Multi-Adjustment Strategy for Phase Current Reconstruction of Permanent Magnet Synchronous Motors Based on Model Predictive Control

Abstract

In response to the model predictive control (MPC) driving system, this paper proposes a multi-adjustment strategy for phase current reconstruction based on a coupled current sampling method. The proposed coupled current sampling method eliminates the need to modify the inverter’s internal wiring. The current signals utilized in the proposed method are all external current signals from the inverter and do not involve any current signals from the internal circuitry of the inverter. By analyzing the current sampling mechanism of duty-cycle model predictive control (DC-MPC) as a modulation method, the underlying principles of the non-reconstructible current regions in the coupled current sampling method are revealed. The non-reconstructible regions are accurately delineated into low and high-modulation regions using coupled current sampling. A multi-adjustment strategy for phase current reconstruction is proposed to address the non-reconstructible regions. In the low-modulation regions, phase current reconstruction is achieved through compensated voltage vector pulse injection. In the high-modulation regions, phase current reconstruction is accomplished using the zero-voltage vector insertion approximation method, which maintains the symmetry of the PWM waveform and avoids current distortion. Experimental results on a permanent magnet synchronous motor validate the effectiveness and feasibility of the proposed approach.

1. Introduction

Permanent magnet synchronous motors (PMSMs) are widely applied due to their advantages of high efficiency, low noise, high dynamic response, and high static stability [1,2,3]. In addition to the classical SVPWM-based magnetic field directional control method, research on model predictive control is also evolving. Model predictive control for PMSM based on discrete space vector modulation with recursive least squares (RLS) parameter identification is proposed in Reference [4], which can identify motor parameters accurately. Reference [5] proposes a multiple-vector finite-control-set model predictive control (MV-FCS-MPC) scheme with fuzzy logic for PMSMs. The method can improve control performance. In various application scenarios, precise three-phase current information is required for the execution of control algorithms in order to achieve optimal control performance. Typically, the three-phase current information is provided by two or three current sensors located on the output lines of the inverter. However, employing multiple current sensors not only increases the risk of faults but also escalates the product costs. Additionally, differences in manufacturing processes among multiple current sensors can introduce errors into the control system [6,7]. Therefore, the emergence of phase current reconstruction techniques based on a single current sensor has become essential. A multiperiod sampling method is proposed to obtain the different two-phase current information for reconstruction [8]. Reference [9] proposes a new single-current-sensor (SCS) control method for a permanent magnet synchronous motor (PMSM) driven by a quasi-Z-source inverter (q-ZSI). It can eliminate the measurement dead-zone problem without any additional compensation strategy. Reference [10] proposes the use of a single current sensor to reconstruct three-phase currents and position sensor-less control of motors, which improves the fault tolerance of the system.

Traditional phase current reconstruction techniques typically employ a single current sensor installed on the DC bus. Based on the relationship between the DC bus current and the inverter switching states, the three-phase currents are sampled at specific moments within each pulse-width modulation (PWM) cycle. During the sampling process, due to the existence of dead band times in the switching devices, diode recovery times, and AD sampling times, the effective voltage vector action time must be greater than the minimum sampling time $T_{min}$ [11]. This inevitably results in a reconstruction dead band in the traditional method, limiting its application in low-modulation regions and spatial vector sector boundary areas [12,13,14,15]. In order to reduce the reconstruction dead band, scholars have proposed two main categories of solutions: one is to modify the PWM waveform, and the other is to change the installation position of the single current sensor. Among the methods that modify the PWM waveform, Reference [16] proposes the vector pulse insertion method, which inserts three measured voltage vectors after each PWM cycle. However, the insertion of pulses leads to an increase in the magnitude of the voltage vector. Reference [17] suggests the pulse-shifting method, which achieves the requirement of two valid current samples within one switching period after pulse shifting. However, the PWM waveforms within the period no longer possess symmetry. Reference [6] proposes an improved hybrid pulse-width modulation (PWM) technique that can eliminate the reconstruction dead band in the sector boundary region without requiring additional compensation. However, it may encounter sampling issues due to vector switching between two PWM control cycles. Reference [18] introduces a vector insertion method that involves inserting measurement vectors and compensation vectors. In the methods that involve changing the installation position of the single current sensor, Reference [19] presents the zero-voltage detection method. This method samples the current during the zero-voltage vector action period. However, if the duration of the zero-voltage vector action cannot satisfy the requirements for sampling two zero-voltage vectors simultaneously, a reconstruction dead band can still occur. Reference [20] discusses the optimal selection of multiple coupled current sampling positions under the space vector PWM (SVPWM) algorithm. The optimal selection achieves dead band-free current reconstruction throughout the entire linear modulation region without the need for additional algorithmic processing. However, the optimal selection requires modifications to the internal circuitry of the inverter, making it challenging to implement in practical applications.

The discussions mentioned above on phase current reconstruction methods for permanent magnet synchronous motors (PMSMs) are all based on the space vector pulse-width modulation (SVPWM) technique as the modulation method. However, with the enhanced computational capabilities of digital signal processors, model predictive control (MPC) algorithms have gained widespread application in recent years. In Reference [21], FCS-MPC was successfully applied in power converters. In model predictive control, FCS-MPC does not need a modulator, has fast a dynamic response, and can directly utilize the discrete characteristics of the converter and the finite switching state [22]. Reference [23] proposes a multi-virtual-vector model predictive control for a dual three-phase permanent magnet synchronous machine (DTP-PMSM), which can regulate the currents in both fundamental and harmonic subspace.

Within one pulse-width modulation cycle, there are differences between MPC and SVPWM in the voltage vectors applied. Therefore, there are differences between MPC and SVPWM in the methods of phase current reconstruction, and reconstructing phase currents under the MPC algorithm has become a new research direction [24].

This paper proposes a multi-strategy phase current reconstruction method using the coupled current sampling for the duty-cycle model predictive control case. The proposed method maintains the symmetry of PWM waveforms in duty-cycle model predictive control while reconstructing the current. We measured the parameters of the experimental platform and validated its reliability [25]. The constructed testbeds demonstrate the correctness and effectiveness of the proposed method. The main contributions of this paper are as follows:

(1)

Proposing a coupled current sampling method for current reconstruction without changing the internal wiring of the inverter.

(2)

The phase current non-reconfigurable region is analyzed for a drive system where the modulation is duty-cycle model predictive control. The non-reconstructible region is divided into a low-modulation region and a high-modulation region.

(3)

For the non-reconfigurable region of phase currents, the compensated voltage vector pulse insertion method and the zero-voltage vector insertion approximation method are proposed to eliminate the low- and high-modulation dead bands, respectively.

2. Duty-Cycle Model Predictive Control

This paper focuses on phase current reconstruction based on duty-cycle model predictive control. The duty-cycle model predictive control algorithm proposed in Reference [24] is employed in this study. This algorithm no longer involves traversing all voltage vectors directly. Instead, it selects the optimal effective voltage vector by calculating the angle of the reference voltage vector, and then determines the optimal duty ratio time based on the angle calculated during the selection of the optimal voltage vector.

The method proposed in Reference [24] is employed to calculate the angle of the reference voltage vector and the duty ratio time. The formula for calculating the reference voltage vector angle is shown as Equation (1).

$${\theta }_{ref}=\arctan \left(\frac{u_{\beta }^{k+1}}{u_{\alpha }^{k+1}}\right)$$

(1)

$u_{\alpha }^{k+1}$ and $u_{\beta }^{k+1}$ are the components of the reference voltage vector on the αβ-axis at moment k + 1, respectively. ${\theta }_{ref}$ is the angle of the reference voltage vector $u_{ref}$. The optimal voltage vector $u_{opt}$ can be selected based on the angle ${\theta }_{ref}$ of the reference voltage vector. The formula for calculating the duty ratio time, as derived from Reference [24], is as follows:

$$t_{opt}=\frac{u_{ref}·u_{opt}}{{\left|u_{opt}\right|}^2}{T}_s$$

(2)

$u_{opt}$ is the effective voltage vector. $t_{opt}$ is the action time of the effective voltage vector. $T_s$ is the sum of effective voltage vector and zero-vector action time. By utilizing Equations (1) and (2), the optimal effective voltage vector and its duration can be obtained. To ensure the symmetry of the PWM waveform, we illustrate the example of the effective voltage vector $U_1$(100). The PWM waveform within one pulse-width modulation cycle is depicted in Figure 1, where the effective voltage vector acts at the midpoint of the cycle and the zero-voltage vector is applied at the beginning and end of the cycle.

3. Coupled Current Sampling

The proposed control system for the multi-adjustment strategy of phase current reconstruction in permanent magnet synchronous motors (PMSMs) based on model predictive control is illustrated in Figure 2. Additionally, the voltage space vector diagram is depicted in Figure 3.

When employing the space vector pulse-width modulation (SVPWM) algorithm, a single pulse-width modulation (PWM) cycle involves the action of four voltage vectors. However, when using the duty-cycle model predictive control algorithm, a PWM cycle consists of only two voltage vectors. For the drive system designed specifically for duty-cycle model predictive control, a coupled current sampling circuit is presented in Figure 4. The coupled currents, sampled by the perforated Hall-effect current sensors, include the direct current (DC) bus current, phase A stator current, and phase B stator current. As discussed earlier, the duty-cycle model predictive control utilizes a single zero-voltage vector and a single effective voltage vector within a PWM cycle. By employing this coupling method, the issue of being unable to detect effective currents during the action of a zero-voltage vector when using DC bus sampling can be resolved. Moreover, this coupling method eliminates the need to modify the internal circuitry of the inverter, in contrast to the coupling method proposed in Reference [20]. The wiring schematic of the method used in Reference [20] is shown in Figure 5, which requires a current signal on the bridge arm between the two phases compared to Figure 4.

3.1. The Principle of Coupled Current Sampling

The relationship between the instantaneous coupled current and the three-phase stator currents of the motor depends on the switching state of the inverter. Under different voltage vector applications, the relationship between coupled current and the motor’s three-phase stator currents varies. Taking $U_5$(001) and $U_0$(000) as examples: when the voltage vector $U_5$(001) is applied, as shown in Figure 4, the inverter switches $V_{a2}$, $V_{b2}$, and $V_{c1}$ are turned on, while $V_{a1}$, $V_{b1}$, and $V_{c2}$ are turned off. In this case, the DC bus current $I_{dc}$ is equal to the C-phase current, $I_{dc}$ = $I_c$, and the coupled current $I_{couple}$ = $I_{dc}+I_a-I_b$ = −2$I_b$. On the other hand, when the voltage vector $U_0$(000) is applied, as shown in Figure 4, the inverter switches $V_{a2}$, $V_{b2}$, and $V_{c2}$ are turned on, while $V_{a1}$, $V_{b1}$, and $V_{c1}$ are turned off. In this scenario, the DC bus current $I_{dc}$ is 0, $I_{dc}$ = 0, and the coupled current $I_{couple}$ = $I_{dc}$ + $I_a$ − $I_b$ = $I_a$ − $I_b$.

The relationship between voltage vectors and the three-phase stator currents of the motor is presented in

Table 1. Relationship between voltage vectors and motor phase stator currents.

Voltage Vector	Coupled Current of the Sensor
$U_0$(000)	$i_a-i_b$
$U_1$(100)	$2i_a-i_b$
$U_2$(110)	$2i_a$
$U_3$(010)	$i_a$
$U_4$(011)	$-i_b$
$U_5$(001)	$-2i_b$
$U_6$(101)	$i_a-2i_b$
$U_7$(111)	$i_a-i_b$

.

Based on the analysis in the previous section, when employing the duty-cycle model predictive control, the voltage vector applied within one PWM cycle consists of the zero-voltage vector $U_0$(000) and one valid voltage vector. When the zero-voltage vector $U_0$(000) and the active voltage vector $U_5$(001) are applied, the corresponding coupling currents are $I_{couple1}=I_a$ − $I_b$ and $I_{couple2}$ = −2$I_b$. Therefore, the relationship between the three-phase stator currents can be derived as $I_b$ = −0.5$I_{couple2}$, $I_a=I_{couple1}$ − 0.5$I_{couple2}$. The relationship among the three-phase currents of the motor is given by $I_a$ + $I_b$ + $I_c$ = 0. Thus $I_c$ = −$I_a-I_b=I_{couple2}$ − $I_{couple1}$.

The relationship between the coupled currents and the three-phase stator currents of the motor is shown in

Table 2. Calculation relationship between coupled currents and motor phase stator currents.

Voltage Vector Applied within a Period	Relationship between Coupled Current and Three-Phase Current
$U_0$(000), $U_1$(100)	$i_a$=$I_{couple2}-I_{couple1} i_b$=$I_{couple2}-2I_{couple1}$ $i_c$=$3I_{couple1}-2I_{couple2}$
$U_0$(000), $U_2$(110)	$i_a$=$0.5I_{couple2}$$i_b$=$0.5I_{couple2}-I_{couple1}$ $i_c$=$I_{couple1}-I_{couple2}$
$U_0$(000), $U_3$(010)	$i_a$=$I_{couple2}$$i_b$=$I_{couple2}-I_{couple1}$ $i_c$=$I_{couple1}-2I_{couple2}$
$U_0$(000), $U_4$(011)	$i_a$=$I_{couple1}-I_{couple2} i_b$=$-I_{couple2}$ $i_c$=$2I_{couple2}-I_{couple1}$
$U_0$(000), $U_5$(001)	$i_a$=$I_{couple1}-0.5I_{couple2} i_b$=$-0.5I_{couple2}$ $i_c$=$I_{couple2}-I_{couple1}$
$U_0$(000), $U_6$(101)	$i_a$=$2I_{couple1}-I_{couple2} i_b$=$I_{couple1}-I_{couple2}$ $i_c$=$2I_{couple2}-3I_{couple1}$
$U_0$(000), $U_1$(100)	$i_a$=$I_{couple2}-I_{couple1} i_b$=$I_{couple2}-2I_{couple1}$ $i_c$=$3I_{couple1}-2I_{couple2}$
$U_0$(000), $U_2$(110)	$i_a$=$0.5I_{couple2} i_b$=$0.5I_{couple2}-I_{couple1}$ $i_c$=$I_{couple1}-I_{couple2}$

when different voltage vector combinations are applied. The coupling current is denoted as $I_{couple1}$ when the zero-voltage vector $U_0$(000) is applied, and as $I_{couple2}$ when a valid voltage vector is applied.

3.2. The Non-Reconstructible Region of the Current in Duty-Cycle Model Predictive Control

The main cause of the dead band in phase current reconstruction is the presence of the minimum sampling time $T_{min}$. The value of $T_{min}$ is primarily determined by the switch device dead band time, diode recovery time, and AD sampling time. The dead band in phase current reconstruction varies with different modulation methods. In the following analysis, we will examine the dead band in phase current reconstruction using the model predictive control (MPC) algorithm.

In one control cycle, when the number of voltage vectors whose action time is greater than or equal to $2T_{min}$ is less than two, there will be a reconstruction dead band. In the case of the duty-cycle model predictive control algorithm, only two voltage vectors are utilized within one modulation cycle, with one vector fixed as the zero-voltage vector. Consequently, the dead band in phase current reconstruction differs significantly from that when using space vector pulse-width modulation (SVPWM) as the modulation method. The dead band in phase current reconstruction with the optimal DC-MPC as the modulation method is depicted in Figure 6. The grey region is referred to as the high-modulation region, which occurs when the duration of the zero-voltage vector is smaller than the minimum sampling time. The yellow region is referred to as the low-modulation zone, resulting from the actuation time of the effective voltage vector being less than the minimum sampling time.

4. Multi-Adjustment Strategies for the Non-Reconstructible Region

To eliminate the dead band in the non-reconstructible region, ensure the symmetry of the pulse-width modulation (PWM) waveform in the duty-cycle model predictive control, and minimize current harmonic content, this paper proposes different vector insertion methods based on the characteristics of the low-modulation region and high-modulation region. In the low-modulation region, the duration of the effective voltage vector is increased, and additional compensated voltage vectors are inserted to mitigate the effects caused by the extended duration of the effective voltage vector. In the high-modulation region, inserting the zero-voltage vector $U_7\left(111\right)$ at the midpoint of each pulse-width modulation cycle as a measurement vector helps maintain the symmetry of the PWM waveform.

4.1. The Non-Reconstructible Region in the Low-Modulation Region

When the reference voltage vector is in the low-modulation region as depicted in Figure 6, the active time of the effective voltage vector is less than twice the minimum sampling time $T_{min}$. Therefore, the reconstruction dead band is caused by the inability to complete current sampling in the first half of the pulse-width modulation cycle. To eliminate the reconstruction dead band, the active time of the effective voltage vector is increased to meet the sampling requirements. To minimize the impact of the increased active time on the synthesized voltage vector within the cycle, while ensuring PWM waveform symmetry and reducing current harmonic content, complementary effective voltage vectors are inserted at the initial and final positions within the cycle for compensation. Taking the example of the voltage vectors $U_0$(000) and $U_1$(100) within a cycle, the adjusted PWM waveforms during the adaptation process are illustrated in Figure 7. The active time of $U_1$(100), denoted as $T_1$, is less than twice the minimum sampling time $T_{min}$, necessitating an extension of $U_1$(100)’s active time to $T_1^{\prime }$ = 2$T_{min}$. Consequently, the PWM waveform of phase A needs to be expanded by $T_{min}-T_1/2$ on both sides to meet the sampling requirements. The inserted complementary voltage vector is $U_4$(011), which acts during the initial and final positions of the pulse-width modulation cycle for a duration of $T_4^{\prime }/2$ = $T_{min}-T_1/2$.

The synthesized optimal voltage vector before and after the insertion of complementary effective voltage vectors are denoted as $U_{opt}$ and $U_{opt}^{\prime }$, respectively.

$$\left\{\begin{array}{c}{U}_0{T}_0+U_1{T}_1=U_{opt}{T}_s\\ U_0{T}_0^{\prime }+U_1{T}_1^{\prime }+U_4{T}_4^{\prime }=U_{opt}^{\prime }{T}_s\end{array}\right.$$

(3)

Furthermore, due to the following Equation (4).

$$\left\{\begin{array}{c}{U}_0=0\\ U_1=-U_4\\ \genfrac{}{}{0pt}{}{T_1^{\prime }=2T_{min}}{T_4^{\prime }=2T_{min}-T_1}\end{array}\right.$$

(4)

Combining Equations (3) and (4).

$$U_{opt}^{\prime }{T}_s=\left(-U_1\right)\left(2T_{min}-T_1\right)+2U_1{T}_{min}$$

(5)

$$U_{opt}^{\prime }{T}_s=U_1{T}_1=U_{opt}{T}_s$$

(6)

The magnitude and direction of the optimal voltage vector remain unchanged before and after the adjustment.

4.2. The Non-Reconstructible Region in the High-Modulation Region

When the reference voltage vector is located in the high-modulation region as shown in Figure 6, the zero-voltage vector’s duration $T_0$ is less than twice the minimum sampling time $T_{min}$, resulting in a reconstruction dead band. To address the high-modulation dead band issue, the zero-voltage vector insertion approximation method is employed. Taking the voltage vectors $U_0$ and $U_1$ as examples for analysis, the high-modulation dead band can be divided into two parts, as depicted in Figure 8. One part is called high-modulation dead band region I, where the zero-voltage vector’s duration is $T_{min}<T_0<2T_{min}$. The other part is called high-modulation dead band region II, where the zero-voltage vector’s duration is $T_0<T_{min}$.

The zero-voltage vector insertion approximation method combines the insertion of the zero-voltage vector $U_7\left(111\right)$ with voltage vector approximation. During the mid-section of each pulse-width modulation (PWM) cycle, the measurement zero-voltage vector $U_7\left(111\right)$ is inserted, and the sampling points are set during the duration of the effective voltage vector and the duration of the zero-voltage vector $U_7\left(111\right)$.

When the reference voltage vector is located in the high-modulation dead band region I as shown in Figure 8, the measurement zero-voltage vector $U_7\left(111\right)$ is inserted during the mid-section of the pulse-width modulation (PWM) cycle, with an action time of $T_7^{\prime \prime \prime \prime }=T_{min}$. The action time of $U_7\left(111\right)$ is then adjusted to $T_0-T_{min}$. The adjusted PWM waveform is illustrated in Figure 9.

The setting of the sampling points is shown in Figure 9, where the first sampling time is adjusted to $T_0^{\prime \prime \prime \prime }/2+T_4^{\prime \prime \prime \prime }/4=T_0/2-T_{min}/2+T_1/4$. The second sampling time is adjusted to $T_s/2+T_{min}/2$.

When the reference voltage vector is in the high-modulation dead band II of Figure 8, the measurement zero-voltage vector $U_7\left(111\right)$ is inserted during the middle of the pulse-width modulation (PWM) period, and its duration is adjusted to $T_7^{\prime \prime \prime \prime }=T_{min}$. However, prior to the adjustment, the action time $T_0$ of the zero-voltage vector $U_0$(000) was less than $T_{min}$. Even if the entire duration of $U_0$(000) is adjusted to $U_7\left(111\right)$, the resulting duration $T_7^{\prime \prime \prime \prime }$ is still less than $T_{min}$. Therefore, voltage vector approximation is performed based on the insertion of zero-voltage vector $U_7\left(111\right)$. When the reference voltage vector is in the high-modulation dead band II, the synthesized voltage vector output of the zero-voltage vector insertion approximation method follows the $V_s^{\prime }$ approximation shown in Figure 8. The approximated PWM waveform is shown in Figure 10. In this pulse-width modulation period, the action time $T_0$ of $U_0$(000) is less than $T_{min}$, and the deficient time $T_{min}-T_0$ is compensated by the action time $T_1$ of $U_1$.

The setting of the sampling points is shown in Figure 10, where the first sampling time is adjusted to $T_s/4-T_{min}/4$. The second sampling time is adjusted to $T_s/2+T_{min}/2$. Using a fixed time for both sampling instances can further simplify the algorithm.

5. Experimental Verification

This section validates the proposed multi-adjustment strategy for phase current reconstruction in permanent magnet synchronous motors based on duty-cycle model predictive control. The experimental platform, as shown in Figure 11, was utilized for the validation. The experimental parameters are listed in

Table 3. Parameters of Permanent Magnet Synchronous Motor (PMSM).

Parameter	Numerical Value
Rated Power	1.5 kW
Rated Speed	2000 r/min
Flux Linkage	0.23 Wb
Phase Resistance	1.27 Ω
d-/q-axis Inductance	6.86 mH
Pole Numbers	8
Moment of Inertia	15.3 kg·cm2

. The direct current bus voltage supplied to the inverter of the permanent magnet synchronous motor was set at 127 V, with a minimum sampling time $T_{min}$ of 5 μs and an inverter switching frequency of 10 kHz.

Firstly, to demonstrate the feasibility of the proposed method in the reconstructible region, Figure 12 shows the current waveforms based on the proposed current reconstruction method in the reconstructible region. Figure 13 illustrates the current reconstruction error waveform. The motor speed is 300 r/min with a load torque of 5 N·m. Figure 11 and Figure 12 present the measured and reconstructed currents and the reconstruction error waveforms for phase A. In the waveforms of phase A, the reconstructed current closely aligns with the measured current, thereby confirming the accuracy of the proposed method in the reconstructible region. The maximum absolute value of the reconstruction error, as observed from the error waveform, does not exceed 0.8 A. Most of the time, the reconstruction error remains low, which is acceptable. The leading cause of the reconstruction error is the time-division sampling within the pulse-width modulation (PWM) cycle. This situation has been present in previous phase current reconstruction methods.

To demonstrate the feasibility of the proposed method in the unreconstructible regions, separate experiments were conducted for the low-modulation region and high-modulation region. Figure 14 illustrates the current waveforms based on the proposed current reconstruction method in the low-modulation region, while Figure 15 shows the current reconstruction error in the same region. Additionally, Figure 16 presents the current waveforms based on the proposed current reconstruction method in the high-modulation region, and Figure 16 displays the corresponding current reconstruction error.

In the low-modulation region experiment depicted in Figure 14 and Figure 15, the motor speed was set at 100 r/min with a load torque of 5 N·m. The phase A measured current closely align with the reconstructed currents in Figure 14, while the maximum absolute value of the current error in Figure 15 does not exceed 1 A. These results confirm the effectiveness of the proposed method in effectively eliminating the reconstruction dead band in the low-modulation region.

In the high-modulation region experiment shown in Figure 16 and Figure 17, the motor speed was set at 600 r/min with a load torque of 5 N·m. The phase A measured current in Figure 16 closely matches the reconstructed currents, with the maximum absolute value of the current reconstruction error not exceeding 1 A. These findings demonstrate the successful implementation of the proposed method in achieving current reconstruction in the high-modulation region effectively.

To further validate the effectiveness of the proposed phase current reconstruction method, speed transients were conducted. Figure 18 shows the current waveforms and current reconstruction errors during motor speed transients, with a motor load torque of 5 N·m. In the speed-up test, the speed was abruptly increased from 300 r/min to 500 r/min, while in the speed-down test, the speed was abruptly decreased from 500 r/min to 100 r/min. From Figure 18, it can be observed that the actual currents and reconstructed current of phase A remain stable during the motor speed transients. The reconstruction error of the phase A current in Figure 18 exhibits no significant fluctuations during the speed variation, consistently maintaining a low level. This validates the effectiveness of the proposed method in handling speed transients.

6. Conclusions

A multi-adjustment strategy for phase current reconstruction based on coupled current sampling is proposed to address the duty-cycle model predictive control modulation method in a drive system. This approach utilizes coupled current sampling to achieve phase current reconstruction when duty-cycle model predictive control is employed as the modulation method, without modifying the internal wiring of the inverter. In the non-reconstructible region, both the low- and high-modulation regions employ compensation voltage vector pulse injection and zero-voltage vector approximation methods, respectively. This multi-adjustment strategy for phase current reconstruction eliminates the reconstruction dead band in the non-reconstructible region and preserves the symmetry of the PWM waveform without introducing current distortion. By employing the above-mentioned approach, we increase the effective duration of the voltage vector in the low-modulation region and insert compensating voltage vectors to mitigate the effects of the increased effective voltage vector duration. In the high-modulation region, we insert zero-voltage vectors at the midpoint of each pulse-width modulation cycle to maintain the symmetry of the PWM waveform. This multi-adjustment strategy for phase current reconstruction not only eliminates the non-reconstructible regions’ dead zones but also preserves the PWM waveform symmetry, avoiding current distortion. Experimental results demonstrate that the reconstructed currents in both the reconstructible and non-reconstructible regions exhibit errors within 1 A compared to the actual current values. The high accuracy of the current reconstruction ensures stable system operation. This method offers a novel solution for phase current reconstruction based on pulse-width modulation model predictive control. The proposed method provides a new solution for phase current reconstruction in duty-cycle model predictive control.