calculated by the voltage difference forward control characteristics, and extended experimental
between the input and the output of the over-modulation block results.
in [12], and finally by the current vector error (difference
between actual and command) evaluated in the two-phase II. FLUX-WEAKENING OPERATION ACCOUNTING FOR RESISTIVE
stator reference in [13]. VOLTAGE DROPS
All these methods are robust because they do not use motor By neglecting saturation and cross-coupling effects between
parameters. But the transient performance of closed-loop the d and q axes, the electrical model of SPM synchronous
voltage controllers is poor and the gain set-up of the regulators motor is given by the following per-units equations,
is difficult, owing to the operation in the proximity of voltage respectively for the d-q components of (steady-state) stator
saturation region. These aspects are discussed in [14], where voltages (1), flux linkages (2), and electromagnetic torque (3):
two flux weakening schemes are compared, the former based
on closed-loop voltage control, the latter on q current error vd = rs id − n ψ q vq = rs iq + n ψ d (1)
detection. An improvement in voltage saturation sensing is
suggested in [15] where the timings of the space vector ψ d = ψ m + x id ψ q = x iq (2)
modulator are considered.
m e = ψ d iq − ψ q id = ψ m iq (3)
Mixed approaches have been also proposed ([16]–[20]),
trying to join the advantages of both the feed-back and feed- where rs , x and ψ m are the stator resistance, the synchronous
forward solutions. In [16] the pre-computed d current inductance, and the magnet flux linkage respectively, n is the
command for maximum torque per ampere is adjusted by the synchronous speed, and id , iq are the d-q current components.
indirect detection of voltage saturation through the space-
vector modulator, while the q current command is determined Particularly, equation (3) reflects the proportionality between
from the torque command and d current feedback. In [17] the the electromagnetic torque and the q current component, i.e.
feed-forward current references determined from maximum the constant torque locus is a line parallel to the d current axis
in the d-q current plane.
power operation are modified on-line, according to the
By the substitution of (2) into (1), and the computation of
respective current errors. In [18] the flux-weakening control is
integrated into the current loop design to achieve minimization the square modulus of the base stator voltage ( vb2 = vd2 + vq2 ) ,
of copper losses. In [19] the flux weakening algorithm the following equation is obtained:
incorporating speed regulation is designed to optimize the id2 + iq2 + a(n) id + b(n) iq + c(n) = 0 (4)
efficiency in steady-state condition, while compensation of
magnetic saliency effects in flux-weakening of SPM motors is which is a circle in the d-q currents plane, whose centre
discussed in [20]. C v (idA , iqA ) and radius (Rv ) are speed dependent (see
In most model-based methods, the influence of the winding Appendix for details). It represents the so called “voltage limit
resistance has either been neglected or simply compensated. circle”, which limits to its inner space the d-q currents
However, this is only appropriate for high power motors, compatible with the base voltage at each given speed.
which have a relatively small stator resistance [21]. In fact,
 By considering the base current ib as the feeding limit, a III. FLUX-WEAKENING CONTROL
(fixed) “current limit circle” is similarly obtained, centred at Once the reachable operating zone is correctly defined, an
the origin of the axes: optimum speed control strategy can be defined for SPM
ib2 = id2 + iq2 . (5) motors, according to selected targets, Fig. 4.
Below the base speed (“constant torque” region), the natural
The operating zone compatible with both the voltage and choice is to impose the d current component equal to zero,
current limits, at a given speed in the flux-weakening region, is assuring the maximum torque-to-current ratio; the maximum
shown in Fig. 1. Results refer to the SPM motor whose data are available torque depends on the current limit only (point “a”),
shown in Table I. One notices an asymmetry between the and the trajectory of the feeding d-q currents follows the q
(achievable) “motoring” (M) and “braking” (B) zones, clearly current axis (line “ado”), moving towards the origin at
due to the presence of the q coordinate of the voltage limit decreasing torque (the explanation refers for simplicity to
circle centre. motoring operation, but the extension to braking operation is
If the resistive voltage drops are neglected in (1), i.e. rs → 0 , immediate).
the parameters of the voltage limit circle are modified because Above the base speed, in the flux-weakening region, the
of b(n) → 0 . The centre of the voltage limit circle falls always maximum available torque depends on both the limits of
voltage and current. It is obtained by the intersection between
on the d-axis, i.e. the q coordinate is zero at any speed, the voltage limit circle (at that speed) and the (fixed) current
iqA (n) → 0 . As a consequence the braking and motoring limit circle (points like “b” or “c” in Fig. 4). Hence, the
regions are symmetrically displaced in the d-q current plane, as maximum torque is achieved for a negative (demagnetizing) d
represented in Fig. 2. Then, if the resistive voltage drops are current, and it decreases at increasing speed.
neglected, the maximum available torque vs. speed in each of 1,50
1.5 neglecting the resistive
these regions can be considerably over or under-predicted voltage drop
respectively, as shown in Fig. 3. 1,00
1.0
considering the resistive
voltage drop

iq 0.5
0,50
(p.u.)
(p.u.)
q-axis current (p.u.)

0.0
torque

0,00
torque

m max M -0.5
-0,50

id
-1.0
-1,00

Cv -1.5
-1,50
Rv 00 11 22 33 44 5
5 6
6 7
7
m max B speed (p.u.)
speed (p.u.)
Fig. 3. Maximum torque vs. speed capability computed accounting or
neglecting the resistive voltage drop.
1.5
d-axis current (p.u.)
Fig. 1. Operating zone in the d-q currents plane (including resistive voltage
n (p.u.) 1.00 iq
1.19 a
q-axis current (p.u.)

drops). 1 b
1.44

iq 1.94 d
c
0.5 3.18 d'
c'
q-axis current (p.u.)

mmax 5.97

0
id
e o
Cv id
Rv
-0.5
mmax -1 -0.5 0 0.5 1
d-axis current (p.u.)
Fig. 4. Flux-weakening control trajectories at different speeds
(motoring operation).

d-axis current (p.u.) In order to maximize the torque-to-current ratio at flux-

Fig. 2. Operating zone in the d-q currents plane (neglecting resistive voltage weakening, the trajectory of the feeding d-q currents, at
drops). decreasing torque, should follow the branch of the voltage limit
circle directed towards the origin of the axes. Then, two cases ~ ~
id1 = min ( id1,2 (n)), id′ 1 = max ( id1,2 (n)) (7)
arise depending on the speed level:
a) for low (flux-weakening) speeds, the voltage limit circle Then, the current limit circle equation (5) is used to evaluate
intersects the q current axis (e.g. point “d” of the arc “bd”); the corresponding q current values ( iq1 > 0 , iq′1 < 0 ), and the
in this case optimization is achieved with zero d current for coordinates of the intersection points are found, both in the
low torque and no-load, as in the constant torque region motoring P1 (id1 , iq1 ) and braking P1′(id′ 1 , iq′ 1 ) region, as shown
(the optimum trajectory is “bdo”);
in Fig. 5.
b) for high (flux-weakening) speeds such an intersection is
lost: the optimum trajectory remains on the voltage limit B. Intersection between voltage limit and d-current axis
circle (arc “cc’e”) and even at no-load operation a negative This point is indicated as P2 in Fig. 5. It is achieved by
d current component is necessary (point “e” in Fig. 4). putting the q current equal to zero in equation (4). A further 2nd
For the sake of practical implementation, in order to avoid order equation for the d current is obtained, whose greater
complex computations or onerous mapping, a simplified (right) root is the abscissa of the intersection point of interest:
control trajectory is proposed, where the arc of voltage limit id2 + a(n) id + c(n) = 0 → id1,2 (n) (8)
circle, bounded by the intersections with the current limit circle
and the d current axis, is replaced by the respective chord (e.g. id 2 = max (id1,2 (n)) = idA (n) + idA (n)2 −c(n) (9)
use “ce” instead of “cc’e”, as shown in Fig. 4). Hence the
being idA (n) = − a(n) / 2 the abscissa of the voltage limit circle
control trajectories become a piecewise-linear (like “bd’o”) for
centre. Hence, the coordinates of the intersection point are
low flux-weakening speeds, or the same chord (like “ce”) for
found as P2 (id 2 , 0) .
high flux-weakening speeds.
The equation of the chord linking P1 ( P1′ ) with P2 is now
In order to set-up this simplified strategy, the points
calculated in the d-q currents plane. To simplify the
bounding the chords of the voltage limit circle are evidenced in
implementation of the control, it is useful to assume the d
Fig. 5 for a given speed, for both motoring and braking
current component as the dependent variable. In case of
operations. The following subsections discuss the analytical
motoring operation one has:
computation of these points.
i d = i d 2 ( n) + k ( n) ⋅ i q (10)
1 P1
P1 with the angular coefficient k(n) given by:
iiQq i ( n) − i d 2 ( n)
k(n) = d1 (11)
(p.u.)

0.5 iq1 (n)

iiDd while for braking operation one has to consider:

q-axis current

P2
P2
p.u.

0 i ′ ( n) − i d 2 ( n)
k ′(n) = d1 . (12)
iq′1 (n)
-0.5

speed (p.u.)
1
-1 P1' 1.37
iq
-1 -0.5 0 0.5 1 P1
2.2
q-axis current (p.u.)

p.u.
d-axis current (p.u.) 0.5
Fig. 5. Intersections of the voltage limit circle with the current limit circle
( P1 , P1′ ) and the d current axis ( P2 ).
id
0

A. Intersections between voltage and current limit circles

These points are computed by the system of the respective -0.5
equations (4) and (5). By eliminating the q current component,
a 2nd order equation for the d current is obtained, whose roots P1'
represent the abscissas of the searched intersection: -1
~
A(n) id2 + B(n) id + C(n) = 0 → id1,2 (n) (6) -1 -0.5 0 0.5 1
d-axis current (p.u.)
(coefficients are detailed in the Appendix).
Fig. 6. Control trajectories for two different flux-weakening speeds.
Due to the asymmetry of the voltage limit circle with respect
to the d current axis, when the resistive voltage drops are taken Then, the logic of the flux-weakening control can be
into account, two distinct roots are obtained, one corresponding summarized as follows:
to motoring ( id1 ), the other to braking ( id′ 1 ) operation:
if iq > 0 (motoring region) then IV. APPLICATION AND RESULTS
calculate the d current from the chord equation (10), with
angular coefficient (11) and the known speed; An experimental system has been arranged to verify the
feasibility of the presented flux-weakening control strategy, as
else if iq < 0 (braking region) then shown in Fig. 9. A prototype SPM motor has been used (see
calculate the d current from the chord equation (10), with Table I), designed for a position-tracking application which
angular coefficient (12) and the known speed; requires high torque at start up and low torque during the (high
if id > 0 then assume id = 0 . speed) movement. The motor has been equipped with a
quadrature encoder providing 4800 (1200 x 4) pulses-per-
This logic produces the control trajectories indicated in revolution, and it is fed by a commercial drive featuring
Fig. 6, for two different (low and high) flux-weakening speeds. standard AC brushless control by means of a TMS320F2406
A block-diagram of the flux weakening controller is shown Digital Signal Controller (DSC).
in Fig. 7. The desired trajectory in the d-q current plane is The experimental set-up includes a host PC and a scope, the
generated through the respective commands id* and iq* applied former used to run the user interface (RS-232 connected) and
in a feed-forward control scheme. The speed feedback n is the DSC development and debugger tools (JTAG connected),
compared to its command n * in a PI regulator, whose output is the latter to display variables computed in the control
the q current command: this is saturated according to the algorithm in real-time. To this purpose a 4 channel digital-to-
maximum available (speed-dependent) limits, respectively iq1L analog converter (DAC) has been interfaced through the high
and iq′1L for motoring and braking operations. Then the speed serial peripheral interface (SPI) of the DSC, while the
equation of the chord (10) is implemented to produce the d encoder signals are sent through the dedicated Quadrature
current command, by the computation of the (speed-dependent) Encoder Pulse (QEP) module. The firmware of the controller
coefficients id 2 and k , and proper limitation. The most has been modified to incorporate the proposed flux-weakening
meaningful functions employed in the controller are shown in control strategy.
Scope
Fig. 8.
DAC

SPI I/F
JTAG Emulator pod
Control Board &
Power Electronics RS232 Serial cable
Control firmware
Power output QEP I/F
/
PC
Communication
software,
SPM Encoder development and
debugger tools

Fig. 9. Experimental set-up.

The resulting drive scheme is reported in Fig. 10, showing

the vector-control arranged in d-q coordinates and the flux-
Fig. 7. Block diagram of the flux-weakening controller.
weakening controller which provides the current commands. PI
1.5
1,50 regulation is used for the current and speed loops, while simply
Q current limit
q-current limit (motoring)
(motoring)
proportional (P) regulation for the position loop. The
1.0
1,00 q-current
Q current limit
limit (braking)
(braking)
(p.u.)

i q1 L d-current generation of the reference trajectory for position-tracking is

D current no-load
no-loadlimit
limit
(p.u.)

0.5
0,50
computed through a specific algorithm, featuring sinusoidal
limits

shaped acceleration/ deceleration profiles, based on the

QD current

0.0
0,00 statements of the requested movement (position displacement,
d-q current

id 2 maximum acceleration/ deceleration and speed). In order not to

-0.5
-0,50
exceed the pre-set calculation time (i.e. 150us), the speed-
dependent flux-weakening functions are evaluated off-line and
-1.0
-1,00
iq′1L stored in look-up-tables for their use in real-time. The current
-1.5
-1,50 control loop is executed synchronously with the PWM period
00 11 22 3
3 44 5
5 66 77 at 6.66 kHz sampling frequency, while the speed and position
speed (p.u.) loops are executed every twenty current loops at 0.33 kHz
speed (RPM)
Fig. 8. Flux-weakening functions. sampling frequency. Adjacent-vectors space-vector pulse width
modulation (AV-SVPWM) is employed in the controller.
 possibility to introduce optimization criteria The original
contribution consists in the simplification of the algorithm,
basically a linear relationship, which could allow faster
implementation by low-cost digital signal controllers also
without the recourse to memory-consuming look-up-tables.
Experimental results obtained using a position-tracking
application as test case confirmed the feasibility of the method,
which appears applicable to a wide range of emerging
applications, such as automotive or washing machines, where
SPM motors capable of wide constant-power ranges are
requested. Further developments include the introduction of
Fig. 10. Drive scheme with flux-weakening controller.
decoupling routines in the current loop, and the adoption of a
Before proceeding with the experimental implementation, proper algorithm based on the detection of the inverter voltage
the insertion of the flux-weakening feature within the saturation in order to guarantee safe flux-weakening operation
commercial vector-controlled drive has been simulated, using and better operating conditions for current regulators.
the MATLAB/Simulink software toolbox, aiming at evaluating
possible unpredictable side-effects. Figs. 11 and 12(a) refer to
a movement of 50000 encoder pulses, with 4500 rpm
maximum speed (in the flux-weakening region) and (2)
7000 rev/s2 maximum acceleration/deceleration: the reference
trajectories are shown in Fig. 11(a), while the actual position,
speed and d-q current references are shown in Fig. 11(b). A (a)
plot in the d-q plane is reported in Fig. 12(a), with the speed (3)
dependent motoring ( P1 (id1 , iq1 ) ) and braking ( P1′(id′ 1 , iq′ 1 ) )
operating limits. Due to the entity of the acceleration, the
(1)
motoring limit is reached during this period and followed until y
maximum speed is reached, where the references follow the x
1 div.(Y) = 1.57 p.u. (speed)
flux-weakening control characteristics (damped oscillations 1 div.(Y) = 0.49 p.u. (all other variables)
involve both the motoring and braking branches). The case of 1 div.(X) = 50 ms

lower acceleration (2000 rev/s2) is reported for comparison in

Fig. 12(b) in the d-q current plane only. (7)
(4)
The experimental results are presented in Figs. 13 and 14.
They refer to position-tracking movements of 100000 encoder (6)
pulses, with a maximum acceleration/deceleration of
2000 rev/s2 and maximum speed of 4500 (2.2 p.u.) in Fig. 13
and 6000 rpm (about 3 p.u.) in Fig. 14. Due to the lower (b)
acceleration level, the operating limit of the current circle is (5)
not attained, and the d-q variables (both references and actual
currents) show a regular behaviour. Oscillations on the current y
feedbacks at the higher speed point out the difficulty of PI x
current regulators to establish their commands in the proximity Fig. 11. Position tracking @4500 rpm, high acceleration (simulation):
of the voltage saturation region, especially for the d current position (1), speed (2), and acceleration (3) trajectories, q and d current
component shown in Fig. 14(a). Nevertheless the statements of references (4,5), actual position (6) and speed (7)
the particular application are satisfied, which could not be
without a proper flux-weakening strategy. TABLE I:
BASE VALUES AND PARAMETERS OF THE TEST MOTOR
V. CONCLUSIONS Number of poles pairs 3
Base/maximum speed (rpm) 2046/12800
In this paper, an approach to flux-weakening control of SPM Base torque (Nm) 0.742
Base current (Arms) 7.92
synchronous motors is presented, accounting for resistive Base voltage (Vrms) 10.96
voltage drop. The control strategy is based on a feed-forward Synchronous inductance (pu) 0.4682
scheme, with the d-q current references computed from the Stator resistance (pu) 0.3302
motor model as a function of the speed and the current and Magnet flux linkage (pu) 0.6387
Inertia (kg–cm2) 0.132
voltage feeding limits. The proposed method maintains the
basic features of the analytical-based feed-forward flux-
weakening approaches, such as fast transient response and
 q-axis current reference (p.u.)

(4)
(3)

(a)

(1), (2)

2.048 V = 3.18 p.u. (speed)

d-axis current reference (p.u.) 2.048 V = 1 p.u. (all other variables)

(a) high acceleration movement

d current reference (1) and feedback (2), acceleration (3) and speed (4)
q-axis current reference (p.u.)

(4)
(3)

(b)

(1), (2)
d-axis current reference (p.u.)
(b) low acceleration movement 2.048 V = 3.18 p.u. (speed)
2.048 V = 1 p.u. (all other variables)
Fig. 12. Position tracking @4500 rpm (simulation):
trajectories of the d-q current reference and points P1 and P1′ .

REFERENCES q-current reference (1) and feedback (2), acceleration (3) and speed (4)

[1] Miller, T.J.E.; Soong, W.L.: “Field weakening performance of brushless

synchronous AC motor drives”, IEE Proc. Electr. Power Appl., vol. 141,
n.6, Nov. 1994.
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Appl., vol. 41, pp. 790-800, May/June 2005.
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[4] Zhu, Z.Q.; Chen, Y.S.; and Howe, D.: “Maximising the flux-weakening
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2000, vol. 2, pp. 552-557.
[5] Morimoto, S.; Takeda, Y.; Hirasa, T.; and Taniguchi K.: “Expansion of
(4)
operating limits for permanent magnet motor by current vector control 2.048 V = 3.18 p.u. (speed)
considering inverter capacity,” IEEE Trans. on Industry. Applications, 2.048 V = 1 p.u. (all other variables)
vol. 26, Sept./Oct. 1990, pp.866–871.
[6] Morimoto, S.; Takeda, Y.; and Hirasa, T.: “Flux-weakening control
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2.048 V = 1 p.u. (all other variables)

q current feedback (1), speed reference (2) and feedback (3),

rotor position (4)
Fig. 14. Position tracking in the flux weakening region up to 6000 rpm.
 between the University of L'Aquila and industrial partners. His research
APPENDIX – ANALYTICAL RESUMES
interests are focused on advanced control of ac drives, including vector,
a) Equation of the voltage limit circle in the d-q currents sensorless, and fuzzy logic control, digital motion control, DSP-based systems
plane: for real-time implementation, and modeling and simulation of electrical drives.
He has authored more than 90 technical papers on these subjects.
id2 + iq2 + a(n) id + b(n) iq + c(n) = 0
being: Enzo Chiricozzi was born in Vallerano, Italy, on
June 8, 1941. He received the degree in electrical
a(n) = 2 x ψ m n 2 / z(n)2 ; b(n) = 2rs ψ m n / z(n)2 engineering from University of Rome, Italy, in
1967. In 1969 he has been appointed assistant of
c(n) = (2rs ψ 2m n 2 − vb2 ) / z(n)2 Electrical Machine chair. From 1974 to 1977 he
joined the University of L'Aquila as Associate
with:
Professor of Electrical Machines. From 1978 to
z(n)2 = rs2 + (nx)2 1980 he was a Visiting Associate Professor at the
University of Rome, where he was engaged in
The coordinate of the centre are C v (idA , iqA ) , with: research and teaching in Design of Electrical Machines. Since 1980 he is
with the Electrical Engineering Department of University of L'Aquila as full
idA (n) = − a(n) / 2; iqA (n) = −b(n) / 2
professor of Electrical Machines. At the University of L’Aquila he has covered
The radius is given by: the following charges: President of Council of Electrical Engineering degree
Course, from 1980 to 1986; Head of the Department of Electrical Engineering,
Rv (n) = 12 ( a(n)2 + b(n)2 − 4c(n))1 2 from November 1984 to February 1992; President of College of Department’s
Heads and of Athenaeum Scientific Commission, from february 1991 to
b) Equation giving the intersections between the voltage and February 1992; Dean of Faculty of Engineering, from November 1995 to
current limit circles in the d-q current plane: October 2004. His main research areas are the modeling of electrical
machines, optimized design of high efficency induction motors,
A(n) id2 + B(n) id + C(n) = 0 synchronous and induction generators for wind driven generator-set, power
where: electronics and electrical drives. He is author of more than 85 papers and
three notebooks: "Electrical Machines Theory", "Power Electronics and
A(n) = a(n)2 + b(n)2 ; B(n) = 2a(n)(c(n) + ib2 ); Electrical Drives", and "Electrical Machine Dynamics".
C(n) = (c(n) + ib2 )2 − b(n)2 ib2
Roberto Petrella (S’99–M’00) was born in Pescara,
In case of neglecting the resistive voltage drops (both in Italy, in 1971. He received the M.S. degree in
cases a) and b)): electronic engineering (with honors) and the Ph.D.
degree from the University of L’Aquila, L’Aquila,
b(n) r →0 = 0 ; z(n) r →0 = nx Italy, in 1996 and 2001, respectively. He received
s s
praise from the evaluating commission for the
c) Equation giving the intersections between the voltage excellent results obtained in the development of a
limit and the d-current axis in the d-q current plane: research and industrial project during the final
project. He was with the Department of Electrical
id2 + a(n) id + c(n) = 0 Engineering, University of L’Aquila, as a Research Fellow in 1997 and as a
It is independent on the coefficient b(n) , hence same Postdoctoral Fellow within the sensorless control of ac drives research area
intersections are achieved if resistive voltage drops are taken from 2001 to 2005. His research activity during that period was almost
completely devoted to that field through his participation in several projects
into account or not.
sponsored by both the national Minister of Research and from companies.
Since November 2006, he has been an Assistant Professor of electrical drives
with the Department of Electrical, Management and Mechanical Engineering,
Marco Tursini (M’99) was born in S.Pio delle
University of Udine, Udine, Italy. His main research interests nclude modeling
Camere, Italy, in 1960. He received the M.S. degree
and control of power converters and electrical drives for dc and ac motors,
in electrical engineering from the University of
modulation techniques for power converters, measurement and estimation
L’Aquila, L’Aquila, Italy, in 1987. In 1987, he joined
techniques for drives (sensorless control), and architecture and application of
the Department of Electrical Engineering, University
high-performance signal processors and programmable logic for real-time
of L’Aquila, as an Associate Researcher. He became
control. More recently, he has begun activities and research in the field of
an Assistant Professor of power converters, electrical
renewable-energy generation systems, i.e., grid-connected photovoltaic
machines, and drives in 1991, and an Associate
inverters. He has coauthored more than 50 technical papers.
Professor in 2002. In 1990, he was Research Fellow
Dr. Petrella serves as a Reviewer for the IEEE Transactions On Industry
at the Industrial Electronics Laboratory, Swiss Federal Institute of Technology
Applications and IEEE Transactions On Industrial Electronics. In 2002, he was
of Lausanne, where he conducted research on sliding mode control of
a member of the National Organizing Committee of the 3rd International
permanent magnet synchronous motor drives, and in 1994 at the WEMPEC,
Conference on Energy Efficiency in Motor Driven systems held in Treviso,
Nagasaki University. Since 1990 he has been involved in several national
Italy.
research projects and took the responsibility of several research contracts

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