Performance Evaluation of Interior Permanent Magnet Synchronous Machines using
Deadbeat-Direct Torque Flux Control in an Indirect Matrix Converterwith a Reactor Free Boost Converter
Goh Teck Chiang

Jun-ichi Itoh

Jae Suk Lee

Robert D. Lorenz

Nagaoka University of Technology
Nagaoka Niigata, 940-2188, Japantcgoh@stn.nagaokaut.ac.jp
itoh@vos.nagaokaut.ac.jp

University of Wisconsin-Madison, WEMPEC
Madison, WI 53706 USA
lee82@wisc.edu
r.d.lorenz@ieee.org

Abstract – This paper discusses the performance of aninterior permanent magnet synchronous machine by using
deadbeat-direct torque flux control (DB-DTFC) in a hybrid
power circuit structure, which consists of an indirect matrix
converter (IMC) and a reactor free boost converter (RFBC).
The first section of this paper documents the performance of
DB-DTFC when carrier comparison PWM and space vector
modulation (SVM) are used as modulation techniques.
Corresponding Volt-sec solutions for each modulation technique
are shown via simulation and experiments. The second section
discusses DB-DTFC properties in the proposed IMC/RFBC
circuit. The results demonstrate that DB-DTFC is capable ofdelivering fast dynamic torque response in one sample period
even when (i) variable switching frequency is applied in the
inverter of the IMC and (ii) DC offset current occurs in the
output current of the IMC.

boost reactors, were removed while reducing the size andweight of the system, yet achieving high efficiency (up to
94% was demonstrated [5, 6]).
However, for the HEV application, a robust motor control
technique is required to deliver torque over a wide range ofcontrolled speed. The proposed IMC/RFBC circuit has notbeen integrated with a regularly sampled direct torque control(DTC) that directly controls both flux linkage and torque [7,8]. It should be noted that the proposed IMC/RFBC circuit
structure uses variable switching frequency to achieve zerocurrent switching (ZCS) with a corresponding reduction inswitching losses. Variable switching frequency is not directlycompatible with DTC configured for regular sampling inwhich PI controllers are used to control both flux and torque.
Furthermore, adapting to load torque and speed changes andto parameter variations is slow because regularly sampled
DTC that uses PI controllers does not deal with the crosscoupling between torque and flux linkage.
This paper clarifies the performance of an interior
permanent magnet synchronous machine (IPMSM) by using
a robust motor control technique known as Deadbeat-direct
torque and flux control (DB-DTFC) in the proposed
IMC/RFBC circuit. DB-DTFC is a regularly sampled
alternative to PI-DTC that is capable of achieving fast
dynamic torque response [9, 10]. Furthermore, torque andflux linkage are directly controlled via DB-DTFC in a fully
decoupled manner. In the proposed IMC/RFBC circuit, due tothe RFBC connection, DC offset occurring in the output
current depending on the polarity and value of the battery
current. Since the torque is subjected to the motor current ingeneral, this phenomenon is required to study and analyze asa part to confirm the proposed IMC/RFBC circuit is capable
to operate with DB-DTFC to produce a fast torque response.
The first section of this paper evaluates the performance of
DB-DTFC when using the Volt-sec vectors produced by two
standard PWM schemes, namely space vector modulation(SVM) and carrier comparison PWM, in an inverter.
Sufficient results are provided to distinguish the maximum
Volt-sec and torque ripple that are produced by the twomodulation schemes. The second section discusses theperformance of the DB-DTFC in the proposed IMC/RFBC
circuit structure. The performance of a standard inverter isdiscussed in first section because the secondary stage of the
IMC is similar to an inverter; however, in IMC the control of
the inverter will be implemented with variable switchingfrequency. In addition, the proposed circuit structure has
known properties that must be dealt with, i.e. DC offset

Index Terms— Indirect Matrix Converter, PWM, AC/AC
converter, Over modulation, Square wave, Trapezoidal wave

I.

INTRODUCTION

Energy saving converters driving high speed synchronous
motors have been studied extensively for transportation
applications such as the hybrid electric vehicle (HEV). The
classical circuit structure, which is composed of a back-toback (BTB) converter and a boost converter (BC), is typicallyapplied in such applications [1, 2]. However, the classicalcircuit faces size and thermal challenges. First of all, theclassical circuit requires numbers of film capacitors in the DC
bus for the control. These passive components, capacitors
and boost reactors, are heavy and bulky. Therefore, size
reduction of converters for automotive application ischallenging. Furthermore, temperature control is anotherserious issue for transportation applications. As these passive
components disallow to operate under a high temperatureenvironment, cooling system becomes essentially important.
Including the cooling system for these passive components,
the size of the entire system becomes even larger.
One of AC/DC/AC converter topologies actively
considered for HEV applications is the indirect matrix
converter (IMC) [3, 4]. The IMC can be manufactured insmall size because electrolytic capacitors are not required tomaintain a DC link voltage. In [5, 6], a circuit structure wasproposed in which an IMC is connected to a boost converterwith batteries connected to the neutral point of a motor,
effectively creating a reactor free boost converter (RFBC).
In the proposed IMC/RFBC circuit structure, two passive
components, DC link electrolytic capacitors and separatelinkage, λpm is the permanent magnet flux linkage, Rs is thestator resistance, and ωr is the angular velocity.
3(1)
T em = P [λ pm i q − ( L q − L d )i q i d ]4⎛ L −L ⎞(L − L )λ (k ) + λpmLq
Tem (k + 1) − Tem (k ) 3= P[vd (k )λq (k )⎜ d q ⎟ + vq (k ) d q q⎜ Ld Lq ⎟
Ts
Ld Lq
4
⎝
⎠
+
+

Fig. 1 Proposed circuit structure.

current occurring in the output current due to the neutral pointconnection. These phenomenons are discussed and evaluatedin the last section to document that the proposed circuit
structure is capable of delivering fast dynamic torqueresponse with DB-DTFC.
II.

CIRCUIT TOPOLOGY

Fig. 1 shows the proposed IMC/RFBC circuit
configuration based on an indirect matrix converter [3, 4].
The indirect matrix converter can be divided into primarystage and secondary stage. The primary stage for the 3-phase
input power source consists of twelve IGBT devices, which isalso known as a current source rectifier. It can be replacedwith RB-IGBT to achieve higher efficiency. The structure
is direct AC-to-AC conversion and it does not require
electrolytic/ film capacitors to control the DC link voltage.
An LC filter is used at the primary side to smooth the input
current during the switching intervals. The secondary stage
consists of six IGBTs in a standard voltage source inverter
configuration that is connected to a motor. Moreover, a boost
converter and batteries, which are used as the secondary input
power source, are connected at the DC bus. The boost
converter is connected to the neutral point of the motor andutilizes the leakage inductance of the motor for its operation;
thus acting as a RFBC. The proposed circuit achieves acompact hybrid power system that can deliver high energy
conversion efficiency.

ωr (k )Ld Lq

Rsλq (k )L2d L2q((L2q − L2d )λd (k ) − L2q λpm]

Also, the IPMSM state equation is expressed in terms ofcomplex vector form of stator flux linkage (λdq) in discrete
time in the rotor frame as (3).
λ dqs ( k + 1) = λ dqs ( k ) + v dqs ( k )T s
⎛R⎞R− ⎜⎜ s + jω r ⎟⎟ λ dqs ( k )Ts + s λ pm T s
Ls
⎝ Ls
⎠

(3)

By substituting (3) into (2), (2) becomes a function of
torque and stator voltage. This relationship can be rewritten
as (4) to show the linear relationship of d and q-axis voltage
with slope, including the command changes in torque [10].
(4)v q ( k ) T s = Mv d ( k ) T s + B

where,⎛⎞( Lq − Ld )λ q (k )⎟M =⎜⎜ ( L d − L q ) λ d ( k ) + L q λ pm ⎟⎝⎠⎛⎞ ⎡ 4 Δ T em
Ld Lq
ω T
⎟
B =⎜
− r s (( L q − L d )⎜ ( L d − L q ) λ q ( k ) + λ pm L q ⎟ ⎢⎣ 3
L
d Lq
⎝
⎠
2
2
2
2
( λ d ( k ) − λ q ( k )) − L q λ d ( k ) λ pm )−R sTs λ q (k )L 2d L 2q(( L 2q − L 2d ) λ d ( k ) − L 2q λ pm]

The deadbeat controller block shown in Fig. 2 represents(4), where the vdq voltage vector is calculated. These signals
are forwarded into the IMC controller to obtain the desired

III. DEADBEAT-DIRECT TORQUE & FLUX CONTROL
Since DB-DTFC is developed via a model inverse solution,
the DB-DTFC calculates the Volt-sec vector solution needed
to produce the desired torque and flux by the end of eachswitching (sample) period. Moreover, inverters source with“Volt-seconds”, DB-DTFC operates with one control law
over the entire operating space.
The IPMSM torque equation is shown in (1). The
differential torque equation can be written in discrete time as(2) [10], where Ts is the switching period (sampling time), P
is the number of poles, vd is the d-axis voltage, vq is the qaxis voltage, Ld is the d-axis inductance, Lq is the q-axis
inductance, λd is the d-axis flux linkage, λq is the q-axis flux

(2)((Lq − Ld )(λ2d (k 2 ) − λ2q (k 2 )) − Lqλd (k )λpm )+−Fig. 2 DB-DTFC control diagram for the proposed circuit.

switching pulses for inverter by using variable switchingfrequency carrier comparison PWM (for the case of inverter,
the front end is connected with a standard full bridge rectifier,the controller is a 10 kHz carrier comparison PWM or a space
vector modulation (SVM)). The control details for the
proposed IMC/RFBC structure has been discussed in [3, 4].
Furthermore, since the flux linkage cannot be measured, astator flux linkage observer based on a voltage model and acurrent model is included to estimate the flux in time domain.
In addition, a stator current observer is included in order toreduce the sampling delay and improve the estimation for theflux linkage. The stator current at the next sample instants is
estimated in the discrete time via the stator current observer[9, 10].

modulation schemes. Besides, the estimated flux is also
shown closely tracking with the flux command, as the torquecommand has changed.
B.

Volt-sec utilization for DB-DTFC modulation schemes
Fig. 4 shows the graphical solution of Volt-sec between
the two modulation schemes. The motor speed is 500 RPM
and the torque command is controlled as a step transient from
0 Nm to 2 Nm. It takes several time steps to achieve thecommanded torque due to insufficient amount of voltage.
The total sample time required to achieve the torque isobtained, which is the total steps that the voltage magnitude(Vdqs) requires to produce and reach the desired torque.
Each time step also represents the maximum voltage
Torque [N.m]

IV. PERFORMANCE COMPARISON OF AN INVERTER BETWEENCARRIER COMPARISON PWM AND SVM

2

In DB-DTFC using a fixed switching frequency, the useof stator flux linkage as a control variable allows theconstruction of a graphical representation of the Volt-sec
vector solution that achieves the commanded torque andstator flux magnitude in one sample period. This section
discusses the difference and maximum of Volt-sec that can beachieved by applying either space vector modulation (SVM)
and carrier comparison PWM to produce the desired Volt-sec.
vector. Second, the torque line from the two modulations arecompared and analyzed experimentally. Note that thecontroller is similar to Fig. 2. However, for this work, theinverter is disconnected from the IMC/RFBC and directly
connected with a full bridge rectifier. Then, the inverter
controller is changed into the standard carrier comparison
PWM (10 kHz switching frequency) and SVM, for evaluationof each modulation scheme. The motor parameters used for
simulation are shown in Table 1.

0

Table 1. Simulation/Experiment and motor parameters
DC link
300 V
Switching
10 kHzvoltagefrequency
Motor rated
1280 RPM Stator
1.5 ohm
speed
resistanced-axis8 mH
q-axis22 mH
inductanceinductancePoles
4
Rated torque2.26 N.m
Inertia0.0016Flux induced
0.12
A.

Simulation results for DB-DTFC modulation schemes
The simulation results of the inverter from each
modulation scheme are shown in Fig 3, where 3(a) is thecarrier comparison PWM and 3(b) is the SVM. The motor
speed is controlled by the load to be 1000 RPM and a step
signal is provided as the torque command.
For the simulation, stator flux linkage that minimizes
copper losses is used at given torque commands. Both theresults demonstrate that the estimated torque lines can
respond very fast to the torque commands, regardless of the

T*

1
Tem
Flux linkage [Wb]
0.14

s

0.13
s_em

0.12 Output voltage V [V]
uv
200
0
-200
5

Output current iu,iv,iw [A]

0
-5
0.1

0.14
Time [s](a) Carrier comparison PWM
0.12

0.16

Torque [N.m]
2

T*

1
Tem

0
Flux linkage [Wb]
0.14

s

0.13

s_em

0.12 Output voltage V [V]
uv
200
0
-200
5

Output current iu,iv,iw [A]

0
-5
0.1

0.12

Time [s]

0.14

0.16

(b) SVM
Fig. 3 Simulation results for the two modulation schemes for a torque steptransient and the motor speed constant at 1000 RPM.

magnitude can be produced by the modulation. In this case,the average voltage magnitude is 139 V for SVM and 137 V
for carrier comparison PWM. The voltage utilization of the
SVM is 1.5% higher than that of the carrier comparison
PWM. Even though the carrier comparison produces a lower
voltage magnitude, the total time steps required to change thetorque is not significantly different from SVM.

SVM

1.90
1.85

Tem = 2 N.m
1.80

Tem (k+1)TsTem (k)Ts

0.08
0.06

1.75
56

58

60

62

Carrier comparison
SVM

0.04
0.02

Tem = 0 N.m
0.1

0.105

64

66

Time [ms]

68

70

72

74

(a) Comparison of torque ripple when motor speed is 300 rad/sec.
2

Vdqs (k+1) Ts

00.11 0.115 0.12
d-axis volt-sec

Vdqs (k) Ts
0.125 0.13

Fig. 4 Graphical Volt-sec. solution for the two modulation schemes

C.

Experimental results for DB-DTFC modulation schemes
Fig. 5 shows the torque responses, to a ramp torquecommand, obtained by from the two inverter modulation
schemes, SVM and carrier comparison PWM. The motor
speed is 300 rad/sec in Fig. 5(a) and 550 rad/sec in Fig. 5(b),respectively. Note that in the experiments, the carriercomparison PWM includes third harmonic injection. Under
the medium speed condtions as shown in Fig. 5(a), no
signficant difference can be noticed between the twomodulations. Both estimated torque lines can achieve thecommand value. For Fig. 5(b), the speed is increased to 550
rad/sec, and carrier comparison PWM is able to obtain thetorque close to the desired value because a higher voltage
magnitude can be produced.
V.

Carrier-PWM

1.95

PERFORMANCE EVALUATION OF THE PROPOSEDIMC/RFBC CIRCUIT STRUCTURE

This section discusses the performance of the proposed
IMC/RFBC circuit structure with the implementation of DBDTFC. The proposed circuit has several properties that need
to be addressed. First, in order to reduce the switching losses,
frequent zero vectors are required in the inverter stage of the
IMC. This is because the zero vector periods cause theoutput current to circulate within the inverter and the DC linkcurrent becomes zero, which will enable ZCS on all theswitching devices in the primary stage of IMC. In order toenable ZCS, an unique carrier that has variable switchingfrequency is formed and applied to the inverter stage of IMC.

Carrier-PWM

1.95

Torque [N.m]q-axis volt-sec

0.1

2

1.90

SVM
1.85
1.80
1.75
56

58

60

62

64

66

68

70

72

74

Time [ms](b) Comparison of torque ripple when motor speed is 550 rad/sec.
Fig. 5. Comparison of torque ripple between carrier-PWM and SVM atdifferent operating conditions (a) 300 rad/sec (b) 550 rad/sec

However, variable switching frequency is not favorable in a
traditional inverter as the torque ripple will become higher,
which will increase motor losses [11].
On the other hand, the RFBC that connects to the neutral
point of a motor is a dependent circuit requires the inverter tooperate successfully.
Due to this dependency relationship, the battery current is
added into the inverter current. As a result, the motor current
consists of battery current that will cause a DC offset.
In this section, the fundamental operation of proposed
circuit with the implementation of DB-DTFC is verified insimulation using the motor parameters shown in Table 1.
Then, torque response and ripple are analyzed experimentallywith the IPM motor specified in Table 2.
Table 2. Experimental conditions and motor parameters
Input voltage
200 V
Input frequency
50 Hz
Battery
50 V
Switching
10 kHzvoltagefrequency
Motor rated
180 V
Motor rated
6.1 A
voltagecurrent
Motor rated
1800
Number of Poles
6
speed
RPM

StatorresistanceFlux
inducedInertia

1.56
ohm
0.308

d-axis inductance

11.5
mH
23 mH

q-axis inductance

Notice that the input current remains constant and then thebattery power increases gradually during the acceleration; asso, the DC offset in the output current becomes significantly
noticeable as the battery current becomes larger.

0.00255

A.

Voltage Utilization for the DB-DTFC IMC
Similar to the previous fixed switching frequency
modulation comparison for the inverter, the voltage
utilization of IMC for the variable frequency carriercomparison PWM is discussed here. Fig. 6 shows thegraphical Volt-sec. solution for the IMC variable frequency
carrier comparison PWM and inverter SVM. Note that inthis case, the value of DC voltage of the inverter is similar to
the DC link voltage of the IMC. The motor speed is 900 RPM
and the torque is controlled as a step transient from 0 Nm to 2
Nm. In this case, the average voltage magnitude produced
by SVM and IMC variable frequency PWM is 145 V and 143
V respectively. Note that, even though the IMC produces
more switching counts per sample period (Ts), the averagevoltage magnitude in time domain is nearly the same as thestandard carrier comparison PWM, which is 1.5 % less thanthe SVM.
0.1

Tem = 2 N.m
IMC variable frequency
carrier comparison

0.08

Tem (k+1)Ts

0.06
0.04

Tem (k)TsSVM
Vdqs (k+1) Ts

0.02
0Tem = 0 N.m

Vdqs (k) Ts

0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135
d-axis volt-sec
Fig. 6 Graphical Volt-sec. solution for the IMC variable frequency carriercomparison PWM and inverter SVM showing the voltage utilization of the
SVM is 1.5% higher than that of the IMC carrier comparison PWM.

B.

Simulation Results for the DB-DTFC IMC/RFBC
Fig. 7 demonstrates the effectiveness of the DB-DTFC in
the proposed circuit. The motor parameter is similar to Table
1, the input voltage is 200 V, the input frequency is 50 Hz,
the battery voltage is 100 V and the switching frequency is 10
kHz.
Closed loop velocity control (ASR as shown in Fig. 2) isused to accelerate and decelerate the motor. Feasible
control over the two input power sources (generator andbattery) is also demonstrated in the results. The acceleration
starts at 0.1s, it can be noticed that the estimated torque rises
as a step transient immediately. Also, the input power for theentire acceleration range is controlled by the battery power.

Fig. 7 Control of acceleration and deceleration with DB-DTFC showing thatthe battery power is used during acceleration and the generator power is usedduring deceleration.

The DB-DTFC acceleration results demonstrate that
despite the utilization of battery current, which causes anoffset in output current, the drive produces an estimatedtorque closely matching the commanded torque.
At time 1.1s, the motor speed achieves the desired speed
value and the torque is nearly zero. The motor speed
remains at the same speed for 0.3s. Deceleration starts at
1.4s, the input power for the entire deceleration range ispowered by generator power (input source). A negative
torque is produced that closely matches the torque command,
similar to the case of acceleration, until the speed reaches tozero at 2.5s. This result shows that the hybrid power
management from two input sources can enable the DBDTFC to produce the torque commanded by the velocity loop.
Fig. 8 shows the input and output signals of the idq
components in the stator current observer, under the same
conditions as Fig. 7. The input signals consist of a highamount of ripple because the battery current is included in the
output current. From the results, it shows that the DC offset
caused by battery current does not affect the dq-axis
components of the output current. Moreover, the statorcurrent observer is able to filter out the ripple and estimate
the next sample signal accurately. The results also show thatthe output signals track the input signals as the torquecommand changes.

T*

Torque Tem [N.m]Tem

2 [V/div]

2 [A/div]

Input current ir [A]Output current iu [A]

40 [ms/div]

5 [A/div]

Fig.9. Experimental result obtained from IMC only showing fast torqueresponse tracking the torque command

Fig. 8 Input and output signals for the idq components in the stator current
observer.

C.

Experimental Results for the DB-DTFC IMC/RFBC
Table 2 shows the experiment condition and motor
parameters that have tested in the proposed circuit structure.
Note that velocity control is not used in the following resultsin order to analyze the true torque response. Initially, theload machine runs at low speed nearly at 100 RPM. The
proposed circuit/motor is then driven by the speed of the load
machine during the start-up.
Fig. 9 shows the experimental results obtained from the
IMC only, i.e. the RFBC is disconnected from the IMC. A
torque step command from 0 Nm to 5 Nm is applied. Torqueripple occurs at nearly 0 Nm due to the “cogging torque”.
From the results, the estimated torque very closely tracks thetorque command. Furthermore, the torque response isextremely fast to reach 5 Nm.
Fig. 10 shows the experimental result which is obtained
from DB-DTFC using the proposed IMC/RFBC circuit. In
this result, the battery power is used instead of input current
when the output current is responding to the torque.
Comparing to the result in Fig. 9, the input current remains
unchanged, indicating that battery current is utilized as the
input power source. However, due to the absence of any
active power management for the two input sources (grid andbattery), part of the battery energy goes into the grid (input
power) which results in spikes in the input current.
The DB-DTFC torque response for Fig. 10 can be analyzed
further in Fig. 11. The torque command with the estimatedtorque is clearly demonstrated. The battery current increases
to 3 A immediately responding to the torque.

Fig. 10 Experimental result obtained from the proposed circuit structure
showing the battery current increasing immediately in response to the
output current while the input current is shown to remain unchanged.

Fig. 11 Experimental result obtained from the proposed circuit structure
showing that battery power is utilized instead of input power and that thetorque response is fast to achieve the torque command.

Similarly, dynamic fast torque response can be produced toreach the desired value (5 Nm). The DC offset on the
output current can be noticed in the result. This result
demonstrates that the estimated torque as well as the torqueresponse is not affected by the DC offset component.

Fig. 12 compares the torque ripple by using FFT analysis
on the estimated steady state torque (at 5 Nm). Fig. 12(a)shows the condition of Fig. 9 and Fig. 12(b) shows thecondition of Fig. 11. Fig. 12 (b) uses a smaller scaling on
the frequency so that it can clearly indicate that the torqueripple does not increase due to the RFBC connection. Thatis, the existence of battery current in the motor current does
not produce nor increase the torque ripple. Comparing Figs.
12 (a) and (b), though the modulation scheme for inverter isapplied with the variable frequency carrier comparison PWM,
the torque ripple can remain low.

SVM, in a fixed switching frequency inverter. From theexperimental implementation, the results show that the SVM
was able to deliver 1.5 % more voltage magnitude than the
carrier comparison PWM.
The second section documented the torque response andripple behavior obtained when DB-DTFC was implemented
using the proposed IMC/RFBC circuit.
The results
effectively show that DB-DTFC is capable of delivering fasttransient torque response when battery power is used fromthe RFBC connection. Furthermore, the torque ripple wasshown to be low even when the inverter stage of the IMC is
implemented with a variable frequency carrier comparison
PWM.
REFERENCES

Fig.12(a) Analysis of harmonic components on the estimated steady state
torque. Experiment condition is consistent to Fig. 9. The graphicaldivision for FFT is 20 db/div and 25 Hz/div.

2 [V/div]

Torque Tem [N.m]Battery current ibat [A]

5 [A/div]

FFT analysis of Torque40 [ms/div]
20 [db/div]

12.5 [Hz/div]

Fig. 12(b) Analysis of harmonic components on the estimated steadystate torque. Experiment condition is consistent to Fig. 11. The graphicaldivision for FFT is 20 db/div and 12.5 Hz/div

VI. CONCLUSIONSThis paper presents the performance of DB-DTFC under
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