Fault Diagnosis Method for Position Sensors in Multi-Phase Brushless DC Motor Drive Systems Based on Position Signals and Fault Current Characteristics

Abstract

Multi-phase brushless DC motors (BLDCMs) have broad prospects in the power propulsion systems of electric vehicles, submarines, electric ships, etc., due to their advantages of high efficiency and high power density. In the above application scenarios, accurately obtaining the rotor position information is crucial for ensuring the efficient and stable operation of multi-phase BLDCMs. Therefore, by analyzing the fault conditions of position sensors in this paper, a fault diagnosis method for position sensors in multi-phase brushless DC motor drive systems based on position signals and fault current characteristics is proposed, with the aim of improving the reliability of the system. This method utilizes the Hall state value determined by the Hall position signal and the current characteristics under the fault state to achieve rapid fault diagnosis and precise positioning of the position sensor. Its advantage lies in the fact that it does not require additional hardware support or complex calculations, and can efficiently identify the fault conditions of position sensors. To verify the effectiveness of the proposed method, this paper conducts experiments based on a nine-phase brushless DC motor equipped with nine Hall position sensors. The results of steady-state and dynamic experiments show that this method can achieve rapid fault diagnosis and location.

1. Introduction

Multi-phase brushless DC motors have broad application prospects in fields such as aerospace, electric vehicles, and industrial automation in electric vehicles and electric ships [1,2,3,4,5]. With the continuous expansion of its application scope, the reliability and security of the system have become key performance indicators. Reference [6] proposed a novel symmetrical winding multi-phase BLDCM structure and its optimized design method. This method is not limited by the number of winding phases and can be expanded based on the winding arrangement rule within a limited control complexity, thereby enhancing the torque density and system efficiency of the motor. On this basis, aiming at the open-circuit fault problem of the symmetrical winding multi-phase BLDCM, a fault-tolerant control strategy was proposed in reference [7]. By dynamically adjusting the conduction mode of the windings in specific sectors and optimizing the spatial distribution of the magnetomotive force (MMF), the torque ripple caused by faults is effectively reduced. BLDCMs require control over the commutation sequence and duration of each phase through position sensors to achieve precise control over the output torque. Proper processing of position signals ensures that the motor commutation occurs at the correct locations, allowing the motor to operate as intended [8,9]. Therefore, position signals are of utmost importance. Various sensorless schemes such as the pulse injection-based method [10,11,12,13], flux/inductance threshold-based method [14], inductance model-based method [15,16,17], intelligent algorithm-based method [18], observer-based method [19,20,21,22,23], virtual flux linkage method [24,25,26], special position estimation-based method [27,28] and sensing coil-based method [29,30,31] have been developed over the past three decades. However, most of the sensorless methods still have certain limitations, which cannot cover the entire speed range operation stably.

In multi-phase BLDCM drive systems, Pulse Width Modulation (PWM) and position sensors are still employed to achieve precise current control and commutation, relying on the accurate position feedback provided by position sensors (such as Hall effect sensors) at every instant of rotor rotation to realize efficient rotational motion [31]. However, in practical operations, position sensors may fail due to various reasons, such as harsh environments and vibrations [32,33,34]. Failure of position sensors can lead to confusion in the commutation logic of the motor drive system, reducing the motor’s output torque and even preventing normal operation [35]. Consequently, to enhance the reliability of multi-phase BLDCM drive systems, it is necessary to conduct research on fault diagnosis of position sensors.

In the realm of traditional three-phase BLDCM research, the fault diagnosis methods of position sensor are divided into three categories: the methods based on knowledge analysis, the methods based on model and observer, and the methods based on signal analysis.

Knowledge-based methods achieve fault classification and error compensation by learning features from fault samples through neural networks and optimization algorithms [36,37,38,39,40]. An asynchronous motor fault diagnosis method based on a 3D convolutional neural network (3D CNN) was proposed in [37]. The proposed method provides an efficient scheme for asynchronous motor fault diagnosis, improves the accuracy and real-time performance of fault diagnosis by preserving the spatial relationship of current signals, and is suitable for real-time monitoring requirements in industrial scenes. Reference [38] explores the characteristics of different types of neural networks; fault diagnosis systems based on CNN and DNN can effectively locate faults with an accuracy of over 95%. Knowledge-based methods do not require precise models and offer high compensation accuracy. However, such methods rely on large amounts of high-quality data and involve heavy computation, making it difficult to meet the real-time requirements of high-phase motors.

Model-based and observer-based methods achieve fault diagnosis through current estimation and error analysis, with advantages of load independence and certain robustness to parameter time-variability [41,42,43,44,45,46]. Reference [41] uses Kalman filter optimal estimation to obtain the accurate speed at the commutation moment of the motor, and then predicts the next commutation moment; however, under complex working conditions, the motor speed fluctuates sharply, making the reliability of fault detection questionable. A real-time multi-sensor joint fault diagnosis method for permanent magnet traction drive system (PMTDS) based on structural analysis was proposed in [42]. This method does not need additional hardware. Through structural analysis, the inherent redundancy of the system is mined, and the rapid detection and location of multi-sensor faults in PMTDS are realized, taking into account engineering practicability and diagnostic accuracy. Such methods are highly dependent on the accuracy of the model and have high algorithm complexity. In view of the limitations of the above two types of methods, researchers have gradually turned more attention to signal analysis-based methods in recent years.

The method based on signal analysis does not need complex models and only relies on existing signals [47,48,49,50,51,52,53,54,55]. A three-stage fault mitigation scheme for BLDCM Hall sensor signal imbalance fault was proposed in [51]; however, this method relies on offline detection at startup, and cannot diagnose new faults in time. Reference [52] proposed a method based on position signal, switch drive signal, and non-conducting phase current for the fault diagnosis of the position sensor of a doubly salient electromagnetic motor (DSEM). The method for generating additional position information based on redundant position sensors to achieve fault location was proposed in [53]. This method has the advantage of not being affected by changes in speed and load, but correspondingly increases the cost of diagnosis. And for the fault situation where the position signal is maintained at a high or low level, the method may not be able to quickly identify the fault, resulting in a fault phase current of up to 30 degrees electrical angle of the motor. To address cost reduction, a fast fault diagnosis technology that can diagnose the faults of a single and two position sensors was introduced in [54]. However, because the method depends on the time threshold τ, there is a certain balance between realizing fast fault diagnosis and maintaining the robustness of the system. Therefore, how to maintain the robustness of the system while realizing fast fault diagnosis is a challenge that needs to be solved. A combinable circuit that can detect the fault of the Hall position sensor relying only on three position signals was further proposed in [55], which is suitable for diagnosing a single position sensor fault, but the fault detection time is lengthy in some sectors.

Reference [9] proposes a fault detection approach based on the features of the Hall signal state sequence (Hall state integers) of three-phase BLDCM. Its core is to achieve rapid identification of sensor anomalies by comparing the deviation between the actual Hall states and the preset normal sequence. This method does not require complex models and provides a concise and effective framework for position sensor fault diagnosis. However, in multi-phase BLDCM control systems, since more position sensors are required to obtain rotor position information, the fault scenarios are more complex and higher requirements are placed on diagnostic speed. To this end, this paper extends upon [9] by generalizing the fault identification logic based on Hall state integers from three-phase systems to multi-phase systems, so as to adapt to the fault diagnosis requirements under multi-phase conduction modes.

Based on the multi-phase conduction characteristics of multi-phase brushless DC motors, this paper proposes a fault diagnosis method centered on position signals and fault current characteristics. Firstly, the influence of position sensor failure on the operation of the motor was analyzed. Secondly, fault diagnosis was carried out by using the position signal characteristics and current characteristics under fault conditions. Finally, in order to verify the effectiveness of the proposed method, experimental verification was carried out on a nine-phase brushless DC motor equipped with nine position sensors. The rest of this paper is organized as follows. The second section introduces the working principle of the nine-phase brushless DC motor and analyzes the fault conditions of the position sensor. The proposed fault diagnosis method is introduced in detail in Section 3. The results of the fault test are shown in Section 4. Finally, Section 5 summarizes this article.

2. Operation Principle of Nine-Phase BLDCM and Fault Analysis of Position Sensor

2.1. Operation Principle of Nine-Phase BLDCM

For symmetrical winding multi-phase BLDCMs, the armature windings are evenly distributed in space with only one neutral point. The nine-phase BLDCM and its drive system can be simplified to the equivalent circuit shown in Figure 1, where the motor is represented as a series combination of resistance, inductance, and back-EMF. Each phase armature winding is connected to the midpoint of the corresponding bridge arm of the inverter, and the number of windings is equal to that of the bridge arm. Here, U_dc is the DC bus voltage, C₁~C₂ are filter capacitors, T₁~T₁₈ are power switching devices, D₁~D₁₈ are diodes, A₁~A₉ are phase windings, R_s is the phase resistance, L_s is the equivalent phase inductance, e_A1~e_A9 are the phase back-EMFs, and N is the neutral point.

According to the equivalent circuit of the system shown in Figure 1, the voltage equation of the nine-phase BLDCM with symmetric winding can be expressed as

$$u_{\mathrm{A}i}=R_{\mathrm{s}}{i}_{\mathrm{A}i}+L_{\mathrm{s}}{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}i}}{\mathrm{d}t}}+e_{\mathrm{A}i}+u_{\mathrm{N}}$$

(1)

where u_Ai are the phase voltages, i_Ai are the phase currents, and u_N is the neutral point voltage, i = 1, 2, …, 9.

The armature winding is a star connection. According to Kirchhoff’s current law, the phase currents satisfy the following relationship as

$$i_{\mathrm{A}1}+i_{\mathrm{A}2}+i_{\mathrm{A}3}+\dots +i_{\mathrm{A}8}+i_{\mathrm{A}9}=0.$$

(2)

Equation (1) describes the relationship between the phase voltage, current, back electromotive force, and neutral point voltage of each phase winding. The expression for the neutral point voltage UN will be further derived in conjunction with the current constraint Equation (2) of the star shaped connection (see Equation (7)).

With the increase of the number of phases in the symmetrical winding multi-phase BLDCM, a larger flat top width of the back-EMF should be designed in order to make full use of each phase winding and achieve smooth output torque. Therefore, the trapezoidal wave back-EMF flat top width of the nine-phase BLDCM is usually designed to be 160°. In addition, the nine-phase BLDCM adopts the suspended one-phase conduction mode similar to the three-phase motor, so that the actual operation is carried out in the mode of eight-phase winding conduction. In this eight-phase conduction operation mode, the logical relationship between the back-EMF and the corresponding conduction phase current and the position signal is shown in Figure 2.

It can be seen from Figure 2 that when the nine-phase BLDCM adopts the eight-phase winding conduction mode, the motor is controlled to commutation every 20° electrical angle according to the Hall signal feedback from the Hall effect sensor. The entire electrical cycle is divided into 18 sectors. Each sector opens four upper and four lower bridge arm switches simultaneously. The phase commutation process is carried out between the left and right bridge arms, and the ratio of positive and negative phase current is 1:1. The forward and reverse conduction angle of each phase armature winding is 160°, which corresponds to the flat top width of the back-EMF.

Similar to the principle in [9], where the three-phase BLDCM divides the Hall states into six operating sectors through the binary combination of Hall signals, for the nine-phase BLDCM, this paper extends this method to multi-phase applications, and the Hall states of the nine-phase BLDCM can also be expressed as

$$\begin{array}{l}s=256\cdot H_1+128\cdot H_2+64\cdot H_3+32\cdot H_4\\ +16\cdot H_5+8\cdot H_6+4\cdot H_7+2\cdot H_8+1\cdot H_9\end{array}$$

(3)

where the Hall state s corresponds to the current flow state of the motor. In the healthy state, assuming a clockwise direction, the Hall state s produces a repeat sequence 341→340→342→338→346→330→362→298→426→170→171→169→173→165→181→149→213→85→341. The Hall states 341 to 85, respectively, correspond to 18 sectors in the case of clockwise rotation of the motor, and the specific corresponding relationship is shown in Figure 3. The rotor position information is determined according to the Hall state s determined by nine Hall signals within a 360-degree electrical angle period, and then the conduction sequence and time of each phase of the motor are controlled.

As shown in the 0°~20° sector in the shaded part of Figure 2 and Figure 3, the corresponding Hall state is 341, and the corresponding conduction phase winding should be A₁⁺, A₂⁻, A₃⁺, A₄⁻, A₅⁺, A₆⁻, A₇⁺, A₈⁻, that is, A₁, A₃, A₅, A₇ phase winding positive guide pass, A₂, A₄, A₆, A₈ phase winding negative guide pass. A₉ phase winding is a suspended phase. Finally, the corresponding Hall state and conducting phase winding relationship of each sector under clockwise rotation of the motor are obtained as shown in

Table 1. The corresponding Hall states and conduction phase windings for each sector when the motor rotates clockwise.

Sector	Hall State s	Conduction Phase (+ for Positive, − for Negative)
0°~20°	341	A1+, A2−, A3+, A4−, A5+, A6−, A7+, A8−
20°~40°	340	A9−, A1+, A2−, A3+, A4−, A5+, A6−, A7+
40°~60°	342	A8+, A9−, A1+, A2−, A3+, A4−, A5+, A6−
60°~80°	338	A7−, A8+, A9−, A1+, A2−, A3+, A4−, A5+
80°~100°	346	A6+, A7−, A8+, A9−, A1+, A2−, A3+, A4−
100°~120°	330	A5−, A6+, A7−, A8+, A9−, A1+, A2−, A3+
120°~140°	362	A4+, A5−, A6+, A7−, A8+, A9−, A1+, A2−
140°~160°	298	A3−, A4+, A5−, A6+, A7−, A8+, A9−, A1+
160°~180°	426	A2+, A3−, A4+, A5−, A6+, A7−, A8+, A9−
180°~200°	170	A1−, A2+, A3−, A4+, A5−, A6+, A7−, A8+
200°~220°	171	A9+, A1−, A2+, A3−, A4+, A5−, A6+, A7−
220°~240°	169	A8−, A9+, A1−, A2+, A3−, A4+, A5−, A6+
240°~260°	173	A7+, A8−, A9+, A1−, A2+, A3−, A4+, A5−
260°~280°	165	A6−, A7+, A8−, A9+, A1−, A2+, A3−, A4+
280°~300°	181	A5+, A6−, A7+, A8−, A9+, A1−, A2+, A3−
300°~320°	149	A4−, A5+, A6−, A7+, A8−, A9+, A1−, A2+
320°~340°	213	A3+, A4−, A5+, A6−, A7+, A8−, A9+, A1−
340°~360°	85	A2−, A3+, A4−, A5+, A6−, A7+, A8−, A9+

.

2.2. Fault Analysis of Position Sensors

In the event of Hall sensor failure—due to component damage, power loss, or disconnection of output lines—the detected Hall signal typically ceases to fluctuate in response to the rotor’s position. Instead, it becomes static, either “high” or “low”, devoid of any positional information regarding the rotor. Therefore, when the Hall sensor fails, according to its output signal H_i (i = 1, 2, …, 9) differences before and after the fault, the fault performance of the position sensor is divided into four types as shown in Figure 4. They are as follows: (1) H_i before and after the fault is low level, which is defined as low level fault 1; (2) H_i before the fault is high level, and Hi after the fault is low level, which is defined as low level fault 2; (3) H_i is high before and after the fault, which is defined as high level fault 1; (4) H_i is low level before the fault, but high level after the fault, which is defined as high level fault 2.

As can be seen from Figure 4, the actual Hall signal in the fault state will deviate from the ideal Hall signal. At this point, sectors cannot be correctly determined based on the Hall state, which will lead to incorrect commutation. Therefore, the location of faults should be detected in a timely manner so that fault-tolerant control strategies can be adopted promptly.

3. Proposed Fault Diagnosis Method

3.1. Fault Diagnosis and Location

As can be seen from Figure 3, in the healthy state of the position sensor, the values of the Hall state obtained by the binary combination of the Hall signal are a fixed sequence. When the position sensor i malfunctions, it can be seen from the fault analysis in the first section that H_i is always 1 or 0. The incorrect Hall signal under the fault condition will definitely lead to values other than the fixed Hall state. Therefore, fault diagnosis can be made based on whether the Hall signal meets the Hall state value under a healthy state. The specific formula is as follows.

$$h_{\det }=\left\{\begin{array}{l}1s\not\subset S=\left\{\begin{array}{l}341,340,342,338,346,330,\\ 362,298,426,170,171,169,\\ 173,165,181,149,213,85\end{array}\right\}\\ 0\mathrm{others}\end{array}\right.$$

(4)

In the formula, h_det = 1 indicates that the position sensor is faulty, and h_det = 0 indicates that the sensor is normal. S is the set of normal Hall state values. When the value of Hall state s does not belong to the set S, it indicates that the position sensor is faulty. The expected Hall state value can be determined based on the value of the Hall state before the fault. Each expected Hall state value corresponds to a set of fixed Hall signals. Therefore, after determining the fault of the position sensor, the faulty position sensor can be located by judging the wrongly jumping Hall signal, as shown in the following formula

$$h_{\det i}=\left\{\begin{array}{l}1if\left(h_{\det }=1\mathrm{and}{H}_i\ne H_{\exp i}\right)\\ 0\mathrm{others}\end{array}\right.$$

(5)

In the formula, h_deti = 1 indicates that the position sensor i is faulty, and h_deti = 0 indicates that the sensor i is normal. H_i and H_expi represent the current and expected Hall signals, respectively.

The process of fault diagnosis and location of position sensor 1 through the Hall state timing table is shown in Figure 5a,b. Figure 5a and Figure 5b, respectively, show the schematic diagrams of diagnosis and location of low-level and high-level faults in Hall sensor 1. From the ideal Hall signal represented by the dotted line in the figure, it can be seen that in a healthy state, the Hall signal H₁ should remain at a high level within the range of 0° to 180°, then switch from a high level to a low level at 180°, and then remain at a low level within the range of 180° to 360°, and so on in a cycle. Meanwhile, the value of the Hall state will also change according to the ideal state.

When the Hall sensor 1 experiences a low-level fault as shown in Figure 5a, the Hall signal H₁ jumps to a low level in advance and remains unchanged. At this point, the originally expected Hall state value should have been 298, but the fault caused the Hall state s to mistakenly jump to 106. When the value of the fault detection flag h_det becomes 1, the fault can be diagnosed immediately. Then, based on the Hall signal combination corresponding to the Hall state value 362 being 101101010, and the current Hall signal combination constituting the Hall state 106 being 001101010, and comparing these two groups of Hall signals, it can be determined that the position sensor 1 corresponding to the Hall signal H₁ has malfunctioned.

The high-level fault situation of Hall sensor 1 is shown in Figure 5b. Within the electrical angle range of 220° to 240°, the Hall signal H₁ jumps to a high-level state in advance and remains unchanged. At this point, the originally expected Hall state value should be 173, but the fault caused the Hall states to mistakenly jump to 425, and the value of the fault detection marker h_det became 1, allowing the fault to be diagnosed immediately. Then, based on the Hall signal combination corresponding to the Hall state value 169 being 010101001, and the current Hall signal combination constituting the Hall state 425 being 110101001, and comparing these two groups of Hall signals, it can be located that the position sensor 1 corresponding to the Hall signal H₁ has malfunctioned.

However, fault detection based on Hall signals may cause the error commutation time to be too long. As shown in Figure 6, the Hall signal H₁ remains at a high level. Faults cannot be detected at 180°, and only the Hall state s value 427 can be detected at 200°, which does not match the expected 170. Therefore, in order to reduce the error commutation time, it is necessary to achieve fault detection in sectors ranging from 180 to 200° as much as possible. The expected Hall state is 170 within the 180° to 200° sector. In the case of a fault in position sensor 1, 426 remains unchanged, which will cause abnormal current phenomena in the multi-phase BLDCM. Therefore, the current conditions generated by the nine-phase BLDCM during the above-mentioned fault operation time are considered below to find the fault detection features.

According to Table 1, during normal operation of nine-phase BLDCM, the conduction phase winding corresponding to Hall state 426 is A₂⁺, A₃⁻, A₄⁺, A₅⁻, A₆⁺, A₇⁻, A₈⁺, A₉⁻, and the conduction phase winding corresponding to Hall state 170 is A₁⁻, A₂⁺, A₃⁻, A₄⁺, A₅⁻, A₆⁺, A₇⁻, A₈⁺. In the fault condition shown in Figure 6, the A₉ and A₁ phase windings, which should have been commutated when the back electromotive force reached the boundary of the flat top width, will be delayed in commutation. At this time, the motor maintains A₂, A₄, A₆, and A₈ phase windings in the positive wizard state, and A₃, A₅, A₇, and A₉ phase windings in the negative wizard state. The winding conduction diagram under H_PWM-L_ON modulation strategy is shown in Figure 7.

Figure 7a and Figure 7b, respectively, show the current flow path when PWM = ON and PWM = OFF in one switching cycle of normal conduction cycle. It can be seen from Figure 7a that when PWM = ON, the current flows from the positive terminal of the power supply into phases A₂, A₄, A₆, A₈, and returns to the negative terminal of the power supply through phases A₃, A₅, A₇, A₉, forming a closed loop. A₁ phase winding is a suspended phase, and no current passes through. At this time, the corresponding voltage equation of each phase winding terminal is

$$\left\{\begin{array}{l}{u}_{\mathrm{A}p}=U_{\mathrm{dc}}=R_s{i}_{\mathrm{A}p}+L_s{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}p}}{\mathrm{d}t}}+e_{\mathrm{A}p}+u_N\\ u_{\mathrm{A}n}=0=R_s{i}_{\mathrm{A}n}+L_s{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}n}}{\mathrm{d}t}}+e_{\mathrm{A}n}+u_N\end{array}\right.$$

(6)

where i_Ap = −i_An, e_Ap = −e_An = E, p = 2, 4, 6, 8, n = 3, 5,7, e_A9 ≠ E. The neutral point voltage u_N can be obtained as

$$u_{\mathrm{N}}={\displaystyle \frac{4U_{dc}+E+e_{\mathrm{A}9}}{8}}$$

(7)

When the PWM modulation frequency is high, the carrier period is much smaller than the electromechanical time constant L_s/R_s, so the influence of winding resistance can be ignored. By substituting Equation (7) into Equation (6), the common terms in the equation can be eliminated, and the rate of change of A9 phase current during PWM conduction can be obtained:

$${\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}9}}{\mathrm{d}t}}=-{\displaystyle \frac{4U_{\mathrm{dc}}+E+9e_{\mathrm{A}9}}{8L_{\mathrm{s}}}}$$

(8)

This rate of change directly reflects the impact of back electromotive force on current dynamics (abnormal back electromotive force during faults can cause this rate of change to deviate from the normal range).

It can be seen from Figure 7b that when PWM = OFF, the current flows into the winding of phases A₂, A₄, A₆, and A₈ through the freewheeling diode, while the current flows out from the winding of phases A₃, A₅, A₇, and A₉ without passing through the negative electrode of the power supply, forming a closed loop. A₁ phase winding is a suspended phase, and no current passes through. The corresponding voltage equation is

$$\left\{\begin{array}{l}{u}_{\mathrm{A}p}=0=R_s{i}_{\mathrm{A}p}+L_s{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}p}}{\mathrm{d}t}}+e_{\mathrm{A}p}+u_N\\ u_{\mathrm{A}n}=0=R_s{i}_{\mathrm{A}n}+L_s{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}n}}{\mathrm{d}t}}+e_{\mathrm{A}n}+u_N\end{array}\right.$$

(9)

According to Equations (7) and (9), the current change rate of A₉ phase winding can be obtained as

$${\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}9}}{\mathrm{d}t}}=-{\displaystyle \frac{E+9e_{\mathrm{A}9}}{8L_{\mathrm{s}}}}$$

(10)

According to Equations (8) and (10), the average value of the current change rate of A₉ phase winding in one PWM cycle can be obtained as

$${\left.{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}9}}{\mathrm{d}t}}\right|}_{\mathrm{avg}}=-{\displaystyle \frac{4D{U}_{\mathrm{dc}}+E+9e_{\mathrm{A}9}}{8L_{\mathrm{s}}}}$$

(11)

It can be seen from Equation (11) that since the dc bus voltage U_dc and the equivalent phase inductance L_s are fixed values, the current change rate di_A9/dt is mainly affected by the back-EMF e_A9 and duty cycle D, providing a theoretical basis for subsequent fault diagnosis based on overcurrent characteristics. As shown in Figure 8a, in normal operation, e_A9 = −E, di_A9/dt = 0 under duty cycle D control, and phase current i_A9 is maintained near the given current value i_ref. Since the amplitude of the back-EMF of A₉ phase winding decreases after the fault, according to Equation (11), it can be obtained that di_A9/dt < 0, the phase current i_A9 of A₉ phase winding continues to increase negatively, and the amplitude exceeds the given current value i_ref. Meanwhile, the phase current i_A1 of A₁ phase winding has i_A1 = 0 due to delayed commutation.

Similarly, it can be obtained through analysis that after low level fault 2 occurs in position sensor 1, Hall signal H₁ jumps to low level in advance, A₉ phase winding commutation to A₁ phase winding in advance. At this time, A₂, A₄, A₆, and A₈ phase winding are in positive conduction state, A₁, A₃, A₅, and A₇ phase windings are in negative conduction state, and the change rate of phase current i_A1 of A₁ phase winding is

$${\left.{\displaystyle \frac{\mathrm{d}{i}_{\mathrm{A}1}}{\mathrm{d}t}}\right|}_{\mathrm{avg}}=-{\displaystyle \frac{4D{U}_{\mathrm{dc}}+E+9e_{\mathrm{A}1}}{8L_{\mathrm{s}}}}$$

(12)

in the equation, since the back-EMF e_A1 of phase A₁ has not reached its peak value E, it follows that di_A1/dt < 0. The amplitude of the phase current i_A1 continues to increase beyond the reference current value i_ref. Meanwhile, the phase current i_A9 of phase A₉ is zero because of the advance commutation. The back-EMF and current change situation at this time is shown in Figure 8b.

The aforementioned analysis results of current fault characteristics can be utilized to accurately reflect the fault conditions of multi-phase BLDC under multi-phase conduction modes. Figure 9a,b illustrate the current conditions of the windings in the eight-phase conduction mode corresponding to Hall state 426, under normal conditions and delayed commutation due to a fault in the position sensor 1, respectively. According to the phase currents relation Equation (2) of the star connection, the sum of the positive guide current and the negative guide current should be zero. However, the fault leads to an increase in the amplitude of phase current i_A9, which results in a decrease in current for the negatively conducting phases A₃, A₅, and A₇ that are in the same conduction group as phase A₉, while the current for the positively conducting phases A₂, A₄, A₆, and A₈ increases. Since the current changes in other phases are average, the change of phase current i_A9 is particularly significant. At the same time, its phase current i_A1 is zero because the phase A₁ winding is not conducted. These variations allow us to precisely locate the fault location sensors.

In conclusion, if the Hall sensor 1 fails and is not diagnosed in time and a fault-tolerant control strategy is not adopted, obvious fault current characteristics will appear, which can be used as fault detection features. Therefore, the i_det1 judgment marker for Hall sensor 1 to diagnose faults based on fault current characteristics is defined as follows

$$i_{\det 1}=\left\{\begin{array}{l}1,\left(\left(\left|i_{\mathrm{A}9}\right|>i_{\mathrm{th}}\right)\cap \left(\left|i_{\mathrm{A}1}\right|<{\epsilon }_{\mathrm{A}}\right)\cap \left(\left|i_{\mathrm{others}}\right|<i_{\mathrm{th}}\right)\right)\\ \cup \left(\left(\left|i_{\mathrm{A}1}\right|>i_{\mathrm{th}}\right)\cap \left(\left|i_{\mathrm{A}9}\right|<{\epsilon }_{\mathrm{A}}\right)\cap \left(\left|i_{\mathrm{others}}\right|<i_{\mathrm{th}}\right)\right)\\ 0,\mathrm{others}\end{array}\right.$$

(13)

In the formula, i_det1 = 1 indicates that the Hall sensor 1 exhibits current characteristics, and ith is a preset fixed value, which is determined based on the given reference current i_ref of the system and the expected normal operating current fluctuation range (current ripple). Specifically, ith = k·i_ref. In this experiment, k is taken as 1.4. ε_A is also a current threshold, which is set based on the noise characteristics of the current sampling system (including sensor noise, zero drift, ADC quantization error). To avoid misdiagnosis, its value should be greater than the maximum value of the sampling error. i_others indicates the phase currents other than i_A1 and i_A9.

Specifically, the value of the constant k needs to be determined based on experiments on current ripple characteristics during the normal operation of the motor: its value is based on experiments on normal current fluctuation characteristics under full operating conditions (including steady state, acceleration, deceleration, loading, and unloading processes) of the nine-phase BLDCM, statistically obtaining the ratio of the maximum peak value of current ripple to the reference current i_ref. To cover such fluctuations and reserve a safety margin to prevent misjudgment, k is finally set to 1.4, ensuring that ith = k·i_ref can reliably distinguish between normal ripples and fault over currents. Full operating condition experiments show that the threshold corresponding to this fixed k value can cover the current ripple range under all normal operating states of the motor. In contrast, the peak values of current anomalies caused by position sensor faults (such as aperiodic over currents resulting from commutation delay or advance) are far beyond this range. The two are significantly different, so they can be effectively distinguished without dynamic adjustment. Meanwhile, the original design intention of this method is “no need for complex calculations” to meet the real-time diagnosis requirements of multi-phase motors. If a dynamic adjustment strategy is adopted, additional algorithms such as working condition identification and ripple prediction need to be introduced, which will increase computational complexity and contradict the advantages of this method. Experimental verification also shows that fixing k = 1.4 can still quickly and accurately diagnose faults under dynamic working conditions without missed judgments or misjudgments.

The determination of the noise threshold ε_A is based on the noise characteristics of the current sampling system: under the condition where the motor is shut down and only the sampling circuit is powered on, the output signal of the sampling circuit is collected, and the maximum peak-to-peak value of the noise signal is calculated. Subsequently, ε_A is set to 1.5 times this peak-to-peak value to effectively filter out the interference of sampling noise on fault judgment. It is worth noting that high temperatures may cause zero drift and increased noise in the current sampling system; however, the value of ε_A has fully covered the maximum sampling errors in high-temperature environments (including sensor temperature drift, ADC quantization error, etc.), which can prevent misjudgments caused by noise induced by high temperatures.

Combined with the dual judgment mechanism of “abnormal Hall state and abnormal current characteristics”, this threshold can further filter out single-dimensional abnormal interference (such as only abnormal current signals or only abnormal position signals), thereby ensuring reliable diagnosis and fault-tolerant control even under the influence of variables like high temperature and short circuit.

By conducting the above derivation process for the fault conditions of other Hall sensors, the corresponding fault detection marks of each Hall sensor can be obtained as shown in

Table 2. The determination sign based on current characteristic of Hall position sensor in fault state.

i	ideti = 1
1	((|iA9| > ith) ∩ (|iA1| < εA) ∩ (|iothers| < ith)) ∩ ((|iA1| > ith) ∩ (|iA9| < εA) ∩ (|iothers| < ith))
2	((|iA1| > ith) ∩ (|iA2| < εA) ∩ (|iothers| < ith)) ∩ ((|iA2| > ith) ∩ (|iA1| < εA) ∩ (|iothers| < ith))
3	((|iA2| > ith) ∩ (|iA3| < εA) ∩ (|iothers| < ith)) ∩ ((|iA3| > ith) ∩ (|iA2| < εA) ∩ (|iothers| < ith))
4	((|iA3| > ith) ∩ (|iA4| < εA) ∩ (|iothers| < ith)) ∩ ((|iA4| > ith) ∩ (|iA3| < εA) ∩ (|iothers| < ith))
5	((|iA4| > ith) ∩ (|iA5| < εA) ∩ (|iothers| < ith)) ∩ ((|iA5| > ith) ∩ (|iA4| < εA) ∩ (|iothers| < ith))
6	((|iA5| > ith) ∩ (|iA6| < εA) ∩ (|iothers| < ith)) ∩ ((|iA6| > ith) ∩ (|iA5| < εA) ∩ (|iothers| < ith))
7	((|iA6| > ith) ∩ (|iA7| < εA) ∩ (|iothers| < ith)) ∩ ((|iA7| > ith) ∩ (|iA6| < εA) ∩ (|iothers| < ith))
8	((|iA7| > ith) ∩ (|iA8| < εA) ∩ (|iothers| < ith)) ∩ ((|iA8| > ith) ∩ (|iA7| < εA) ∩ (|iothers| < ith))
9	((|iA8| > ith) ∩ (|iA9| < εA) ∩ (|iothers| < ith)) ∩ ((|iA9| > ith) ∩ (|iA8| < εA) ∩ (|iothers| < ith))

, where i represents the label of the Hall position sensor, and i = {1, 2, 3, … n}, where n represents the total number of Hall position sensors. Based on the current characteristics in the table, the faults of the Hall position sensors corresponding to the labels can be determined.

In summary, the position sensor fault location marker F_i obtained based on the Hall signal timing table and fault detection based on current characteristics is defined as follows

$$F_i=\left\{\begin{array}{l}1,\left(h_{\det i}=1\right)\cup \left(i_{\det i}=1\right)\\ 0,\mathrm{others}\end{array}\right.$$

(14)

In the formula, F_i = 1, indicating that the Hall position sensor labeled i is faulty; F_i = 0 indicates that the ith Hall position sensor is normal.

3.2. Fault-Tolerant Control

After diagnosing a faulty Hall sensor, the Hall signal should be reconstructed immediately to achieve the fastest recovery of motor operation. A suitable solution is to establish the reconstructed signal (as a backup Hall signal) before the potential fault, and once the fault is diagnosed, the reconstructed signal obtained from the normal Hall signal can be used to replace the faulty Hall signal immediately. Because multi-phase BLDCM requires higher rotor position detection accuracy, the fault-tolerant control method adopted is to obtain a continuous rotor position through healthy Hall signal, and then reconstruct the Hall signal according to the angle corresponding to the fault Hall signal.

The rotational speed of the nine-phase BLDCM can be obtained in the following way

$$n={\displaystyle \frac{\omega \cdot 60}{2\pi }}={\displaystyle \frac{60}{\gamma t_{\mathrm{sample}}p}}$$

(15)

where ω is the mechanical angular speed of the motor and p is the number of rotor poles of the nine-phase motor, which is equal to 2 in the nine-phase BLDCM; γ is the average count between the adjacent rising edges of the nine position pulse signals, denoted by

$$\gamma ={\displaystyle \frac{{\displaystyle \sum _{i=1}^9{f}_i{\gamma }_i}}{{\displaystyle \sum _{i=1}^9{f}_i}}}$$

(16)

where {i∣i = 1, 2, …, 9} is the number of nine Hall position signals; f_i is the fault symbol of the ith Hall sensor, where f_i = 1 in the normal case and f_i = 0 in the fault case; γ_i is the calculated value between the adjacent rising edges of the ith Hall signal.

The angle is calculated by the formula

$$\begin{array}{l}{\theta }_t={\theta }_{t-1}+pt\omega {\displaystyle \frac{180}{\pi }}={\theta }_{t-1}+pt{\displaystyle \frac{180}{\pi }}{\displaystyle \frac{2\pi n}{60}}\\ ={\theta }_{t-1}+6pnt\end{array}$$

(17)

where θ_t is the rotor position at time t and θ_t−1 is the angle of the adjacent last Hall signal jump along the corresponding rotor position at time t. Based on Equations (15)–(17), as long as one position sensor is normal, the rotor position can be calculated, and then the reconstructed Hall signal can be obtained.

The summary of the fault-tolerant control operation process is as follows: ① Speed calculation: Based on the adjacent transition edge interval of the healthy Hall signal, calculate the mechanical angular velocity ω of the motor through Equations (15) and (16); ② Rotor position estimation: Using the rotor position θ_t−1 corresponding to the previous Hall signal, combined with the speed ω and time interval, calculate the current rotor position θ_t in real time; ③ Fault Hall Signal Reconstruction: Based on the estimated θ_t, match its corresponding normal Hall state (Table 1), reconstruct the Hall signal of the fault sensor, and replace the fault signal to participate in commutation control.

The motor control flow chart after adopting the proposed fault diagnosis method is shown in Figure 10. When the Hall signal is obtained according to the Hall position sensor during the operation of nine-phase BLDCM, the fault is first diagnosed by the fault diagnosis and fault-tolerant control module to ensure the correct position of the motor. Then the signal passes through the speed controller and the current controller after generating the duty D through the PWM signal generator control inverter to achieve accurate control of motor.

4. Experimental Results and Analysis

To verify the correctness of the theoretical analysis, this paper constructs a nine-phase BLDCM drive system as an experimental platform, as shown in Figure 11. The control circuit adopts DSP (TMS320F28335) and FPGA (EP1C6Q240C8) as the central control unit. The sampling frequency of the position signal (Hall signal) and stator current signal involved in fault detection in this experiment is 10 kHz. This sampling frequency can meet the requirements of capturing Hall signal transitions and fault current characteristics. In terms of the sampling circuit, the LEM voltage sensor (LV25-P) is selected to sample the DC bus voltage, and the LEM current sensor (LAH50-P) is adopted simultaneously to sample the phase current. The motor is loaded by using the MAGTROL hysteresis brake (AHB-12), and the torque sensor (TM307) is used to measure the actual motor torque. During the experiment, the Hall signal fault was simulated through the switch, and the Hall signal used by the controller was set to a constant value. The experimental results were recorded using a Yokogawa eight-channel digital oscilloscope (model DLM4058).

The motor used in this experiment is a symmetrical winding nine-phase BLDCM, and its specific parameters are listed in

Table 3. Motor parameters.

Parameter	Value	Unit
Rated voltage UN	42	V
Rated current IN	23	A
Rated torque TN	8	N·m
Rated speed nN	2500	r/min
Phase resistance R	0.012	Ω
Phase inductance L	0.064	mH

.

4.1. Steady-State Experiments

(1) Single position sensor fault: Since the fault diagnosis process of each Hall position sensor is the same, the fault of position sensor 1 is taken as an example for experimental verification in the following.

Figure 12 and Figure 13 shows the position signal H₁ of position sensor 1 under four fault conditions, the position signals H₂ and H₉ of adjacent two-phase position sensors, the corresponding three-phase currents i_A1, i_A2, i_A9, the fault location mark F₁, and the speed n of position sensor 1 under steady-state conditions. Where n and load are set to 1000 r/min and 4 N·m, respectively.

Figure 12a shows the experimental results when the position sensor 1 has a low-level fault 1. As can be seen from the figure, after the fault occurs, the position signal H₁ remains at a low level, causing the A₉ phase winding to fail to commutate correctly, and the phase current i_A9 remains on continuously. At the same time, the phase current i_A1 of the A₁ phase winding is delayed in being turned on. At this time, due to the decrease in the opposite electromotive force of the A₉ phase, the phase current i_A9 suddenly increases. The current fault feature idet1 of position sensor 1 satisfies |i_A9| > i_ref, and the current value of i_A1 is zero at the same time. At this point, the fault is immediately diagnosed. The key point of this experiment is to verify the effectiveness of the proposed diagnostic method. Therefore, after diagnosing the fault situation, the normal Hall signal was restored immediately, so the subsequent operation of the motor was not affected. Figure 12b shows the experimental results when the position sensor 1 experiences a low-level fault 2. The Hall signal H₁ jumps from a high-level state to a low-level state in advance. At this time, the expected Hall state does not match the actual Hall state, and the fault of the position sensor can be quickly diagnosed and located according to the Hall state timing table.

The experimental results when the position sensor 1 experiences a high-level fault 1 are shown in Figure 13a. At this time, the Hall signal H₁ of the position sensor 1 remains at a high level, similar to the situation when it remains at a low level during a low-level fault 1. Due to the fault, the A₉ phase winding cannot be commutated correctly, and the phase current i_A9 remains conducting continuously. At the same time, the phase current i_A1 of the A₁ phase winding is delayed in opening, and the phase current i_A9 suddenly increases. The current fault characteristic idet1 of the position sensor 1 satisfies |i_A9| > i_ref, and the current value of i_A1 is zero at the same time. At this point, the fault is immediately diagnosed. Figure 13b shows the experimental results when the position sensor 1 has a high-level fault 2. The position signal H₁ jumps in advance, and the fault of the position sensor can be quickly diagnosed and located according to the Hall state timing table.

(2) Two position sensor faults: Since nine Hall position sensors are needed for the nine-phase BLDCM to obtain the corresponding rotor position, the following two adjacent position sensors 1 and 2 and two non-adjacent position sensors 1 and 6 faults are taken as examples for experimental verification.

Figure 14 shows the experimental diagram of the diagnosis process for the simultaneous failure of position sensors 1 and 2. From top to bottom in the figure are Hall signals H₁ and H₂, phase currents i_A1, i_A2 and i_A9, and the fault location markers F₁ and F₂ of position sensors 1 and 2. The rotational speed and load are set to 800 r/min and 2 N·m, respectively. As shown in Figure 14, position sensors 1 and 2 malfunctioned at the same time, with high-level faults 2 and low-level faults 2 occurring, respectively. Due to the premature jump of their level states, the expected Hall state was inconsistent with the actual Hall state. Based on the Hall state timing table, the faults of these two position sensors were quickly diagnosed and located.

Another fault situation of the two position sensors is shown in Figure 15. Although faults occurred simultaneously, the fault conditions at this time were as follows: position sensor 1 had a low-level fault 1, and position sensor 6 had a high-level fault 2. The fault situation of position sensor 6 was quickly diagnosed and the fault of the position signal was located. However, after the failure of position sensor 1, the fault signal was the same as the expected signal. Therefore, the fault could only be diagnosed immediately when the current fault characteristic i_det1 was satisfied |i_A9| > i_ref and the current value of i_A1 was zero. But due to the rapid change of current, the fault was diagnosed immediately before serious consequences occurred. It is conducive to switch to the fault-tolerant control strategy in a timely manner according to the corresponding fault situation.

4.2. Dynamic Experiments

In order to verify the effectiveness of the proposed method under dynamic conditions, fault diagnosis experiments were carried out for the position sensor under four working conditions of acceleration, deceleration, loading, and load shedding.

Experimental results for position sensor 1 failures during acceleration, deceleration, loading, and load shedding are shown in Figure 16, Figure 17, Figure 18 and Figure 19, where the blue arrow points to a magnified view of the dashed box (magnified on the timeline only). According to the enlarged plot of the dashed box, it can be seen that based on the proposed fault diagnosis method, fault detection and localization can also be achieved under dynamic conditions.

Figure 16 shows the experimental results of a low-level fault 2 in position sensor 1 under acceleration conditions. When the motor accelerates from 300 to 800 r/min, the H₁ signal jumps to a low level in advance, and the fault diagnosis flag F₁ is quickly triggered and the fault is accurately located. Figure 17 shows the experimental results of high-level fault 2 in position sensor 1 under deceleration conditions. During the deceleration of the motor from 800 to 300 r/min, the H₁ signal jumps to high level in advance, and the diagnostic flag is also triggered quickly.

The two sets of experiments jointly demonstrate that in dynamic variable speed scenarios, the proposed method can achieve reliable fault detection through the collaborative diagnostic mechanism of Hall signal anomalies and current characteristic mutations, verifying its stability and effectiveness in acceleration/deceleration processes.

Figure 18 clearly shows the experimental results of low-level fault 1 of position sensor 1 under loading conditions. As the load increases, the amplitude of the phase current increases; after the fault occurred, due to a commutation logic error, the phase current i_A9 exceeded the threshold ith, and the fault location indicator F₁ was quickly triggered, verifying the sensitive capture ability of the method for faults under loading conditions. Figure 19 shows the experimental results of low-level fault 1 of position sensor 1 under reduced load conditions. When the load decreases, the phase current i_A9 still exceeds the threshold ith after the fault, and the F₁ flag can still respond quickly.

The two sets of experiments jointly demonstrate that in the scenario of sudden load changes, the proposed method can achieve reliable and rapid detection of position sensor faults through the abnormal over limit characteristics of phase currents and fault localization logic, verifying its adaptability and robustness to load variation conditions.

4.3. Performance Analysis of Fault Detection

Our existing steady-state and dynamic experimental results (Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19) contain precise time information captured by the oscilloscope (switch action time and Fi jump time of manually simulated faults). We will systematically reanalyze all experimental waveform diagrams and accurately measure the time difference between the switch action time and the Fi jump time of manually simulated faults. The motor runs for a long time under healthy conditions, records the output status of F_i, and counts the number of false alarms.

Based on the preliminary analysis of existing experimental data, the statistical results are as follows:

Steady-state condition: When a low-level fault occurs, due to the limitation of current rise time, the average detection delay is 128 μs; when a low-level fault occurs, the average detection delay is 89 μs; when high-level fault 1 occurs, due to the limitation of current drop time, the average detection delay is 135 μs; when high-level fault 2 occurs, the average detection delay is 93 μs; when adjacent sensors (H₁ and H₂) fail, the average detection delay is 115 μs; when non adjacent sensors (H₁ and H₆) fail, the average detection delay is 123 μs. Overall, the average detection delay under steady-state conditions is 114 μs, which is much smaller than the motor commutation interval (the time for a 20° electrical angle commutation interval of the motor at 2500 r/min is about 667 μs).

Dynamic operating conditions: The motor accelerates from 300 to 800 r/min with an average detection delay of 113 μs; decelerates from 800 to 300 r/min, with an average detection delay of 128 μs; the average detection delay under loading conditions is 125 μs, and the average detection delay under unloading conditions is 137 μs. In summary, the average detection delay under dynamic operating conditions is 125 μs, which is also much smaller than the motor commutation cycle, ensuring that the diagnosis is completed before the next commutation, avoiding the accumulation of erroneous commutation, and verifying the speed of the method in real-time diagnosis.

The motor operates for a long time under healthy conditions, with zero false alarms. Due to the fact that F_i needs to satisfy both Hall state anomaly (h_deti = 1) and current characteristic anomaly (i_deti = 1), the dual criteria effectively avoid false alarms caused by single signal noise (such as current sampling noise and Hall signal glitches).

Through quantitative statistics in

Table 4. Fault detection performance statistics.

Working Condition	Average Detection Delay	False Positives
Steady-state experiments	114 μs	0
Dynamic experiments	125 μs	0
Healthy experiments	—	0

, it can be intuitively demonstrated that the detection delay of the proposed method remains stable and fast under different fault types and operating conditions, meeting the real-time diagnosis requirements of multi-phase BLDCM. The extremely low false alarm rate ensures that the method will not interfere with normal operation, enhancing the feasibility of engineering applications.

4.4. Construction of the Actual Rotor Position Angle Under Fault-Tolerant Conditions

In order to verify the feasibility of the fault-tolerant operation, experiments are carried out on the single sensor fault and the double position sensor fault, where the single sensor fault takes the position sensor 1 fault as an example, as shown in Figure 20a. The faults of the two position sensors are the faults of position sensor 1 and position sensor 2, and the faults of position sensor 1 and position sensor 6, as shown in Figure 20b and Figure 20c, respectively. Figure 20 shows that the actual rotor position angle θ can be constructed under fault-tolerant control.

As shown in Figure 20, the experimental results of fault-tolerant control of position sensor are presented in Figure 20a, which shows the fault-tolerant performance of position sensor 1 after failure. Figure 20b shows the fault-tolerant results after both position sensor 1 and position sensor 2 have faults. Figure 20c is the fault-tolerant result after both position sensor 1 and position sensor 6 have faults. As shown in Figure 20, regardless of whether there is a single sensor fault or a dual sensor (adjacent/non adjacent) fault, the proposed fault-tolerant control method can accurately reconstruct the actual rotor position angle, providing a key guarantee for the continuous and stable operation of the motor.

5. Conclusions

Aiming at the fault problem of Hall position sensors in multi-phase brushless DC motors, taking the nine-phase BLDCM as the research object, a fault diagnosis method based on fault current characteristics is proposed. This method first conducts a preliminary diagnosis by using the preset Hall state values, and quickly identifies faults by comparing the sequence characteristics of the Hall signals. In order to further improve the diagnostic efficiency, the current characteristics after the fault were analyzed, and the fault location was achieved based on the fault current characteristics. Ultimately, by integrating the position signal and current characteristics, the precise positioning of the fault location sensor was achieved. The main contributions of the proposed method are as follows.

(1) The proposed method does not require additional detection devices, but can be applied to dynamic conditions, which is helpful to reduce the cost of the system and broaden the application range of the diagnosis method.

(2) For the first time, a position sensor fault diagnosis method based on existing position signals and phase currents is proposed for the nine-phase BLDCM, which can realize independent and fast fault diagnosis for each position sensor, and help to switch to the fault-tolerant strategy in time to minimize the impact of faults on system performance.

(3) The method proposed in this paper has wide applicability. It can be adapted to a variety of multi-phase BLDCM systems using Hall sensors. Combined with the method presented in this paper, the control reliability of multi-phase BLDCM can be significantly improved to ensure the stable operation of the system.