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https://doi.org/10.62909/ejeee.2026.002 Edison Journal for Electrical and Electronics Engineering
Article
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Three-phase PMSM Comparison between DTC and MPTC
2
Saif Talal Bahar
1,
*
,
and Falah Younis Hamode
2,
3
1
Department of Electromechanical Techniques, Ba’quhba Technical College, Middle Technical University,
4
Baghdad, Iraq; saif.talal@mtu.edu.iq
5
2
Faculty of Computing & Information Technology, Sohar university, Oman; FHamode@su.edu.om
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* Correspondence: Tel.: +96893666704
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Abstract: This paper compares the control performance, average switching frequency, and param-
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eter robustness of a Direct Torque Control (DTC) system and a Predictive Torque Control (MPTC)
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system based on the stator magnetic flux coordinate system of a permanent magnet synchronous
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motor (PMSM). The DTC system has a simpler architecture and a lower average switching fre-
11
quency, but its magnetic flux and torque ripple are larger than those of the MPTC system. The MPTC
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system outperforms the DTC system in terms of performance.
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Keywords: PMSM; MPTC; Three-phase; Inverter Model.
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1. Introduction
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Permanent magnet synchronous motors (PMSMs) are widely used in new energy
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vehicles, high-speed rail traction, and other fields due to their advantages, such as high
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efficiency, high power density, and high-power factor [1]. Vector control, as a classic con-
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trol theory for AC motors, is relatively mature in the PMSM field, but it requires continu-
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ous rotor position information and rotational coordinate transformation [2]. DTC technol-
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ogy, based on a stationary coordinate system, uses a hysteresis comparator to determine
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the voltage vector through a switching table. It requires no coordinate transformation, has
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a simple structure, is easy to implement, and has also been widely used in the PMSM field
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[3]. In recent years, with the improvement of microprocessor computing power, finite
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state set model predictive control, which uses a cost function as an evaluation index and
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traverses all switching states of the inverter into the motor predictive model to select the
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switching state with the best control effect, has attracted attention in the PMSM control
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field [4]. PMSM model predictive control can be implemented based on either the rotor
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rotating coordinate system or the stator coordinate system. The former is similar to vector
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control, requiring coordinate transformation and rotor position, while the latter requires
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real-time torque angle information. The controlled object can be the stator current com-
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ponent, flux linkage, and torque. The cost function of the former does not require
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weighting coefficients, while the latter requires the design and adjustment of weighting
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coefficients [5, 6].
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2. Materials and Methods
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2. Mathematical Model of PMSM
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Given the nonlinear characteristics and parameter coupling of the PMSM, the follow-
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ing assumptions are required for its modeling:
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1) The three-phase stator windings and stator currents are 120° out of phase and con-
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nected in a star configuration.
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2) The motor flux linkage is linear, and eddy current losses and hysteresis losses are
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not considered.
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Citation: Bahar, S. T. and Hamode,
F. Y., Three-phase PMSM Compari-
son between DTC and MPTC. 2026.
4. 9-15
Academic Editor: Prof Dr. Moham-
med Azmi Al‑Betar
Received: 26/6/2026
Revised: 7/7/2026
Accepted: 10/7/2026
Published: 12/7/2026
Copyright: © 2026 by the authors.
Submitted for possible open access
publication under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/license
s/by/4.0/).
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2026, Vol.4 10 of 15
3) Higher harmonics are ignored, and the permanent magnet magnetomotive force
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is a standard sine wave.
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The stator voltage, flux linkage equations, torque, and motion equations of the motor
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are derived as shown in equations (1) to (4).
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48
s
e
s
e
1
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50
s
f
s
2
51
52
e
3
2
p
3
53
54
e
m
p
d
m
d
m
4
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In the formula:
, is the stator voltage d and q axis components (V);
, are
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the stator current d and q axis components (A);
, is the stator winding phase resistance
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(Ω);
, is the rotor electrical angle (rad/s);
, are the d and q axis flux linkage com-
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ponents (Wb); p=d/dt is the differential operator;
, is the permanent magnet flux link-
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age (Wb);
, is the electromagnetic torque (N·m); P is the number of pole pairs;
, is
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the load torque referred to the shaft end (N·m); J is the moment of inertia of the mechanical
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load referred to the shaft end (kg·m²); m is the rotor mechanical angular velocity (rad/s);
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B is the viscous friction coefficient, B>0.
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2.1 Two-Level Voltage Source Inverter Model
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Taking the most commonly used 2L-VSI in a three-phase PMSHM system as an ex-
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ample, it has a general structure and operating principle, and can be easily extended to
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other inverter topologies [7]. Because the inverter has discrete characteristics, its specific
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switching states generate eight corresponding basic voltage vectors, as shown in Figure 1.
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Among them, u0 and u7 are zero-amplitude voltage vectors, and u1, u2, ..., u6 are non-
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zero voltage vectors with different phases. These different voltage vectors correspond to
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different switching actions of the inverter. Figure 2 shows the inverter topology and the
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generation principle of all switching actions.
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Fig. 1 Basic voltage vector distribution diagram
Fig. 2 Topology of 2-level voltage source inverter
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Figure 2 shows a 2L-VSI topology containing three-phase branches, each with two
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Insulated-Gate Bipolar Transistors (IGBTs), connecting the corresponding load terminals
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to the positive or negative bus of the inverter [8]. The switch has three gating signals,
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defined as Sa, Sb, and Sc. The value of the switch signal S is either 0 or 1, representing on
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or off, respectively. Normal inverter operation requires that the upper and lower bridge
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arms S and S’ cannot be on simultaneously; otherwise, a short circuit will occur on the DC
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side, damaging the inverter. Therefore, for a three-phase branch, when the upper bridge
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arm is on, the lower bridge arm must remain off. Each phase branch has two switching
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states: upper arm on, lower arm off, and upper arm off, lower arm on. Extending this to
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the entire three-phase branch generates eight switching states [9].
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The switching table and corresponding basic voltage vector generated by the switch-
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ing actions of the inverter are shown in Table 1.
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Table 1. basic voltage vector generated by the switching actions of the inverter
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Basic voltage vector
Inverter upper arm
State combination
0
0
0
（000）
1
1
1
（111）
1
0
0
（100）
1
1
0
（110）
0
1
0
（010）
0
1
1
（011）
0
0
1
（001）
1
0
1
（101）
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Each different switching state in the inverter defines a set of phase voltages relative
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to the negative bus. The three-phase AC voltages generated by different switching states
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can be expressed as:
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94
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In the formula, Udc is the DC bus voltage. In summary, the 2L-VSI has 8 switching
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states and generates 8 basic voltage vectors in a two-phase stationary coordinate system.
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2.3 Direct Torque Control
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The control block diagram of the direct torque system is shown in Figure 3, which
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includes a PI regulator, a switching meter, an inverter, coordinate transformation, flux
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linkage, and torque hysteresis, PMSM, etc. [10]. The principle of Figure 3 is as follows: the
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given motor speed is compared with the detected speed, and the difference between the
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two speeds is used as an error signal. After passing through the PI speed regulator, the
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output is the reference torque signal Te*, which is compared with the torque signal Te
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calculated by the q-axis current in the control system. The difference between the two
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enters the torque hysteresis controller. The principle of flux linkage hysteresis control is
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to compare the given flux linkage with the flux linkage ψ calculated by the d-axis voltage
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and current in the control system. The difference between the two enters the flux linkage
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hysteresis controller. Finally, the two signals are effectively modulated in the two
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hysteresis controllers and finally switched. The switch outputs the corresponding voltage
111
vector, thereby controlling the inverter to control the permanent magnet synchronous mo-
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tor and achieve the purpose of speed regulation [11].
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Fig. 3 block diagram of the direct torque control
Fig. 4 Block diagram of FCS-MPTC strategy for
PMSM system
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2.4 Model Predictive Torque Control
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The MPTC strategy for the PMSM system uses torque and flux linkage as the main
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controlled objects. Its cost function includes both torque error tracking and flux linkage
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error tracking [12]. The MPTC strategy uses cost function optimization to replace the
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torque hysteresis, flux linkage hysteresis, and offline lookup table in traditional DTC, thus
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enabling the selection of a more accurate voltage vector. Based on equations (6), (7), and
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(8), the torque and flux linkage prediction model of the MPTC strategy is established in a
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two-phase rotating coordinate system:
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125
126
127
128
129
1
1
1 8
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131
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In the formula, id(k+1) and iq(k+1) are the predicted current values obtained from
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equation (9). Based on the prediction model of torque and flux linkage, the following cost
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function is designed:
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J
ref
1
2
ref
1
2
9
136
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In the formula, λψ is a weighting factor in the cost function, which aims to balance
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the importance of torque and flux linkage. By selecting an appropriate voltage vector, ei-
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ther the torque tracking error or the flux linkage tracking error can be minimized;
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however, these two objectives cannot be achieved simultaneously. Therefore, it is neces-
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sary to design a weighting factor to balance their priorities. Figure 4 shows the control
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block diagram of the FCS-MPTC strategy in the PMSM system. The implementation pro-
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cess of the MPTC strategy on the PMSM is basically the same as that of the MPCC strategy,
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also including current sampling, prediction model establishment, cost function minimi-
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zation, switching sequence output, and rolling optimization [13].
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3. Results
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Based on simulation results, this section compares the performance of the traditional
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DTC strategy and the MPTC strategy. The biggest difference between these two schemes
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lies in the different sizes of the alternative voltage vector sets. To improve the realism and
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reliability of the simulation, the PMSM parameters in the simulation test are kept con-
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sistent with the PMSM parameters in the experiment. The main parameters of PMSM are
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shown in Table 2.
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Table 2. The main parameters of PMSM
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157
158
159
160
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As depicted in the ocular representations designated as Figures 5 and 6, it becomes
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progressively obvious that once the force stabilizes and achieves a constant state condi-
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tion, the variation in force oscillates within an outlined range, specifically between 4Nm
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and 8Nm. It is positively apparent that the exercise of direct torque control methods re-
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sults insignificant and evident fluctuations in turn principles, that can lead to functional
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incompetence’s and inconstancy in structure performance; still, when engaging the more
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progressive technique famous as Model Predictive Torque Control (MPTC), individual
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can see a notable reduction in the size of these revolution vacillations, with enhancing the
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overall balance and efficiency of bureaucracy. This comparative reasoning of twist action
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under clashing control strategies underlines the significance of selecting appropriate con-
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trol methods in order to advance twisted item administration and ensure the dependabil-
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ity of machinelike wholes in miscellaneous applications.
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Fig. 5 torque waveform with DTC
Fig. 6 torque waveform with MPTC
As depicted in Figure 7, it is apparent that the stator alteration relation exhibits a
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degree of vacillation, vacillating about a mean advantage of nearly 0.41 Wb, while to-
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gether professed a vacillation range that spans from 0.42 Wb to 0.405 Wb, thereby hap-
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pening in a vacillation worth that may be restricted as 0.015 Wb. As depicted in Figure 8,
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Parameter
Value
Unit
Parameter
Value
Unit
load torque
8.5
N.m
Rs
1.3
Ω
Vdc
300
V
Ld=Lq
9
mH
P
3
-
PMflux
0.41
Wb
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it is apparent that the stator alteration relation exhibits a degree of vacillation, vacillating
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about a mean advantage of nearly 0.41 Wb, while together professed a vacillation range
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that spans from 0.4104 Wb to 0.4097 Wb, thereby happening in a vacillation worth that
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may be restricted as 0.0007Wb. When engaging the methods known as MPTC, individuals
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can celebrate a greatly diminished level of ripple effects distinguished from the common
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methods that have been historically appropriated in this field.
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Fig.7 stator flux amplitude with DTC
Fig.8 stator flux amplitude with MPTC
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4. Conclusions
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Both the method famous as direct torque control particularly planned for constant
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magnet simultaneous motors, usually refer to as PMSM DTC, and the methodology of
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predicting twist control that is to say established stator coordinates, shortened as MPTC,
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basically exploit magnetic fluctuation and necklace as the basic elements for control pur-
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poses, while together engaging the heading of output service caused apiece inverter as
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the key variable for control adaptations, and two together blueprints exhibit several joint
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traits that are important. This scholarly paper endeavors to conduct an inclusive, con-
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trasting, and meticulous examination of these two distinct control actions, focusing spe-
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cifically on their relative control performance, overall influence, and strength against dif-
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ferences in parameters that grant permission to influence their movement. In particular,
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the MPTC approach is recognized for its ability to considerably mitigate turn ripple,
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which refers to the unacceptable fluctuations in necklace manufacturing, in addition to
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stabilizing differences in attractive modification that can unfavorably impact the perfor-
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mance of the engine. Such verdicts highlight the potential advantages of the MPTC ar-
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rangement in embellishing the functional efficiency and dependability of lasting belt syn-
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chronous motors through enhanced control devices.
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Conflicts of Interest: The authors declare no conflict of interest.
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