IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 4, JULY/AUGUST 2011
1749
Deadbeat-Direct Torque and Flux Control of Interior
Permanent Magnet Synchronous Machines With
Discrete Time Stator Current and Stator
Flux Linkage Observer
Jae Suk Lee, Student Member, IEEE, Chan-Hee Choi, Student Member, IEEE,
Jul-Ki Seok, Senior Member, IEEE, and Robert D. Lorenz, Fellow, IEEE
Abstract—This paper presents a discrete time deadbeat-direct
torque and flux controller (DB-DTFC) for interior permanent
magnet synchronous machines (IPMSMs). A Gopinath-style discrete time flux linkage observer is developed which contains two
different flux estimation methods based on current and voltage models for flux linkage. This observer produces correctly
estimated flux linkages needed for accurate DB-DTFC implementation. In order to eliminate the sampling delay due to a characteristic of digital control computation, a complex vector model-based
rotor reference frame current observer is also developed. Combining the discrete time current and flux linkage observers, the
correct single time step (deadbeat) air-gap torque and stator flux
linkage control at the (constant) switching frequency is achieved
and experimentally evaluated.
Index Terms—Current and flux linkage observer, deadbeat
control, direct torque control (DTC), interior permanent magnet
machine.
I. I NTRODUCTION
C
URRENT vector control (CVC) is the most widely used
approach to manipulate the air gap torque of interior
permanent magnet synchronous machines (IPMSMs) [1]–[4].
For CVC, closed loop control of the stator current vector
(d–q components) is implemented with the inverter voltage
vector as the sole manipulated input. It should be noted, that
when using CVC, both air gap torque and flux linkage are open
loop variables. Open loop air gap torque dynamics (for the
magnet and reluctance torque) are limited by the stator current
dynamics but flux linkage has intrinsic first order dynamics.
Manuscript received June 16, 2010; revised September 2, 2010, November 3,
2010, January 10, 2011, and February 20, 2011; accepted February 22, 2011.
Date of publication May 12, 2011; date of current version July 20, 2011.
Paper 2010-IDC-231.R4, presented at the 2009 IEEE Energy Conversion
Congress and Exposition, San Jose, CA, September 20–24, and approved for
publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by
the Industrial Drives Committee of the IEEE Industry Applications Society.
J. S. Lee is with the Electrical and Computer Engineering, The University of
Wisconsin-Madison, Madison, WI 53706 USA (e-mail: lee82@wisc.edu).
C.-H. Choi and J.-K. Seok are with the School of Electrical Engineering,
Yeungnam University, Gyeongsan 712-749, Korea (e-mail: johnny@ynu.ac.kr;
doljk@ynu.ac.kr).
R. D. Lorenz is with the Mechanical Engineering, The University of
Wisconsin-Madison, Madison, WI 53706-1572 USA (e-mail: Lorenz@engr.
wisc.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2011.2154293
Bus voltage and current limits affect the stator current dynamics and thus degrade the torque and flux linkage dynamics.
In general, current regulation is severely compromised when
operating at or near the voltage limits and control laws are
modified to deal with these limits.
Since IPMSM torque is comprised of both magnet torque
(a vector cross product Lorentz force used for induction machine field oriented control (IM FOC) [5]) and reluctance
torque (a vector dot product as used in SR motor drives [6]),
CVC-based torque manipulation is not a simple extension of
field oriented control. For IPMSMs, the current vector command for CVC is generally not linearly related to torque or
flux. Instead, the current vector components are those computed
to theoretically yield minimum losses while still achieving
the desired total torque. The loss minimization can be based
on copper losses, iron losses, inverter losses, or some combination. For example, the commonly used “maximum torqueper-ampere” method [1]–[4] computes the theoretical current
vector to minimize copper losses. Such “optimal” current vector
computations can be implemented with varying degrees of
complexity, in which saturation and parameter adaptation can
be included to improve the optimization [7].
Direct torque control (DTC) is an alternative control structure, initially developed for induction machine (IM) drives [8],
[9], but more recently investigated also for IPMSMs [10]–[13],
in which closed loop control is applied directly to both the
air gap torque and stator flux linkage, using (as in CVC), the
inverter voltage vector is the sole manipulated input. Because
of the difficulty in decoupling the manipulated inputs (the
d–q voltage components) from their effects on the air gap
torque and stator flux linkage, bang/bang hysteresis control
has been the primary implementation for commercial forms
of IM DTC drives [14]. In that case, the inverter switching
frequency varies continuously and unpredictably, which can
be problematic when inverter losses (and heating) are critical
system limits.
For classical DTC, the focus is principally on closed loop
torque control dynamics, which are essentially the fastest
possible, within the limitations of the inverter voltage. These
dynamics are generally faster than CVC torque dynamics, due
to the limited dynamics of the closed loop current regulators
commonly used for CVC. In DTC, the stator flux linkage
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command can be manipulated to minimize some combination
of losses (similar to the CVC current command calculator),
although this is not automatically part of classical DTC.
With use of classical DTC, unpredictable ripple appears on
torque due to variable switching frequency. The unpredictable
torque ripple can exceed a tolerance band in the case of low selfinductance [15] and it causes degradation of dynamic control of
a motor. As a solution to the problem, direct mean torque control (DMTC) was presented for a surface-mounted permanent
magnet synchronous machine (SPMSM) [15] and an induction
machine [16]. Using DMTC, an optimal switching sequence
that achieves desired torque and maximum torque ripple can be
calculated. Constant switching frequency is used to implement
DMTC and the mean value of torque over one sampling period
is equal to commanded torque.
Since inverter (and device) thermal loading is often critical, a
predictable, defined switching frequency can be beneficial. To
achieve the torque and flux control advantages of DTC with
a constant switching frequency, classical PI control structures
have been investigated [17]–[23]. Without decoupling the manipulated inputs (the d–q voltage components) this will generally lead to oscillatory dynamics. Thus, an opportunity exists to
develop fixed (defined) switching frequency DTC methods that
properly deal with the cross-coupled inputs.
This paper focuses on applying deadbeat-direct torque
and flux controller (DB-DTFC) using methods similar to
those already used successfully for induction machine drives
[24]–[28]. Deadbeat control is a well-established computer
control technique in which the inverse (machine) model is
solved for the inputs (d–q voltage) that would achieve the
desired outputs (air gap torque and stator flux) in just one PWM
period, i.e., “dead in one beat.” A correctly formed deadbeat
control structure inherently decouples the manipulated inputs.
For IM drives, this DB-DTFC has been shown to be simple
to implement and quite insensitive to parameter errors [29].
In addition, the same control law can be used in the voltage
limits, unlike CVC methods, where the current regulator has to
be modified to deal with limited bus voltages.
This paper proposes and develops a feasible DB-DTFC solution for IPMSMs, which will both achieve the desired smooth
torque and flux performance and allow a very explicit understanding of how it operates in normal operation. Experimental
results using the proposed DB-DTFC on a 1.5 kW IPMSM
drive are used to evaluate the performance and demonstrate how
the desired properties have been achieved.
The discrete time form of (1) is shown as in (2) that are valid
for the short time period of typical PWM frequencies
r
(k)Ts
λrdqs (k + 1) = λrdqs (k) + vdqs
Rs
Rs
−
+ jωr λrdqs (k)Ts +
λpm Ts .
Ls
Ls
(2)
The air-gap torque equation is developed as shown in (4)
using the complex vector form of the stator flux linkage and
stator current. The torque differential equation is shown in (5).
In (5), · denotes a differential operator
3
Tem = P
4
3
Ṫem = P
4
r r
λds iqs − λrqs irds
(3)
λ̇rds irqs + λrds i̇rqs − λ̇rqs irds − λrqs i̇rds .
(4)
The differential stator flux linkage and stator current from (1)
are substituted into (4). Then, the torque differential equation
can be rewritten as (5) and (6) is the discrete time form of (5)
Ṫem
r
Ld −Lq
3
r r
r (Ld − Lq )λds +λpm Lq
= P vds λqs
+vqs
4
Ld Lq
Ld Lq
r2
ωr r
(Lq −Ld ) λds −λr2
+
qs −Lq λds λpm
Ld Lq
r
Rs λrqs 2
2
2
+ 2 2 Lq −Ld λds −Lq λpm
(5)
Ld Lq
Tem (k+1)−Tem (k)
Ts
Ld − Lq
3
r
r
= P vds (k)λqs (k)
4
Ld Lq
r
+vqs
(k)
+
(Ld −Lq )λrds (k)+λpm Lq
Ld Lq
ωr (k) (Lq −Ld ) λrds (k)2 −λrqs (k)2
Ld Lq
−Lq λrds (k)λpm )
Rs λrqs (k) 2
Lq −L2d λrds (k)−L2q λpm . (6)
+
L2d L2q
II. D EADBEAT D IRECT T ORQUE AND F LUX C ONTROL
The permanent magnet synchronous machine equations in
the rotor reference frame can be written as the Faraday’s
Law stator flux linkage differential equation by (1) [30]. The
equation is written using d–q complex vector notation where
fdq = fd + jfq [5]
r
= Rs irdqs + λ̇rdqs + jωr λrdqs
vdqs
where λrds = Ld irds + λpm and λrqs = Lq irqs .
(1)
An expression can be developed for the change in torque
ΔTem (k) = Tem (k + 1) − Tem (k).
(7)
This can be rewritten to show the linear relationship of the
d- and q-axis stator voltages with a slope and a constant including ΔTem (k) as the commanded change in air gap torque, (7)
r
r
(k)Ts = M vds
(k)Ts + B
vqs
(8)
LEE et al.: DEADBEAT-DIRECT TORQUE AND FLUX CONTROL OF IPMSMS
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where
(Lq − Ld )λrqs (k)
(Ld − Lq )λrds (k) + Lq λpm
Ld Lq
B=
(Ld − Lq )λrds (k) + Lq λpm
4ΔTem
ωr Ts −
(Lq − Ld ) λrds (k)2 − λrqs (k)2
3P
Ld Lq
M=
−Lq λrds (k)λpm )
Rs Ts λrqs (k) 2
2 r
2
(Lq − Ld )λds (k) − Lq λpm .
−
L2d L2q
Using (8), multiple possible stator voltage vectors can be
calculated which achieve the commanded change in air gap
torque over the next sample time instant. Each of these solutions
would yield deadbeat torque control, but the stator flux linkage
would vary in an uncontrolled fashion. To achieve deadbeat flux
linkage control, (3) is formed with the approximated discrete
time stator flux linkage equation and the stator resistance terms
are treated as being negligible. In addition, the cross-coupling
term of the stator flux linkage in (5) is decoupled. Then, (5) is
approximated as
r
(k)Ts .
λrdqs (k + 1) = λrdqs (k) + vdqs
(9)
For operating conditions when voltage is not near the limits,
multiple stator flux linkage solutions exist. For constant stator
flux linkage magnitude (a circular trajectory), the stator flux
linkage would be given by
λ∗s (k)2 = λrds (k + 1)2 + λrqs (k + 1)2
2
r
r
= (λrds (k)+vds
(k)Ts )2 + λrqs (k)+vqs
(k)Ts . (10)
Fig. 1 shows a graphical form of the stator voltage solution
of DB-DTFC for IPMSMs including the desired torque line and
a constant stator flux linkage circle following (10).
The stator voltage (Volt-sec) vectors for this special case
are graphically shown as the blue vectors along the circular
constant stator flux linkage plot in Fig. 1. Among multiple
possible stator voltage vectors, two stator voltage vectors fall
on the constant stator flux linkage circle. The hexagon in Fig. 1
represents the voltage limits of the inverter. The peak voltage of
hexagon is two-thirds of the DC bus voltage. The stator voltage
vector within the voltage limits is chosen to achieve DB-DTFC.
III. D IGITAL I MPLEMENTATION OF
F LUX L INKAGE O BSERVER
Since stator flux linkage is not measurable, modified
Gopinath-style flux observers have been developed to estimate
stator flux linkage in the continuous time domain [31]–[37] and
in the discrete time domain [38], [39] for an induction machine.
In this paper, a discrete time Gopinath-style stator flux
linkage observer for IPMSMs is proposed. The stator flux
linkage observer combines two different flux linkage estimation
methods similar to [34]. The two methods are based on a current
Fig. 1. Graphical representation of DB-DTFC voltage solution for IPMSMs.
model and a voltage model, analogous to the known induction
machine flux linkage observers [34], [35].
The first step is to estimate the stator flux linkage through
a current model. The current model is developed based on the
stator flux linkage and current equations as (11). The current
model can be written in the discrete time form as (12)
λrds = Ld irds + λpm
(11)
λrds (k) = Ld irds (k) + λpm .
(12)
The second step to estimate the stator flux linkage is a voltage
model-based observer development. The stator flux linkage is
decoupled to simplify the stator flux linkage observer model
and to eliminate effect of the cross-coupling. Then the voltage
model in the continuous time can be approximated by
d r
r
λ
= vdqs
− Rs irdqs .
dt dqs
(13)
When converting (13) from the continuous to discrete time,
it should be noted that stator voltage is the only latched manipulated input to the system and the stator current is not a
latched input, but rather is a ramped signal. Therefore, a latched
interface should not be applied to convert from continuous to
discrete time. The exact stator flux linkage observer model is
very complicated [38]. An approximate solution is proposed as
shown in Fig. 2. In Fig. 2(a), the stator voltage is latched (zeroorder hold) and an additional integration (ramp) is added for
the discrete time model of the stator current (first-order hold).
From Fig. 2(b), the discrete time form of the voltage model can
be written as
λrdqs (k + 1) − λrdqs (k)
r
= vdqs
(k)Ts −
Ts
R̂s irdqs (k + 1) + irdqs (k) .
2
(14)
The current model is recommended at low frequencies because the voltage model is sensitive to stator resistance as seen
in (13). The voltage model is preferred at high frequencies
because it has virtually no parameter sensitivity in that region.
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state equations. For the stator flux linkage observer, the crosscoupling is decoupled when the stator current observer is
developed.
To form the discrete time stator current observer, a latched
stator voltage is applied. The decoupled and latched input
discrete time version of IPMSMs model is written as
irdqs (k + 1) = e− τ̂ irdqs (k) +
T
Fig. 2. Proposed voltage model of the stator flux linkage observer for implementation of the DB-DTFC algorithm. (a) The proposed voltage model of
the stator flux linkage observer in continuous time domain. (b) The proposed
voltage model of the stator flux linkage observer in discrete time domain.
Therefore, the single closed-loop observer combining the current and voltage models for IPMSMs is a key element in this
paper. The combined stator flux linkage observer in the discrete
time domain is shown in Fig. 3. In the stator flux linkage
observer block diagram, Kf o and Kif o denote a proportional
gain and an integral gain of the stator flux linkage observer
controller.
This flux linkage observer has a form similar to a Gopinathstyle observer. The transition between the voltage model and
the current model is determined by the bandwidth for which the
stator flux linkage observer controller is tuned.
The stator flux linkage is not a measurable physical variable.
Therefore, the proposed stator flux linkage observer is verified
by measuring the angle of the estimated stator flux linkage.
The stator flux linkage can be divided into d-axis and q-axis,
and the angle between the two axes is coincident to the angle
information from an encoder which is zero
r
λqs (k + 1) − Lq irqs (k + 1)
θλ_test (k) = tan−1
λrds (k + 1) − Ld irds (k + 1)
0
= 0.
(15)
= tan−1
λpm
Fig. 4 shows the experimental result of the angle between
d and q axes of the estimated stator flux linkage using the stator
flux linkage observer.
IV. ROTOR F RAME -BASED S TATOR C URRENT O BSERVER
To implement the deadbeat-direct torque control algorithm,
the stator current at the next sample instant needs to be estimated. It can be estimated by a stator current observer in the
rotor reference frame. The stator current observer, as implemented and experimentally evaluated, is based on the IPMSMs
r
(k) vdqs
R̂s
1 − e− τ̂
T
(16)
where τ̂ = L̂s /R̂s .
The stator current in next sample time instant can be estimated with the discrete time version of the stator current
observer. The block diagram of the continuous and discrete time
stator current observer for IPMSMs is shown in Fig. 5. In the
block diagram, Kco and Kico denote a proportional gain and an
integral gain of the stator current observer controller.
Fig. 6 shows the frequency response of the proposed stator
current observer by measuring estimation accuracy on q-axis
stator current. Estimated q-axis inductance is detuned ±50%
from its correct estimation value. The frequency response function shows leading property because the stator current observer
estimates next sample time stator current. With a functional
stator current observer and the stator flux linkage observer,
the DB-DTFC system can be implemented. Fig. 7 illustrates
the block diagram of the entire control structure showing all
portions integrated together including the stator current and the
stator flux linkage observers.
V. E XPERIMENTAL R ESULTS
The mechanical characteristics and the parameters of the
IPMSMs used during the experiment are arranged in Table I.
A. Experimental Verification
DB-DTFC is implemented in the inverter with 10 kHz of
PWM sampling frequency. Fig. 8 shows the experimental test
set up with a SPMSM load machine mechanically coupled to
the IPMSM test machine.
To compare dynamic response and parameter sensitivity of
DB-DTFC versus CVC, the CVC algorithm is also implemented. A bandwidth of the CVC tuned to be 1 kHz and the
input stator current command for CVC is generated based on a
maximum-torque-per-ampere (MTPA) look-up table.
Fig. 9 shows the overall block diagrams for both the MTPA
CVC and the DB-DTFC in the IPMSM test machine.
To confirm deadbeat properties, dynamic responses are observed. Fig. 10 shows a step change in torque command at
300 μ-s. The magnitude of the step command was limited to
be a feasible command signal of 0.4 N.m while the mechanical
rotor speed of the IPMSM is 100 rad/s.
Fig. 10 shows that the torque response from the DB-DTFC
system tracks the commanded torque in a single time step
(deadbeat) and it is faster response than that from CVC.
Fig. 11 shows the stator voltage and stator flux linkage
dynamics of IPMSMs with the DB-DTFC algorithm when a
feasible step command is applied to the system.
LEE et al.: DEADBEAT-DIRECT TORQUE AND FLUX CONTROL OF IPMSMS
Fig. 3.
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Proposed discrete time, stator flux linkage observer.
Fig. 4. Stator flux linkage observer validation. Experimental setting: ωr =
200 [rad/s], Ts = 100 [μ-s]. Bandwidth of the Gopinath-style stator flux
linkage observer = 20 [Hz].
Fig. 6. Experimental stator current observer estimation accuracy frequency
response function. Bandwidth of the stator current observer = 300 [Hz].
Fig. 5. Proposed stator current observer for implementation of the DB-DTFC
algorithm for IPMSMs. (a) The proposed stator current observer in continuous
time domain. (b) The proposed stator current observer in discrete time domain.
As seen in Fig. 11(a), the stator voltage almost reaches its
maximum voltage at the sample time instant when the step
signal is commanded to the system. Fig. 11(a) and (b) show
changes in the stator voltage vectors and the stator flux linkage
vectors as the commanded torque varies from zero to 0.4 N.m.
The graphical representation of DB-DTFC voltage solutions
at 300 μ-s and 400 μ-s are shown in Fig. 12 when a step torque
command is given to the system.
As seen in Fig. 12, a stator Volt-sec vector that achieves
the desired torque is determined from the DB-DTFC control
law at each PWM sampling time while, in this case, the
stator flux linkage magnitude is controlled to the same value
simultaneously.
Performance of DB-DTFC during overmodulation is also
investigated. A step signal is used as torque command and the
magnitude of the step signal is same as the rated torque of the
IPMSM. Transient torque dynamic of the IPMSM is observed
with three different speed of load machine which are 50 [rad/s],
200 [rad/s] and, 300 [rad/s]; 0.09 [p.u.], 0.36 [p.u.] and
0.54 [p.u.], respectively. The experimental results of torque
response and the stator voltage magnitude are shown in Fig. 13.
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Fig. 7. Block diagram of the entire the DB-DTFC system.
TABLE I
IPMSM PARAMETERS
Fig. 8. Experimental test set up: (a) SPMSM load and (b) IPMSM test.
Fig. 9. Block diagrams for control systems: (a) MTPA-CVC and
(b) DB-DTFC.
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Fig. 10. Experimental results of torque response with DB-DTFC and CVC.
Experiment setting: ωrm = 100 [rad/s], Ts = 100 [μ-s]. Bandwidth of the
current regulator = 1 [kHz].
Fig. 12. Graphical representation of DB-DTFC voltage solution for IPMSMs
at (a) 300 [μ-s] and (b) 400 [μ-s].
Fig. 11. Experimental results of stator voltage and estimated stator flux
linkage using the DB-DTFC algorithm experiment setting: ωrm = 100 [rad/s],
Ts = 100 [μ-s].
As shown in Fig. 13(a), it takes several steps to achieve the
rated torque due to DC bus voltage limitation. The voltage
limitation is observed from Fig. 13(b). Torque dynamic becomes slower as the speed of the load machine increases. Since
more back-emf voltage is generated when load speed increases,
the available voltage is reduced. Therefore, the rate change of
torque becomes smaller and it takes more time to reach the
torque command with higher load speed.
To verify that torque and stator flux linkage are controlled
independently using DB-DTFC, a ramp signal is applied as a
stator flux linkage command. The stator flux linkage is changed
from 0.12 Volt-sec to 0.09 Volt-sec while torque command
stays in constant, 0.5 N.m. The experiment results are shown
in Fig. 14.
As seen in Fig. 14, the estimated air-gap torque and stator
flux linkage track each command in one PWM period. As
expected, the air-gap torque of an IPMSM is controlled very
well during the transient change of stator flux linkage. The
corresponding graphical representation of DB-DTFC Volt-sec
solutions at (a) 0.0502 s is shown in Fig. 15.
During the experiment, the DC bus voltage is reduced to
87.5 [V] so that the stator volt-s vector is easy to view within
the smaller Volt-sec hexagon. From Fig. 15, it is seen that stator
flux linkage is decreased at the sample time instant while the
desired torque is achieved.
B. Parameter Sensitivity
The dynamic performance of DB-DTFC versus the MTPACVC for IPMSMs was also evaluated by measuring the command tracking frequency response. To estimate how the control
systems are sensitive to a parameter estimation error, each
parameter in the control system was individually detuned by
20%. The varied parameters are the stator resistance, d-axis
and q-axis stator inductance, and a permanent magnetic flux
linkage. A broad spectrum chirp signal was used as the torque
command to each system. The peak-to-peak amplitude of the
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Fig. 15. Graphical representation of DB-DTFC voltage solution for IPMSMs
at 0.0502 [s].
Fig. 13. Experimental results of (a) torque response and (b) stator voltage
magnitude with DB-DTFC at different load speed. (a) ωrm = 50 [rad/s]
(b) ωrm = 200 [rad/s] (c) ωrm = 300 [rad/s]. Experiment Setting: Vdc =
300 [volt], λs = 0.11 [Volt-sec].
Fig. 16. Experimental torque command tracking frequency response function with the CVC algorithm. Experiment setting: ωrm = 100 [rad/s], Ts =
100 [μ-s]. Bandwidth of the current regulator = 500 [Hz].
Fig. 14. Experimental results of torque and stator flux linkage response with
DB-DTFC. Experiment setting: ωr = 200 [rad/s], Ts = 100 [μ-s].
chirp signal was 0.6 N.m. The minimum and the maximum
values of the chirp signal were 0.2 N.m and 0.8 N.m each and
the offset was 0.5 N.m. The system response is compared to the
commanded signal to extract magnitude and phase.
Torque command parameter sensitivity is estimated with
200 rad/s rotor speed and 10 kHz switching/sampling frequency. Fig. 16 shows the torque command tracking parameter
sensitivity with MTPA-CVC. The magnitude plot of the torque
command tracking frequency response uses a linear scale,
which helps to focus on parameter sensitivity.
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Experimental results using each observer were presented and
generally confirmed the desired estimation properties.
The stator current and the stator flux linkage observers were
combined to implement the proposed DB-DTFC algorithm for
IPMSMs.
The dynamic response of IPMSM drives using DB-DTFC
and MTPA-CVC were evaluated on the test stand switching/
sampling at 10 kHz. It was demonstrated that torque dynamics
from the DB-DTFC drive system tracks the commanded torque
in a single PWM time step (deadbeat). Additionally, transient
torque dynamics at voltage limit operation was observed.
Parameter sensitivity of the IPMSM drive system with
DB-DTFC and with MTPA-CVC was evaluated using the
command tracking frequency response. It was shown that the
system with the DB-DTFC has superior dynamics and is less
sensitive to parameter estimation error than the system with
MTPA-CVC.
ACKNOWLEDGMENT
The authors wish to acknowledge the Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC) at the
University of Wisconsin-Madison for motivation and support
of this project.
Fig. 17. Experimental torque command tracking frequency response function
with the DB-DTFC algorithm. Experiment setting: ωrm = 100 [rad/s], λs =
0.12 [Volt-sec].
The general roll-off is consistent with the bandwidth of the
current regulator. It is observed that the magnitude tracking is
very sensitive to the permanent magnetic flux linkage over the
entire frequency range. However, phase error is almost zero
with the permanent magnetic flux linkage estimation error. At
low frequencies the magnitude and phase error is almost zero
with variation of the stator resistance and the stator inductance.
The system becomes sensitive to the stator resistance and the
stator inductance at high frequencies.
Fig. 17 shows the torque command tracking parameter sensitivity with DB-DTFC. The experiment is implemented under
same condition as used for MPTA-CVC.
As seen Fig. 17, the magnitude and the phase torque command tracking errors due to parameter estimation are negligible
over the entire frequency range. Also, the DB-DTFC has a virtually constant magnitude ratio and a linear phase shift property,
both of which are consistent with discrete time deadbeat control
design theory.
VI. C ONCLUSION
A DB-DTFC control structure and the corresponding discrete
time model for IPMSMs are developed mathematically and
graphically in the paper.
Digital implementation of the stator current and the stator
flux linkage observers for IPMSMs is also introduced and used
to evaluate the DB-DTFC IPMSM drive. The stator current
and the stator flux linkage observers estimate the stator current
and the stator flux linkage at the next sample time instant.
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Jae Suk Lee (S’09) received the B.S. degrees from
Inha University, Inchon, Korea, and the Illinois Institute of Technology, Chicago, in 2006, and the M.S.
degree from the University of Wisconsin-Madison,
Madison, where he is currently working toward the
Ph.D degree in electrical and computer engineering.
His research interests are high-performance permanent magnet machine drives and discrete observer
design and implementation.
Chan-Hee Choi (S’06) received the B.S. and M.S.
degrees in electrical engineering from the school
of Electrical Engineering, Yeungnam University,
Kyungsan, Korea, in 2004 and 2007, respectively,
where he is currently working toward the Ph.D.
degree in the Power Conversion Laboratory.
His current research interests include highperformance electrical machine drives, sensorless
control of ac machines, and traction drives for hybrid
electric vehicles.
Jul-Ki Seok (S’94–M’98–SM’09) received the B.S.,
M.S., and Ph.D. degrees in electrical engineering
from Seoul National University, Seoul, Korea, in
1992, 1994, and 1998, respectively.
From 1998 to 2001, he was a Senior Engineer
with the Production Engineering Center, Samsung
Electronics, Suwon, Korea. Since 2001, he has been
a Member of the faculty of the School of Electrical Engineering, Yeungnam University, Kyungsan,
Korea, where he is currently an Associate Professor.
From February 2008 to February 2009, he was a
Visiting Researcher in the Electrical and Computer Engineering Department,
University of Wisconsin, Madison. His specific research interests are in high
performance electrical machine drives, sensorless control of ac machines, and
nonlinear system identification related to the power electronics field.
Dr. Seok is currently a member of the Editorial Board of the Institution of
Engineering and Technology (IET) Electric Power Applications.
Robert D. Lorenz (S’83–M’84–SM’91–F’98) received the B.S., M.S., and Ph.D. degrees from the
University of Wisconsin, Madison, and the M.B.A.
degree from the University of Rochester, NY.
Since 1984, he has been a member of the faculty
of the University of Wisconsin-Madison, where he
is the Mead Witter Foundation Consolidated Papers
Professor of Controls Engineering in the Department
of Mechanical Engineering. He is Co-Director of the
Wisconsin Electric Machines and Power Electronics
Consortium (WEMPEC), It is the largest industrial
research consortium on motor drives and power electronics in the world. Prior
to joining the university, he worked 12 years in industry, in Rochester, New
York, principally on high performance drives and synchronized motion control.
He has authored over 230 published technical papers and is the holder of
24 patents with two more pending. He has won 24 IEEE prize paper awards
on power electronics, drives, self-sensing, current regulators, etc.
Dr. Lorenz was IEEE Division II Director for 2005/2006, was the IEEE
Industry Applications Society (IAS) President for 2001, a Distinguished
Lecturer of the IEEE IAS for 2000/2001. He was awarded the 2003 IEEE
IAS Outstanding Achievement award and the 2006 EPE PEMC Outstanding
Achievement award.