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LETTER

IEICE Electronics Express, Vol.14, No.14, 1–11

Fault-tolerant of Hall-effect sensors in permanent magnet in-wheel motor drives Degang Lv and Zeyuan Dua) College of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China a) [email protected]

Abstract: In this paper, Hall-effect sensor faults are investigated in Sinusoidal-current-fed Permanent Magnet In-wheel Motor (PMIM) drives. And an effective methodology for their diagnostic and compensation is proposed. In particular, fault diagnostic only based Hall sensors signal, at the rising or falling edges of Hall signal, fault types of Hall sensors are diagnosed according to the specific type of Hall signal transitions and the current state of Hall signal. Fault-compensation based on reduced-order observer which has been devised to be free from the mechanical parameters (such as, inertia) in rotor position estimation process. The validity and effectiveness of the proposed methods are verified by experiments on PMIM with excessive and variable load. Keywords: PMIM, fault diagnostic, fault-compensation, observer Classification: Circuits and modules for electronic instrumentation References

© IEICE 2017 DOI: 10.1587/elex.14.20170470 Received May 4, 2017 Accepted June 16, 2017 Publicized June 30, 2017 Copyedited July 25, 2017

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Introduction

Permanent brushless DC motor (BLDCM) fed by square-wave current requires six Hall position points in an electrical cycle [1, 2]. Permanent Magnet In-wheel Motor (PMIM) fed by sinusoidal-current requires rotor position information with highresolution from Hall-effect sensors. High-resolution position and velocity estimation of PMIM with Hall-effect sensors and its low-cost vector control drives have been a heated discussion in the research area in recent years [3, 4, 5]. However, in most proposed methods, the fault states of the Hall-effect sensors signals are seldom considered, and few research studies on fault diagnostic and compensations methods are able to overcome the failures of Hall-effect sensors. In PMIM drives with Hall-effect sensors, the position of the Permanent Magnet (PM) flux density wave is measured by three Hall-effect sensors, arranged at 120° electrical degrees in motors axis. Such an arrangement results in a 60° resolution measurement. Although many strategies have been presented for PMIM low-cost vector control based on Hall-effect sensors [6, 7, 8], most of them will give rise to unsatisfactory performance or even installment if any of the sensors is damaged or in fault. Faults of Hall-effect sensors may occur due to violent environment, vibrations, circuit connection faults, etc., which causes the corresponding Hall signals unavailable. To improve the reliability of PMIM drives with Hall-effect sensor, it is necessary to investigate the fault diagnosis and to develop fault compensation methods. In [9], the effect of a single fault and double fault on the 2



Hall-effect sensors signal is analyzed. It is shown that the locus traced by the Halleffect sensors signal vector under stationary reference frame is no longer hexagonal, but becomes deformed. Coordinate transformation based faults detection and identification method is proposed for low-cost field-oriented drives, it is do not rely on any hardware circuit, works for both single and double faults, and does not suffer from fault type error detection. Moreover, instead of using virtual commutation signals [10], the faults are compensated by appropriately modifying improved Luenberger observers. The only drawback is that this method depends on the parameters of the motor, and the rotor position estimation performance will be deformed under changeable load conditions. In [10, 11], a new fault tolerant control (FTC) method is presented based on the Hall transition sequence, which reduces the time of fault diagnosis process (FDP) significantly. Therefore, a Hall signal reconstruction scheme is proposed in order that the FTC can be realized by traditional Hall-sensor-based drives. However, during the FDP, the resulting large transient currents/torque can cause speed fluctuation and deteriorated drive performance. In addition, fault diagnosis and compensation are completed by additional dsPIC controller, which not only increases the cost of the control system, but also cannot be used where the control systems volume is limited. In the study of improvement [11], an improved FTC scheme is proposed based on FDP and vectortracking observer. In this method, the duration of FDP is identified based on the analysis of the relationship between the sensor fault angle and the acceleration increment in each Hall sector. The critical acceleration increment including the sensor fault angle is obtained as the start and end of FDP. During FDP, an openloop observer control is defaulted to remove the undesirable current/torque transient, and then the closed-loop observer is re-enabled and the motor operation is restored. In [12], It is demonstrated that the destabilizing effect of single and double faults on drive performance can be compensated by three state-of-the-art fault tolerant estimation algorithms (the zero-order algorithm, the hybrid observer and the vector-tracking observer), which worked by modifying motion-state estimation methods (include rotor position and speed estimation), respectively. The diagnostic of fault types takes the aforementioned approach [9]. In the end, the merits and demerits of these three techniques are compared in paper. Based on the above research, this paper makes some improvement and innovation on the fault tolerant control technology of PMIM drives: 1) Fault diagnostic is only based on Hall-effect sensors signal. At the rising or falling edges of Hall signal, fault types of Hall sensors are diagnosed according to the specific type of Hall signal transitions and the current state of Hall signal. 2) The rotor position angle is based on the normalized system (per-unit system) and divided into equal positive and negative intervals, which more simplifies the fault compensation angle classification than methods in [12], and, to a large extent, reduces the phenomenon of re-min > re-max in faults status. 3) Fault compensation based on reduced-order observer for PMIM drives is proposed, which has been devised to be free from the mechanical parameters of motor in estimation process, and realizes low cost and high resolution of rotor position tolerance estimation (the recursive least squares method with forgetting factor is used to estimate the speed of fault tolerance). 3


2

Faults diagnostic

In the process of motor fault-free operation, there will be six Hall sector states in an electrical cycle, and the Hall state value is definited as the commutation control word (Hx , x ¼ 07), such as 5 ! 1 ! 3 ! 2 ! 6 ! 4 for counter-clockwise (CCW) or 5 ! 4 ! 6 ! 2 ! 3 ! 1 for clockwise (CW), and 0, 7 in sensors fault status. Different fault types of Hall-effect sensors have different commutation control word combinations. Table I shows the rotor angle division and the corresponding Hall sensors state information considering CCW rotation (CCW is considering both in theoretical analysis and experiments). Table I.

Relationship between rotor position and Hall state

Rotor position

Hall-sensors state (CCW)

Hall trans

180° < re 120°

HA ¼ 1, HB ¼ 1, HC ¼ 0 (H3 )

2

120° < re 60°

HA ¼ 0, HB ¼ 1, HC ¼ 0 (H2 )

1

60° < re 0°

HA ¼ 0, HB ¼ 1, HC ¼ 1 (H6 )

4

0° < re 60°

HA ¼ 0, HB ¼ 0, HC ¼ 1 (H4 )

2

60° < re 120°

HA ¼ 1, HB ¼ 0, HC ¼ 1 (H5 )

1

120° < re 180°

HA ¼ 1, HB ¼ 0, HC ¼ 0 (H1 )

4

The correct identification of Hall signal transitions is the key to detect and confirm the fault type of Hall-effect sensors (include normal and fault operation), which uses XOR (exclusive OR) to mix the latest commutation control word ðHx ; Hx1 Þ that is captured in Hall signal transitions by controller, the results are shown in Table I. Where Hall signals transition of HA is indicated by 1, HB is indicated by 2, and HC is for 4.

Fig. 1.


Combination of Hall states and transitions

The method that signals transition identification can be used not only in the normal operation, but also in the critical state and the fault compensation state when the fault occurs. Specific methods are as follows: define variables, hx;ry ¼ hx at rising edge of hy hx;fy ¼ hx at falling edge of hy (x; y ¼ 1; 2; 3, x ≠ y) For example, as depicted in Fig. 1, there is no Hall sensor failure, hx;ry ≠ hx;fy in any of Hall sensors jumps. However, when any Hall sensor fails, hx;ry ¼ hx;fy . If

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Hall sensor H1 has failed from 1 to 0 as illustrated in Fig. 1, h1;r2 , h1;f2 are equal to 0 at H2 signal transitions, and h1;r3 , h1;f3 are equal to 0 at H3 signal transitions. Then fault types of Hall-effect sensors detection method is given: the Hall transition type is diagnosed in any signal transitions, the Hall state is sampled according to the type of Hall transition, and Hall sensors state values hx;ry , hx;fy are compared according to the formula of Table II. Where fx ¼ 0, x ¼ 1; 2; 3 represents no fault sensors, and fx ¼ 1 represents sensors x is damaged. Finally, the fault types are diagnosed according to Table II. Table II.

3

Fault type detection method

Hall trans

f1

f2

f3

1 (HA )

0

1 jh2;r1 h2;f1 j

1 jh3;r1 h3;f1 j

2 (HB )

1 jh1;r2 h1;f2 j

0

1 jh3;r2 h3;f2 j

4 (HC )

1 jh1;r3 h1;f3 j

1 jh2;r3 h2;f3 j

0

Faults compensation

Strategies based on VTO [13] feature high-precision estimation and good dynamic characteristic. However, the VTO which based on mechanical model of a machine is a third-order system and observer gains from K1 to K3 compute complexity. If there are changes in mechanical parameter, performance degradation of the observers is inevitable. Fault-tolerant based reduced-order observer for PMIM drives is proposed in this paper, including two parts: Motor speed tolerance estimation module and Rotor position estimation module as shown in Fig. 2(a).

Fig. 2.


(a) Block diagram of the fault-tolerant based on reduced-order observer (b) re-min , re-max for single fault (HB ¼ 1)

A. Motor speed tolerance estimation Since the electrical degrees interval of Hall sensors is 60° in normal operation, the rotor speed is calculated as:

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!^ hall ¼

re-prev Tprev

ð1Þ

where !^ hall is rotor angular velocity, re-prev is the angular width of the previous sector and Tprev is the associated time interval. re-prev is equal to =3 for all Hall sectors in the free of faults, and Tprev is measured with a interrupt timer. During the operation (especially when fault occurs) of the motor, there will be a mechanical vibration and Hall signal bounce, resulting in false Hall capture inevitably. In order to solve this problem, this paper adopts the Hall signal debounced module, to confirm the state of Hall sensors by time-lapse after Hall jump is detected. So timing error and incorrect fault type which caused by the bounce of the Hall signal will be overcomed. When Hall-effect sensors failure occurs, fault-tolerant speed calculation is achieved by appropriately modifying the re-prev ðiÞ, re-min ðjÞ and re-max ðkÞ as soon as the fault types is detected by the fault diagnostic procedure. In particular, re-prev is no longer constant as it is in normal operation. After the fault type is confirmed, this paper uses the structure array module to store and output the fault compensation angle ði; j; kÞ, given in Appendix Table III, IV. The structure of the array is a two-dimensional array, in which each member is a structure. The structure contains three variables: re-min , re-max and re-prev . Fig. 2(b) illustrates the angle variation of re-min and re-max with single fault (HB ¼ 1), where re-min is the lower angular boundary of the sector, and re-max is the upper angular boundary of the sector. Especially, this module takes the current fault type of Hall sensors and the sensors states value (which is used to judge the different sectors in the specific fault type) as the index of the two-dimensional array, so as to determine the output value of the current sector only: a½HA;B;C ½fx ¼ re ði; j; kÞ

ð2Þ

The installation position deviation or mechanical alignment of Hall sensors causes the obvious fluctuation of speed !^ hall . In view of the problem, the recursive least square (RLS) [14] is used to estimate the motor speed !^ es which is adopted as the speed input of reduced order observer. Equations of RLS algorithm are given in Eq. (3). 8 ^ ¼ ðk ^ 1Þ þ KðkÞ½yðkÞ ’T ðkÞðk ^ 1Þ ðkÞ > > > > > 1 < PðkÞ ¼ ½I KðkÞ’T ðkÞPðk 1Þ ð3Þ > > > Pðk 1Þ’ðkÞ > > : KðkÞ ¼ þ ’T ðkÞPðk 1Þ’ðkÞ Generally, , KðkÞ, and PðkÞ denote forgetting factor, gain vector and covariance matrix, respectively. The range of the forgetting factor is 0∼1. In order to estimate !^ es , for fault tolerant of the rotor position with the RLS scheme, !^ hall in Eq. (1) is selected as an input, i.e., yðkÞ, and the variables of Eq. (3) are set as yðkÞ ¼ !^ hall ðkÞ; © IEICE 2017 DOI: 10.1587/elex.14.20170470 Received May 4, 2017 Accepted June 16, 2017 Publicized June 30, 2017 Copyedited July 25, 2017

^ ¼ !^ es ðkÞ; ðkÞ

’ðkÞ ¼ I

ð4Þ

where !^ es is the electrical rotor speed estimated from RLS.

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B. Rotor position estimation The motor rotor position is estimated by a reduced order observer, which is shown in Fig. 2(a). Differential equation of reduced order observer is as follows: d ^ ð5Þ es ¼ !^ es þ Kðîn ês Þ dt where ês is the estimated rotor position electrical angle, !^ es denotes the estimated rotor angular velocity, K is the observer gain, and în is rotor position input of reduced order observer. The incoming rotor position în is estimated as in Eq. (6) by using !^ es instead of !^ hall : în ðkÞ ¼ în ðk 1Þ þ Ts !^ es

ð6Þ

where Ts is sampling period. ðTs =2Þ ð1 þ z1 Þ=ð1 z1 Þ in the rotor position estimation module represents the expression of integration (1=s) in the discrete domain, so the transfer function of the reduced order observer is: K ^ 1 ð7Þ in þ !^ es sþK sþK where re-min ês re-max . When Hall-effect sensors failure occurs, re-min and re-max must be updated respectively in any Hall sectors. From Eq. (7), it can be infer that the observer is stable for K > 0. Here we can get more accurate rotor speed and position by RLS. ês ðsÞ ¼

4

Implementation and verification

4.1 Experimental setup In this paper, the proposed algorithm was implemented by TM320F2812 digital signal processor, and standard PI controllers are used for speed and current control loops. Fault tolerant of PMIM is tested by the towed platform of motor, which is shown in Fig. 3. The experimental system is composed of magnetic powder brake, dynamometer, and PMIM drive with Hall-effect sensors, inverter, and DSP2812 controller, experimental data display equipment, etc. The motor parameters used in the experiment are listed in Appendix Table V.


Fig. 3. Experimental test setup for evaluating the proposed method

7


Complex test conditions are given in this paper, such as low speed, excessive or variable load and changable speed under overload, etc., in order to verify the fault tolerance performance of the proposed method and highlight the superiority of the proposed method. The safety and reliability of PMIM drives for the electric vehicle can be ensured by verifying the fault tolerance performance of Hall-effect sensors. 4.2 Fault operation under no load In order to verify the dynamic performance of the proposed method at low speed and no load for a single fault (HA ¼ 1), an experimental records is given in Fig. 4.a, which shows Hall-effect sensors signal HA=B=C and the measured phase current ia . The instants at which the fault occurs and the fault is compensated are both shown in the figure, so as to see the influence of different faults on motor current and the whole process of faults occur, detection and compensation. During the test, the speed reference remains 160 r/min in Fig. 4.a(1), which represents the low-speed operation for the identification and compensation of a single fault. It is obvious that certain transient peak current oscillation is induced on the current during the time interval of the fault diagnose, where the transient time of peak currents lasts for 4 ms with the maximum current 45 A, and the whole transient time is about 45 ms. However, this oscillation is decreased by the fault compensation, and steady-state operation is restored finally. Single fault (HA ¼ 1) is investigated in Fig. 4.a(2), where the driver operates at the rated speed and no load. In this figure, it can be seen that the transient current is much smaller with the maximal value 10 A. Moreover, the transient in currents also lasts for less time, 20 ms approximately. Thus, fault identification and compensation is quicker than Fig. 4.a(1).

Fig. 4.


Experimental results of PMIM in single fault: lower speed in a(1) and rated speed in a(2)

4.3 Under excessive or variable load Given further insight into the performance of the system during Hall sensor fault, the fault-tolerant control methods are verified in complicated conditions. The corresponding experimental diagrams are shown in Fig. 5. The result for single fault (HA ¼ 1) with overload (Tl ¼ 23 N·m) is shown in Fig. 5.b(1). The ripple on the current can be ignorable during the fault diagnostic and identification. And the

8


Fig. 5.


Experimental results of PMIM in single and double faults

deformation on motor performance can be negligible. The torque ripple of motor can be ignored before and after the fault. During the noncompensated portion of the fault transient the drive is almost allowed to maintain a constant speed. It can be predicted that the method has good fault tolerance performance under overload conditions. Fig. 5.b(2) shows the system response to loads between 1.0–1.4 p.u. rated load. The speed reference is kept constant at rated speed. During the time interval of fault detection and identification, the transient time of peak currents lasts for 4 ms with the maximum current 60 A, and the whole transient time is about 30 ms. It is obvious that although phase currents of motor go up and down a lot, good faulttolerance performance can still be seen from the experimental results of Fig. 5.b(2). It can be predicted that performance of fault tolerance may be better under light load or rated load, and it is also indicated that the proposed scheme has a good dynamic fault-tolerant performance. Fig. 5.c(1) shows the system response of double fault (HA ¼ HB ¼ 1) under excessive load (Tl ¼ 23 N·m) situations. In general, to facilitate the discussion on the verification of double faults, it is assume that the transient time of the first fault for the sensor HA has elapsed, and the subsequent fault is applied to the sensor HB . However, this cannot fully reflect the compensation performance for double faults. In this paper, the time interval between the first fault and the second one is set as 5 ms, so it can be considered that the double faults happen at the same time in theory. As shown in Fig. 5.c(1), under this situation, the transient time of currents lasts for 40 ms with the maximum current 50 A, and wrong commutation appears. More importantly, once the double fault is compensated, the phase current maintains consistent before Hall sensors failure. It is clear that double faults can be diagnosed and compensated well with the proposed fault tolerant method.

9


The double fault (HA ¼ HB ¼ 1) with V-shaped reference speed (considering the accuracy of the experimental equipment and the speed not transient, the Vshaped reference speed cannot be accurately given, so a general trend of velocity variation is given in this paper) under rated torque is considered next. In order to observe the influence of the double fault on the motor phase current and the whole compensation process, the time axis is set as 100 ms/div in Fig. 5.c(2). The transient time of the first fault for the sensor HA has elapsed, and the subsequent fault is applied to the sensor HB . Fig. 5.c(2) shows significant oscillation appears in current, whose transient peak current reaches 50 A, lasting for up to 20 ms. 5

Discussions

5.1 Start issue Hall-effect sensor provides absolute position information and the initial position error in normal operation, which can be controlled within 30 electrical degrees. It is also obvious that the proposed method does not consider starting of the motor with already faulted sensors; such start may require special considerations (such as, sensorless technology [15] and high frequency signal injection method [16]) and might be possible. Due to the limited space articles, the simple starting method with faulted sensor will be discussed in the following study. 5.2 Redundancy Under the premise that one or two Hall sensors are in failure, the fault tolerance technology of Hall sensor ensures that the motor is still in normal operation i.e., the redundancy of traditional PMIM drives with Hall-effect sensors is double. In addition, the fault tolerant technology can be used in the low cost applications where motor drives with one or two Hall sensors. Combination of the fault tolerance technology and the sensorless technology can further increase the Hall sensor redundancy and improve the stability of the system. 6

Conclusions

This paper analyzes the characteristics of Hall-effect sensor faults (single fault and double fault), and fault-compensation based on reduced-order observer has been proposed. The steady state and dynamic performance of the fault tolerant technique are tested under different conditions, such as no load, low speed, overload, Vshaped reference speed and variable load. From the experimental data analysis, fault-compensation technology which has been devised to be free from the mechanical parameters of motor (such as, inertia) in rotor position estimation process. In particular, it is suitable for the fault tolerance under complex working environment with the deformation on motor performance can be negligible. Moreover, the PMIM drives with three Hall-effects sensor which controlled by the fault tolerant control technology redundancy is double, the reliability and stability of the PMIM drives system are improved. © IEICE 2017 DOI: 10.1587/elex.14.20170470 Received May 4, 2017 Accepted June 16, 2017 Publicized June 30, 2017 Copyedited July 25, 2017

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Appendix A. Fault compensation angle Table III.

Single fault compensation angle

single fault H1

single fault H2

sectors i

j

k

sectors i

H2 =H3 60°

−180° −60° H1 =H3 60°

single fault H3

j

k

sectors i

120°

−120° H3 =H7 120° −180° −120°

H6 =H7 120° −60°

0°

H0 =H2 120° −120° −60°

H4 =H5 60°

120°

H4 =H6 60°

180°

H5 =H7 120° 60°

0°

H0 =H1 120° 120°

−60°

j

H2 =H6 60°

k

−120° 0°

60°

H0 =H4 120° 0°

60°

120°

H1 =H5 60°

180°

60°

Table IV. Double fault compensation angle double fault H1 ; H2 sectors i

j

k

H0=1=2=3 180° 120°

double fault H1 ; H3 sectors i

j

k

−60° H2=3=6=7 180° −180° 0°

H4=5=6=7 180° −60° 120°

H0=1=4=5 180° 0°

double fault H2 ; H3 sectors i

j

H1=3=5=7 180° 60°

k −120°

180° H2=4=6=8 180° −120° 60°

B. Main parameter of motor Table V. Main parameter Rated voltage/V

48

Pole pairs

23

Rated current/A

11

Rated speed/RMP

520

Rated power/W

500

No-load current/A

2.3

Rated torque/N·m

20

Acknowledgments This paper was supported in part by the National Natural Science Foundation of China (NSFC) under grant No. 51107023, in part by Foundation of Heilongjiang Educational Committee under grant No. 12541157.


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