Online Inverter Fault Diagnosis of Buck-Converter BLDC Motor ...

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 5, MAY 2015

Online Inverter Fault Diagnosis of Buck-Converter BLDC Motor Combinations Jiancheng Fang, Member, IEEE, Wenzhuo Li, Haitao Li, and Xiangbo Xu

Abstract—Brushless dc (BLDC) motors are commonly used in space application for its simplicity and high reliability. The faulttolerant control (FTC) of the motor is important for its continuous operating capacity even under the faulty situation. The fault diagnosis should be achieved in advance in order to implement the FTC strategy. This paper proposes an online model-based inverter fault diagnosis method for three-phase full bridge inverter with buck dc–dc converter based on the high-speed BLDC motor with low inductance and nonideal back electromotive force in a magnetically suspended control moment gyro. The method can detect and identify both open-circuit and short-circuit damages of single switch in buck converter or three-phase full bridge. Also, protective measures are proposed to isolate the fault and avoid the secondary fault. Both simulation and experimental results are taken out to prove the validity and effectiveness of the proposed fault diagnosis method. Index Terms—Brushless dc (BLDC) motor, buck converter, fault tolerance, online fault diagnosis.

I. INTRODUCTION AGNETICALLY suspended control moment gyro (MSCMG) is considered to be the key actuators for the attitude control of space stations, satellites, etc. It has the character of high precision, large moment, and long life owing to the zero friction and enhanced damping of high-speed rotor [1], [2]. Since the operational environment in vacuum is harsh, high reliability and long-life operating ability are required. Normally, the high-speed motor in MSCMG is operating at a constant high speed to supply angular momentum for the high-speed rotor system. The reliability of the motor drives is one of the most important factors to guarantee the safe, continuous, and high performance operation under even some accidents or faults. The research in [3] mentioned that about 38% of the motor failures are found in the power inverter and most of faults are occurred to the power switches. Generally, a fault-tolerant control (FTC) system is composed of fault detection, identification,

M

Manuscript received January 8, 2014; revised May 14, 2014; accepted June 4, 2014. Date of publication June 12, 2014; date of current version December 23, 2014. This work was supported by the Chinese National Innovation Community Foundation under Grant 61121003 and by the Chinese National Natural Science Foundation under Grant 61203112. Recommended for publication by Associate Editor D. O. Neacsu. J. Fang, W. Li, and H. Li are with the Fundamental Science on Novel Inertial Instrument and Navigation System Technology Laboratory, Beijing University of Aeronautics and Astronautics, Beijing 100191, China (e-mail: [email protected]; [email protected]; [email protected]). X. Xu is with the School of Technology, Beijing Forestry University, Beijing 100083, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at htpp://ieeexlore.ieee.org. Digital Object Identifier 10.1109/TPEL.2014.2330420

and remedial actions. The fault detection and identification considered as fault diagnosis which is the basic and important part in FTC system can detect the fault and determine the fault type and location. Thus, online fault diagnosis of the power inverter is important for MSCMG to ensure the continuous operating ability even in the faulty state. Since high operating speed and low power loss are required to the high-speed rotor drive system for space application, low power brushless dc (BLDC) motors tending to have very low inductance with ironless and slotless stator are introduced [4]– [6]. In order to achieve low power loss, a buck type dc-to-dc converter in front of the three-phase full bridge inverter is employed [7]–[11] to avoid the serious current ripples cause by traditional phase pulsewidth modulation (PWM) method [12], [13]. The current closed-loop control is applied to the buck converter. The motor controller is composed of a velocity controller and a current controller to regulate the motor speed and dc-link current. Several research works focused on diagnosis methods of the open-circuit and short-circuit fault in motor drive systems have been carried out during recent decades. The methods can be mainly classified into two categories: time-domain diagnosis method [14]–[28] and frequency-domain diagnosis method [29]–[32]. The frequency-domain diagnosis method adopts advanced digital signal processing technology, which may reduce the risk of false alarm caused by the measurement noise. However, it introduces complex computation and longer diagnosing time. The time-domain diagnosis method is widely used in application for its fast detecting and simplicity. Many literatures focus on the time-domain diagnosis method based on motor current or voltage measurement [14]–[17]. An open-switch fault diagnosis scheme which adopts simple algorithm using the measured phase current information and the operating characteristic of the BLDC motor drives is proposed in [14]. Duan et al. [15] use the average of the absolute value of each phase current to diagnose the open-switch fault of a doubly fed induction generator system. In [16], the proposed method combines the use of normalized quantities with the currents average absolute values as the detection variables to diagnose single open-switch failures. However, the fault diagnosis method based on the measured current signals [14]–[16] may generate false alarm due to the measurement noise especially for the motor with small operating current. The research in [17] compares four kinds of voltage measuring technology used to detect the switch opencircuit fault. The diagnosis methods based on the measurement of inverter pole voltage, phase voltage, and line voltage all need three voltage sensors which may increase the system complexity. The diagnosis methods based on phase voltage and neutral

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FANG et al.: ONLINE INVERTER FAULT DIAGNOSIS OF BUCK-CONVERTER BLDC MOTOR COMBINATIONS

voltage measurement both rely on the system model. Moreover, the closed-loop control will weaken the fault feature in the measured currents or voltages. Although the method based on voltage measurement can achieve fast detection, additional sensors are needed and the closed-loop control impact has not been considered. A real-time open-circuit fault diagnosis method based on the derivative of the absolute current Park’s vector phase is proposed in [18] for two power converters of a permanent magnet synchronous generator drive. In [19], a new voltage-based approach without additional sensors for open-circuit faults diagnosis is proposed by using the information of the reference voltages available from the closed-loop control system. The research works in [18], [19], [23], [31], and [32] mainly focus on the motors adopting the space vector modulation (SVM) control method. For the high-speed BLDC motor of MSCMG using the two-phase conduction method, the buck converter is used to supply smooth and controllable motor input voltage. The control of the transistors in the three-phase bridge inverter without PWM is determined by commutation signals generated by three Hall sensors mounted within the stator. Thus, the above methods for SVM control cannot be directly applied in the high-speed motor of MSCMG due to the different control algorithm and inverter topologies. Recently, model-based method [3], [20]–[25] and artificial intelligence (AI) method [26]–[28] are two common methods in the time-domain diagnosis methods. A diagnosis method based on model reference adaptive system techniques is proposed in [3] to detect and identify the faulty switch. This method has the features of fast diagnosis time and simple structure. In [20], the diagnostic scheme employs the hardware circuit to indirectly obtain the voltages of lower power switches and analyzes the switching function model of the inverter under both healthy and faulty conditions to implement open-switch fault diagnosis in inverters without sensors. Also, a very fast detection scheme using the difference value of the estimated and measured line-toline voltages is proposed in [21] for the conventional three-leg converter by minimizing the use of voltage sensors. In [22], nonlinear observers are adopted to generate the residuals to isolate the faulty switches. A robust observer-based open-circuit FDI scheme adopting a bank of nonlinear proportional-integral observers in dq-frame is proposed in [23] for induction motor drives. A robust open-switch fault detection method based on sliding mode observer and the switching model of half-bridge is proposed in [24]. The research in [25] presents an easy and robust sensor FDI and FTC scheme based on Luenberger state observer for a single-phase PWM rectifier. The AI methods, such as fuzzy-based approach [26], wavelets and neuro-fuzzy system [27], and neural network diagnostic system [28] have been proposed. However, the digital-control-based algorithms have a major drawback of the complicated and excessive computing process. The model-based method and AI method are suitable for the closed-loop control system. However, it should be noted that the methods in [3], [14]–[17], and [19]–[23] all deal with the switch open-circuit fault in traditional three-phase inverter. The openswitch fault in the traditional three-phase inverter will cause the

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motor current reach zero when the faulty switch is gated to turn ON. The motor will work at two-thirds of its torque capabilities. For the three-phase full bridge with buck converter, the open-switch fault in three-phase full bridge will cause the motor current reach zero in the faulty state and the output voltage of buck converter increase because of the effect of inductance and capacitor in buck converter. The high output voltage may introduce secondary fault in the next healthy conducting state. Moreover, few research works focus on the switch short-circuit fault diagnosis in the traditional three-phase inverter, since the fault can be converted to an open-circuit fault by hardware protection [28]. However, for the three-phase full bridge with buck converter, the overcurrent caused by switch short-circuit fault in three-phase full bridge will be self-protected by the current closed-loop control of buck converter in a short period of time without hardware protective measures. Then, unexpected currents will flow among the three phases due to the back EMF voltage especially at high speed, which may induce a secondary fault. Since the switch fault features in traditional three-phase inverter and the three-phase full bridge with buck converter are different, it is meaningful to diagnose and protect the switch faults in three-phase full bridge with buck converter to ensure high reliability for the high-speed motor drive system in MSCMG. This paper proposes a model-based and low-cost switch fault diagnosis method for motor inverter composed of a buck converter and a three-phase full bridge. Based on the analysis of the faulty operating state in closed-loop control system, the residual signals of the voltage observers and the measurements are extracted to diagnose the inverter fault. The effect of nonideal back electromotive force (EMF) caused by practical reasons in production [33] on the estimated voltage is taken into account in the proposed voltage observer. The method can detect and identify both open-circuit and shortcircuit faults fast and exactly with reduced hardware. The faults in buck converter and three-phase full bridge can be distinguished in real time. Meanwhile, protection measures are carried out to prevent the system from secondary fault. The proposed fault diagnosis algorithm is implemented in the existing control system as a subroutine. Simulation and experimental results show the validity and effectiveness of the proposed method. II. BUCK-CONVERTER BLDC MOTOR COMBINATION MODEL The motor input voltage is supplied by buck converter containing two energy storing elements, a coil, and a capacitor shown in Fig. 1. A protective circuit with an MOSFET T8 , a power resistance R1 , and a diode D9 is introduced to discharge the voltage caused by switch open-circuit fault in three-phase full bridge. Fig. 2 shows the equivalent circuit of buck-converter BLDC motor combinations. Fig. 2(a) and (b) shows the equivalent circuits when the switch T7 of buck converter is ON and OFF, respectively. Neglecting the very low stator inductance of the motor, the voltage equations of the buck-converter BLDC motor combinations derived from the state-space averaging method are

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Fig. 1.


Topology of buck-converter motor combinations.

Fig. 3. Operating state under the normal and faulty cases of switch damage in three-phase full bridge. (a) Normal state. (b) Upper switch open-circuit fault state. (c) Lower switch open-circuit fault state. (d) Upper switch short-circuit fault state. (e) Lower switch short-circuit fault state. Fig. 2. Equivalent circuit of buck-converter motor combinations. (a) T 7 is ON. (b) T 7 is OFF.

shown as ⎧ u0 = uin d1 − Δudio (1 − d1 ) − Lf diL /dt − rd7 iL d1 + w1 ⎪ ⎪ ⎨ C0 du0 /dt = iL − i, w2 = 0 ⎪ ⎪ ⎩ u0 = 2Rp i + eL + Δudio (1) where uin and u0 are the input and output voltages of buck converter, Lf and C0 are the inductance and capacitor of buck converter, rd7 is the on-resistance of switch T7 , iL is the inductance current in buck converter, i is the dc-link current of the motor, Δudio is the forward voltage of the diode D0 and D9 , Rp is the single phase resistance satisfying Rp = R + r, R is the stator resistance, r is the switch on-state resistance, eL is the line-to-line back EMF voltage satisfying eL = eup − elow , eup and elow are back EMF voltages of the upper and lower side conducting phases, d1 is the duty cycle of the transistor T7 , w1 and w2 are additive perturbation signals due to occurrence of switch fault in buck converter and three-phase full bridge. Fig. 3 shows the equivalent circuits under the normal and faulty case of single switch damage in three-phase full bridge. We assume that the phase inductance of the ironless stator motor is negligible. The voltage equation of the BLDC motor can be represented as ⎧ ⎪ ⎪ ud = uu + ri + w2−1u ⎪ ⎪ ⎪ ⎪ ⎪ ul = w2−1l + ri ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ uu l = 2Ri + eL + w2−2u + w2−2l ⎪ ⎪ ⎨ uN = w2−1l + Rp i − elow + w2−2l (2) ⎪ ⎪ ⎪ ⎪ ⎪ w2−1 = w2−1u + w2−1l ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ w2−2 = w2−2l + w2−2u ⎪ ⎪ ⎩ w2 = w2−1 + w2−2

where w2−1 and w2−2 are additive perturbation signals due to occurrence of switch open-circuit fault and short-circuit fault in three-phase full bridge. The subscripts u and l represent the upper switch fault and lower switch fault, respectively. Normally, ud ≤ u0 is achieved when the motor is operating at the healthy state. There is a faint possibility that the switch open-circuit fault and short-circuit fault occur at the same time in three-phase full bridge. We assume that when a switch open-circuit fault happens, w2 = w2−1 and w2−2 = 0 are achieved. Also, when a switch short-circuit fault happens, w2 = w2−2 and w2−1 = 0 are achieved. Depending on the drive system shown in Fig. 1, the faults which should be detected and identified are classified as: 1) open-circuit damage of switch in buck converter (F1 ); 2) short-circuit damage of switch in buck converter (F2 ); 3) open-circuit damage of single switch in three-phase full bridge (F3 ); 4) short-circuit damage of single switch in three-phase full bridge (F4 ). III. VOLTAGE OBSERVER From (1), the output voltage of buck converter can be simplified as u0 +

d2 u 0 Lf du0 − Lf C0 2 = uin d1 − Δudio (1 − d1 ) 2Rp dt dt +

Lf deL + w1 , 2Rp dt

(3)

by neglecting the very low stator inductance of the motor and the ultralow on-resistance of switch T7 . It can be learnt that the value of deL /dt cannot be neglected for the motor with nonideal back EMF wave in which the flat width is less than 120 electrical


Fig. 5. Fig. 4.

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Actual and estimated nonideal back EMF voltage waveforms.

Operating states of the BLDC motor.

⎧ ⎪ ⎨ −ω(k)f1 π − ϕ(k1 ) 3 elow (k) = ⎪ ⎩ −ω(k)f [ϕ(k )]

degrees. Then, the voltage equation can be written as ⎧ ⎨ u + Lf du1 = u d − Δu (1 − d ) − e + w 1 in 1 dio 1 L 1 2Rp dt ⎩ u0 = u1 + eL

1

(4)

2 where Lf C0 ddtu2 0 is neglected since the value of Lf C0 is small. Since w1 , w2 contain the fault signals of three-phase full bridge

and buck converter, two simple voltage observers based on (5) and (6) are proposed. The estimated voltages are expressed as u ˆ0 =

1 [uin d1 − Δudio (1 − d1 ) − eL ] + eL 1 + Tk s

u ˆd = 2Rp i + eL

(5) (6)

where Tk = Lf /2Rp satisfies. Since d1 is the controller output, the observers require the measurement of dc-link current i, and the line-to-line back EMF voltage eL . The discrete forms shown as u ˆ0 (k) =

Ts {uin d1 (k) − Δudio [1 − d1 (k)] − eL (k)} Ts + Tk +

Tk u1 (k − 1) + eL (k) Ts + Tk

u ˆd (k) = 2Rp i(k) + eL (k)

(7) (8)

where Ts is the AD sampling period, are used to establish the online observers of the buck converter output voltage and the ˆ0 (k) ≤ uin should be motor input voltage. Moreover, eL (k) ≤ u satisfied to coincide with the actual operating state. Fig. 4 shows the three-phase back EMF voltages during the six conducting periods in one 360 electrical degrees. The back EMF voltages eL (k), eup (k), elow (k) and eun (k) can be given as eL (k) = eup (k) − elow (k) ⎧ st = 1, 3, 5 ⎪ ⎨ ω(k)f1 [ϕ(k1 )] eup (k) = π ⎪ ⎩ ω(k)f1 − ϕ(k1 ) st = 2, 4, 6 3

(9) (10)

st = 1, 3, 5

1

⎧ ω(k)f2 [ϕ(k1 )] ⎪ ⎨ eun (k) = π ⎪ ⎩ ω(k)f2 − ϕ(k1 ) 3

(11)

st = 2, 4, 6 st = 1, 3, 5 (12) st = 2, 4, 6

where f1 (ω) and f2 (ω) are the waveform functions of the upper side phase and the unconducting phase back EMF voltages when the operating state st is odd, ω(k) is the mechanical angular velocity, and st is the motor operating state. ϕ(k1 ) represents the current electrical angle in one conducting period. Since the waveform functions f1 (ω) and f2 (ω) can be measured in the offline mode, eL (k), eup (k), elow (k), and eun (k) should be calculated in real time by the estimated current electrical angle ϕ(k1 ). Using the commutation instants as the reference points which satisfy ωt = 0, the current electrical angle can be estimated as ϕ(k1 ) = ω(k)Ts + ϕ(k1 − 1),

k1 ≥ 2

(13)

where ϕ(1) = ω(k − k1 + 1)Ti is achieved. After each commutation instant, the time interval between the commutation instant and the next sampling instant is calculated as Ti and k1 is cleared zero. Then, in one conducting period, k1 = k1 + 1 is carried out after each sampling instant. Also, 0 < ϕ(k1 ) ≤ π3 should be achieved in order to avoid the estimation error caused by the motor velocity fluctuation. Based on the motor velocity calculated from the Hall position sensors and the estimated current electrical angle, the back EMF voltages can be calculated in real time from (9)–(12). Fig. 5 shows the measured and calculated back EMF voltage waveforms. IV. FEATURE EXTRACTION Two residual signals derived from the estimated signals and the measured signals are expressed as ˜0 = ud + si Δudio − u ˆ0 = w1 , ε1 = u ε2 = u ˜ d = ud − u ˆd = w2 ,

w1 = 0

w2 = 0

(14) (15)

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where si = 1 satisfies when i > 0, si = 0 satisfies when i ≤ 0. Also, two signals which can be used to identify the faulty switch in three-phase full bridge are expressed as ε3 = ud − 2uN − eup − elow + Δuun = w2−2u + w2−1u − w2−2l − w2−1l + Δuun ε4 = sgn (îup ) + sgn (îlow )

(16) (17)

where uN is the motor neutral voltage, Δuun satisfying Δuun = uun − uN − eun can be calculated from the phase voltage of the unconducting phase which may abnormally conduct through the diode of upper or lower switch after the fault of F4 . uun can be calculated through ⎧ −ΔuD 2 , ⎪ ⎪ ⎨ = ud + ΔuD 5 , ⎪ ⎪ ⎩ uN + eun ,

B. Switch Short-Circuit Fault in Buck Converter The fault of F2 will cause the switch T7 keep on turning ON. The inductance current iL and the output voltage u0 will gradually increase. The actual output voltage u0 eventually equals to the system input voltage uin . The motor velocity and dc-link current will both exceed the reference values because of the fault of F2 . Thus, the current closed-loop controller output d1 will be equal to zero. The estimated output voltage u ˆ0 will be close to the value of the line-to-line back EMF voltage. It can be deduced that ε1 > 0 is achieved after the fault of F2 . Also, ε2 = 0 is achieved since there is no fault in the three-phase full bridge. C. Switch Open-Circuit Fault in Three-Phase Full Bridge

uN + eun < −ΔuD 2

When the fault of F3 happens, the motor dc-link current i decreases to zero in the faulty conducting state. From (1), the uN + eun > ud + ΔuD 5 uun output voltage of buck converter can be expressed as ⎧ − ΔuD 2 ≤ uN + eun ≤ ud + ΔuD 5 . 2 ⎪ ⎨ u + L C d u0 = u d − Δu (1 − d ) (18) 0 f 0 in 1 d0 1 dt2 (20) The signal ε4 can reflect the symbolic of the estimated phase ⎪ ⎩ C du /dt = i currents which are given as 0 0 L

îup = (ud − uN − eup )/Rp îlow = (uN + elow )/Rp .

(19)

From (14) to (19), the motor input voltage ud and neutral voltage uN should be measured to calculate the needed fault feature signals. ε1 and ε2 are used to detect the fault type F1 ∼ F4 . ε1 is used to identify the fault type F1 and F2 . ε3 is used to identify the faulty switch of fault type F3 . ε3 and ε4 are used to identify the faulty switch of fault type F4 . V. ANALYSIS OF INVERTER FAULT FEATURE Generally, it is unlikely that different kinds of fault simultaneously happen in the motor inverter. Also, simultaneous faults in different legs are not considered in this paper. Four kinds of single switch fault will be discussed and distinguished later. First, the operating performances of the motor under the four fault conditions of F1 -F4 are analyzed, respectively. A. Switch Open-Circuit Fault in Buck Converter When the fault of F1 happens, the switch T7 turns OFF. Thus, the inductance current iL will gradually decrease to zero because of the existence of the inductance and capacitor in buck converter. Also, the motor current i will decrease to zero eventually. The actual output voltage u0 will decrease and eventually equal to the value of the line-to-line back EMF voltage. The fault of F1 will cause the motor current and velocity decrease. Then, the current closed-loop controller output d1 will increase to the maximum value. Thus, the estimated output voltage u ˆ0 will be close to the input voltage uin . Thus, ε1 < 0 is achieved because of the effect of closedloop control. Since the fault in buck converter will not affect the operating state of the three-phase full bridge, ε2 = 0 is achieved.

neglecting the ultra low on-resistance of switch T7 . Because of the existence of the inductance Lf , the current iL satisfying iL > 0 will not decrease to zero at once. The output voltage of buck converter u0 will increase rapidly. Then, the output voltage of buck converter will experience a second-order concussion after the fault of F3 . The fault of F3 will change the load of the buck converter. Thus, the fault affects both ε1 and ε2 . The actual output voltage u0 increases sharply after the fault of F3 . ε1 > 0 can be achieved since the change of the load of buck converter is neglected in (7). Due to ud > uu l , ε2 > 0 is achieved. D. Switch Short-Circuit Fault in Three-Phase Full Bridge Fig. 6 shows the two kinds of current path with abnormal current flowing in the unconducting phase when the fault of F4 happens in switch T1 under st = 3. From Fig. 6(a) and (b), the motor input voltage under the two states can be obtained as ud = [3Rp i + (eB − eC ) + (eA − eC )]/2

(21)

ud = [3Rp i + (eB − eC ) + (eA − eC ) − ΔuD 3 − riB ]/2 (22) respectively by the three-phase voltages. ε2 < 0 can be deduced from (8), (21), and (22). Because of the effect of the current closed-loop control, the actual output voltage u0 will decrease after the fault due to the abnormal conducting current. Also, since the change of the load of buck converter is neglected in (7), ε1 < 0 may be achieved. The input voltage of the traditional three-phase full bridge equals to the dc-link bus voltage. Since the transistor switching logic changes with the rotor position, the complementary transistor of the faulty one may be gated to turn ON and the complete limb will be short-circuited. It may generate a disaster to the whole system without overcurrent protective circuit.


Fig. 6. Current paths under T 1 short-circuit fault when st = 3. (a) u d > u B . (b) u d < u B .

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Fig. 8. Current paths under the faulty case of fault type F4 . (a) Complete shortcircuit of the limb caused by T 1 fault when st = 4. (b) Complete short-circuit of the limb caused by T 4 fault when st = 1.

TABLE I SYSTEM RATINGS Specifications

Fig. 7. Abnormal conducting of the complete short-circuit of the limb caused by the fault of F4 .

However, for the three-phase full bridge with buck converter, the input voltage of the three-phase bridge equals to the output voltage of the buck converter. The complete short circuit of the limb shown in Fig. 7 will also cause the overcurrent. But the overcurrent process will be very short since the effect of the current closed-loop controller will cause the input duty cycle of buck converter d1 to be zero. Meanwhile, as shown in Fig. 8, the abnormal current which cannot be detected through dc-link current will flow among three phases. The operating state of the complete short-circuit of the limb will be analyzed. After the input duty cycle of the buck converter d1 decreases to zero, the equivalent circuit is shown in Fig. 7. The output voltage of the buck converter is given as ⎧ u0 = −Lf diL /dt − Δudio ⎪ ⎪ ⎨ C0 du0 /dt = iL − i (23) ⎪ ⎪ ⎩ u0 = ri + Δudio . From (23), a second-order differential equation can be deduced as d2 u 0 1 1 du0 1 + + u0 = − Δudio . dt2 C0 R dt Lf C0 Lf C0

(24)

Quantity

Number of poles Moment of inertia, J Torque constant, k τ Back EMF constant, k e Terminal resistance, R Armature inductance, L Converter input voltage, u i n Capacitor of the buck converter, C 0 Inductance of buck converter, L f On-state resistance of the switch, r Forward voltage of the diode D 0 and D 9 , Δ u d i o

2 0.00656 kg· m2 0.006 Nm/A 0.0006 V/r/min 0.1 Ω 2.5 μH 28 V 5 μF 1 mH 0.045 Ω 0.8 V

Using the initial values of u0 (t = 0) = U and u0 (t = 0) = −(U − Δudio )/(C0 r), the time interval t1 of the output voltage of the buck converter u0 decreasing from the initial value U to Δudio can be calculated as t1 = r · C0 .

(25)

From the system ratings shown in Table I, t1 ≤ 1 μs is achieved. Thus, the output voltage of the buck converter will decrease to a small value approximate to zero fast after the fault. ε1 < 0 and ε2 < 0 are achieved. It seems that the feature of fault type F4 is weakened by the existence of the buck converter and current loop controller. However, due to the back EMF voltage especially at the high speed, unexpected current shown in Fig. 8(a) and (b) will flow among the three phases. The abnormal current may generate negative torque and decrease the motor efficiency. Also, high

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magnitude of the abnormal current at high speed may ruin the motor coil and cause a secondary fault. Firstly, the performance of fault type F4 in upper switch T1 during st = 4 shown in Fig. 8(a) should be analyzed. The abnormal current may be generated in all three phases since eB > eC > eA satisfies. The current paths shown by dashed lines indicate that the current of phase C may conduct through the diode D5 or D2 during st = 4. The main current path shown by solid lines is flowing from phase A to B. When phase C is not conducting, the voltage equations of the two conducting phases and the neutral voltage are expressed as uA = ud − ΔuT 1 = ΔuT 4 ≈ 0 (26) uB = ud + ΔuD 3 uN = (ud + ΔuD 3 − eA − eB )/2.

(27)

The actual phase currents of the upper side and lower side are expressed as iup = iB = (ud + ΔuD 3 − eB − uN )/R (28) ilow = −iA = (eA + uN − ud )/Rp . When phase C is conducting through the diode D2 , the neutral voltage is expressed as uN = (ud − eA − eB − eC )/3

(29)

from (18) and (26). Also, when phase C is conducting through the diode D5 , the neutral voltage is expressed as uN = (2ud + 2ΔuD 3 − eA − eB − eC )/3.

(30)

Fig. 8(b) shows the short-circuit fault which happens in lower switch T4 during st = 1. Similarly, when phase C is not conducting, the two conducting phase voltages and the neutral voltage satisfy uA = uT 4 ≈ ud (31) uB = −ΔuD 6 uN = (ud − ΔuD 6 − eA − eB )/2.

(32)

The actual phase currents of the upper side and lower side are expressed as iup = iA = (ud − eA − uN )/R (33) ilow = −iB = (eB + uN + ΔuD 6 )/R. When phase C is conducting through the diode D2 , the neutral voltage is expressed as uN = (ud − 2ΔuD 6 − eA − eB − eC )/3.

(34)

When phase C is conducting through the diode D5 , the neutral voltage is expressed as uN = (2ud − eA − eB − eC )/3.

(35)

It can be learnt that the actual phase current of the two conducting phases satisfy iup < 0 and ilow < 0 after the complete short-circuit of the limb. Compared (28) and (33) with (19), îup < 0 and îlow < 0 are achieved due to the small value of ud .

Fig. 9.

Flowchart of the proposed on-line diagnosis method.

Thus, the estimated negative current values can be used to detect the fault. ε4 = −2 is achieved when the complete short-circuit fault of the limb in the three-phase full bridge inverter happens. VI. FAULT DIAGNOSIS AND PROTECTION A. Fault Detection It can be learnt that the fault in the buck converter will not influence the operating state of the three-phase full bridge. When the fault of F1 or F2 happens, the fault feature will show in ε1 only. When the fault of F3 or F4 happens, the fault feature will show in both ε1 and ε2 . Thus, the fault type of F3 and F4 should be detected only by the fault feature ε2 at first. Then, the fault type of F1 and F2 can be detected by the fault feature ε1 when the fault type of F3 and F4 have not been detected. Fig. 9 shows the flowchart of the proposed online diagnosis method. At first, the detection of fault type F4 and the complete shortcircuit of the limb caused by fault type F4 are achieved by 0, ε2 > eth2 s tf 4 = (36) tf 4 + Ts , ε2 ≤ eth2 s 0, G4 = 0 tf 4s = (37) tf 4s + Ts , G4 = 1 and ε4 = −2 where tf 4 and tf 4s denotes the fault detection time of fault type F4 and the complete short-circuit of the limb caused by short-circuit damage of switch in three-phase full bridge.


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denoted as Δu. The actual input voltage of the motor is given as ud = (Rp + R + R2 )i + eL + Δu.

Fig. 10. Equivalent circuits of fault F3 and F4 . (a) Fault of F3 . (b) Fault of F4 without the complete short-circuit of the limb. (c) Fault of F4 with the complete short-circuit of the limb.

The detection of fault type F3 is achieved by 0, ε2 < eth2 o tf 3 = tf 3 + Ts , ε2 ≥ eth2 o

(38)

where tf 3 denotes the fault detection time of fault type F3 . After the detection of no switch fault in three-phase full bridge, the fault type F2 and F1 can be detected by 0, ε1 < eth1 s tf 2 = (39) tf 2 + Ts , ε1 ≥ eth1 s tf 1 =

0, tf 1 + T s ,

ε1 > eth1 o ε1 ≤ eth1 o

Compared with (6), the residual error equals to Δu since the motor dc-link current satisfies i = 0. From (20), du0 /dt = iL /C0 is achieved. In order to avoid the false alarm caused by measurement error and closed loop control effect, the average value of the motor reference current iref and the measured motor dc-link current i which is approximately equal to the value of inductance current iL can be used to calculate du0 /dt. Thus, the threshold value of eth2 o in (38) can be chosen as eth2 o = 0.5n

Ts (iref + i) ,n > 0. C0

where tf 2 and tf 1 denote the fault detection time of fault type F2 and F1 . The algorithm for the fault detection is given by 1, tf x ≥ Tfault Gx = (41) 0, tf x < Tfault where Tfault denotes the fault detection time satisfying Tfault = ktf .Ts , Gx denotes the fault flag of the five kinds of fault, x represents 1, 2, 3, 4, and 4s, respectively. The integer ktf should be carefully selected considering both the detection time and robustness against false detection. The large value of ktf may cause the fault detection failure. The small value of ktf will increase the possibility of false detection. Since the switch fault in the three-phase full bridge may cause a secondary fault, the detection process should be achieved within a conducting state which is 1 ms at the speed of 5000 r/min. Then, 0 < ktf < 20 should be satisfied to ensure fast detection. From the estimated and actual output voltage of buck converter u0 , the threshold value of eth1 oand eth1 s in (39) and (40) are chosen as eth1 o = −m(uin − E) (42) eth1 s = m(uin − E) where E denotes the maximum magnitude of the line-to-line back EMF voltage. Also, 0 < m < 1 is satisfied. The equivalent circuit of fault F3 is shown in Fig. 10(a). The fault is shown as a resistance R2 with great resistance value connected in series in the circuit. The increasing value of the output voltage of the buck converter caused by the fault is

(44)

The equivalent circuit of fault F4 is shown in Fig. 10(b). The short-circuit fault is shown as the winding of the unconducting phase connected in parallel in the equivalent circuit. According to the equations of the actual and estimated motor input voltage after fault F4 which are given as (21), (22), and (6), the threshold value of eth2 s in (36) is given as eth2 s = −0.5jR(iref + i),

(40)

(43)

j ≥ 0.5

(45)

using the average value of the motor reference current iref and the measured motor dc-link current i to avoid the false alarm caused by measurement noise and the closed-loop control effect. Moreover, the equivalent circuit of the complete short-circuit of the limb caused by fault F4 is shown in Fig. 10(c). The actual motor input voltage can be expressed as ud ≈ 0. Compared with (21) and (22), the actual motor input voltage with the complete short-circuit of the limb is smaller than the one without the complete short-circuit of the limb. Thus, the threshold value shown in (45) is also suitable to the complete short-circuit fault of the limb. The threshold value of eth1 o, eth1 s, eth2 o and eth2 s can be determined by carefully choosing appropriate values of m, n, and j to ensure the fast and accuracy fault detection. In practice, the chosen variables n and j should be according to the selection value of m in the different speed region to avoid false detection since the switch fault in three-phase full bridge which influence both ε1 and ε2 should be detected through ε2 before the false detection of switch fault in buck converter by ε1 .eth2 o ≤ eth1 s and eth2 s ≥ eth1 o should be achieved after the fault. According to the motor current and back EMF voltage in the speed region of 0 to 5000 r/min, m = 0.25 is chosen to ensure reliable detection of buck converter fault. n ≤ 4 m and j ≤ 100 m should be achieved from the experimental test. Moreover, the larger m, n, and j are chosen, the higher reliability of the fault diagnosis will be achieved. The smaller m, n, and j are chosen, the faster detection of the fault diagnosis will be achieved. Moreover, in order to improve the reliability of the fault detection, a dead zone Δz is adopted in the comparator. The (17) can be rewritten as ε4 = s(îup ) + s(îlow )

(46)

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where the function s(x) is expressed as ⎧ 1, x > Δz ⎪ ⎪ ⎨ s(x) = 0, − Δz ≤ x ≤ Δz ⎪ ⎪ ⎩ −1, x < −Δz.


TABLE II FAULT IDENTIFICATION ALGORITHM

(47)

The dead zone Δz is chosen to be Δz = qiref , where 0 < q < 1 is satisfied. The value of q should be carefully selected to minimize the possibility of false error detection. If q is selected too high, the complete short-circuit of the limb caused by fault of F4 may not be detected. Moreover, if q is too small, the probability of false error detection increases.

Fault type F3

F4

G3

G4

Gi

G4s

T1 T2 T3 T4 T5 T6 T1

1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1

1 −1 1 −1 1 −1 −1 −1 1 1 −1 −1 1 1 −1 −1 1 1

0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1

T2 T3

B. Fault Identification

T4

The faulty switch in three-phase full bridge should be identified after the detection of the fault type F3 and F4 . ε3 is chosen to identify the faulty switch. The fault identifying flag of single switch in three-phase full bridge is given as 1, ε3 > 0 (48) Gi = −1, ε3 < 0. The value of ε3 will be analyzed in detail for the upper switch open-circuit fault, lower switch open-circuit fault, upper switch short-circuit fault, and lower switch short-circuit fault, respectively. 1) Upper Switch Open-Circuit Fault in Three-Phase Full Bridge: From (2) and (16), ε3 = w2−1u is achieved when the upper switch open-switch fault happens. Since the fault F3 will cause the output voltage of buck converter increase, ud > uu satisfies. Thus, ε3 > 0 is achieved from (2). 2) Lower Switch Open-Circuit Fault in Three-Phase Full Bridge: ε3 = −w2−1l is achieved when the lower switch openswitch fault happens. ε3 < 0 is achieved from (2). 3) Upper Switch Short-Circuit Fault in Three-Phase Full Bridge: From (2), ε3 < 0 is achieved since ε3 = w2−2u and ε2 = w2 = w2−2u < 0 are obtained when the short-circuit fault happens in the complementary transistor of the unconducting one. When the short-circuit fault happens in the complementary transistor of the conducting one, ε2 < 0 and ε4 = −2 can be detected. Substituting (27), (29), and (30) into (16), respectively, ε3 = w2−2u + Δuu n < 0 can be deduced. Thus, ε3 < 0 is used to identify the upper side switch short-circuit fault. 4) Lower Switch Short-Circuit Fault in Three-Phase Full Bridge: ε2 = w2 = w2−2l < 0 is achieved when the lower switch short-switch fault happens. Similarly, considering the two conditions of short-circuit fault happens in the complementary transistor of the unconducting and conducting one, ε3 = −w2−2l > 0 and ε3 = −w2−2l + Δuu n > 0 can be obtained from (2), (16), (32), (34), and (35). Thus, ε3 > 0 is used to identify the faulty switch. Thus, the fault diagnosis algorithm of the single switch fault in three-phase full bridge shown in Table II can be deduced. The robustness of the fault diagnosis method depending particularly on residuals robustness to system parameter variations and measurement inaccuracy should be analyzed. The estimated

Faulty switch

T5 T6

Current state st st st st st st st st st st st st st st st st st st

= = = = = = = = = = = = = = = = = =

1 2 3 4 5 1 3 4 1 5 2 1 3 1 1 2 2 3

or 2 or 3 or 4 or 5 or 6 or 6 or 6 or 5 or 4 or 6 or 5 or 6 or 6 or 2 or 4 or 3 or 5 or 4

Fig. 11.

Control system with the proposed on-line diagnosis method.

Fig. 12.

Photograph of the experimental prototype.

voltage in (8) may be affected by the system parameter error and measurement inaccuracy in the proposed method. However, since the stator resistance and motor current are small and the


Fig. 13.

Simulated results of switch fault in buck converter. (a) Short-circuit fault. (b) Open-circuit fault.

Fig. 14.

Experimental results of switch fault in buck converter. (a) Short-circuit fault. (b) Open-circuit fault.

line-to-line back EMF voltage is large at the high speed, the estimated voltage is less affected by the variation of the machine parameter and measurement error. The high-speed motor of MSCMG is normally operating at a constant high speed to supply constant angular momentum for the high-speed rotor system. Thus, the stator resistance variation and current measurement error can be ignored. In addition, to avoid the false fault detection due to the variation in the machine parameter error, the threshold values eth2 o and eth2 s could be selected within a safe limit to ensure reliable diagnosis. The online machine parameter observation algorithm could be adopted to get a better performance for low speed application.

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C. Fault Protection 1) Switch Open-Circuit Fault in Three-Phase Full Bridge: The protective circuit with one MOSFET T8 , one power resistance R1 , and one diode D9 shown in Fig. 1 is introduced to discharge the voltage caused by fault of F1 . Normally, T8 is switched OFF to ensure the operating of buck converter. After fault diagnosis of F1 , T7 is switched OFF and T8 is switched ON with certain duty circle to discharge the high output voltage of buck converter in the faulty operating state in order to avoid the secondary fault. 2) Switch Short-Circuit Fault in Three-Phase Full Bridge: After the fault diagnosis of F4 , the complementary switch of

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Fig. 15. Simulated results of switch fault in three-phase full bridge. (a) T 4 open-circuit fault. (b) T 1 open-circuit fault. (c) T 4 short-circuit fault happens when st = 6. (d) T 4 short-circuit fault happens when st = 1. (e) T1 short-circuit fault happens when st = 6. (f) T1 short-circuit fault happens when st = 4.

the faulty one is cut off and the relay connected in series in the circuit of the faulty phase winding is used to isolate the faulty phase. The three-phase windings are isolated by shutting off the three upper switches to avoid the overcurrent caused by the short-circuit fault. 2) Switch Short-circuit Fault in Buck converter: After the fault diagnosis of F2 , the dc-link input voltage supply should be cutoff immediately. The three-phase windings are isolated by shutting off the upper switches to avoid the overcurrent caused by the fault. Meanwhile, in order to discharge the high output voltage of buck converter caused by the short-circuit fault, T8 is switched ON with certain duty circle.

VII. SIMULATED AND EXPERIMENTAL RESULTS The ratings of the BLDC motor under study are listed in Table I. The motor is always operating in steady-state condition in which the current is stable and the rotor speed will not change a lot between the adjacent operating states due to the large rotor inertia and small torque constant. The selection of parameters is important to ensure the high reliability and fast diagnosis time of the proposed fault diagnosis method. m = 0.25, n = 1, j = 4, and q = 0.25 are chosen to generate the threshold value for the proposed diagnosis method. A BLDC motor system with buck converter is established to run the simulation in MATLAB/Simulink. The BLDC motor controller with


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Fig. 16. Experimental results of switch fault in three-phase full bridge. (a) T 4 open-circuit fault. (b) T 1 open-circuit fault. (c) T 4 short-circuit fault happens when st = 6. (d) T 4 short-circuit fault happens when st = 1. (e) T 1 short-circuit fault happens when st = 6. (f) T 1 short-circuit fault happens when st = 4.

the proposed fault diagnosis method is shown in Fig. 11. The photograph of the experimental prototype is shown in Fig. 12. The simulated results of diagnosis processes of fault F1 and F2 at the rotor speed of 5000 r/min are shown in Fig. 13. Also, the experimental results of the BLDC motor used for hardware validation of the fault diagnosis method of fault F1 and F2 are shown in Fig. 14. In the testing, a floating-point TMS320C31 DSP and an Altera EPF10K40 field-programmable gate array (FPGA) were used to build a motor controller with the proposed diagnosis method. The frequency of AD sampling accomplished by an A/D converter AD1674 is chosen to be 20 kHz. The part number of the MOSFETs used in the system is IRF540N of which the maximum continuous drain current and drainto-source breakdown voltage are 33 A and 100 V. A vacuum pump is used to supply vacuum condition in the gyro room.

The switch open-circuit fault was inserted through the FPGA by the permanent off signal of the gate driver. Similarly, the switch short-circuit fault was modeled by turning the gate signal permanently ON. The occurrence of the fault conditions F1 and F2 are denoted by the flags G1o and G2o . ε1 , eth1 s, and eth1 o are generated to detect the fault. G1 and G2 denote the fault diagnosis flags of fault F1 and F2 . In the proposed method, ktf = 5 is chosen. It can be learnt that the experimental results coincide with the simulations and analyses. From the simulated and experimental results, the fault diagnosis time of short-circuit fault and opencircuit fault in buck converter are shown as 0.001 s and 0.003 s, respectively. The simulation and experimental results of the diagnosis process of fault F3 and F4 are shown in Figs. 15 and 16. Fig. 15(a)

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Fig. 17. Experimental results of the transient state under each fault. (a) T 7 open-circuit fault. (b) T 7 short-circuit fault. (c) T 4 open-circuit fault. (d) T 1 open-circuit fault. (e) T 4 short-circuit fault happens when st = 6. (f) T 4 short-circuit fault happens when st = 1. (g) T 1 short-circuit fault happens when st = 6. (h) T 1 short-circuit fault happens when st = 4.

and (b) shows the simulated diagnosis results of fault F3 with the proposed method. The corresponding experimental results are shown in Fig. 16(a) and (b). The occurrence of the fault condition F3 is denoted by the flag G3o . In the proposed diagnosis method, ε2 and eth2 o are generated to detect the open-circuit fault. ε3 is used to identify the faulty switch by the logic shown in Table II. G3 denotes the fault detection flag of fault type F3 . Gi denotes the fault identification flag of switch fault in threephase full bridge. G3 y shows the fault diagnosis flag of the six switches T1 to T6 in three-phase full bridge under the fault condition of F3 , where y = 1, 2, . . . , 6. After the diagnosis of the fault, fault protection measure is taken to discharge the output voltage of buck converter in order to avoid the secondary fault. The fault diagnosis time is shown as Tfault 0.0006 s. Figs. 15(c)–(f) and 16(c)–(f) show the simulated and experimental results of fault F4 . When the lower switch T4 suffers a short-circuit fault, the fault diagnosis processes with the proposed fault diagnosis method are shown in Figs. 15(c), (d), and 16(c), (d). The occurrence of the fault condition F4 is denoted by the flag G4o . ε2 , eth2 s, and ε4 are generated to detect the short-circuit fault. ε3 is used to identify the faulty switch. G4 denotes the fault detection flag of fault type F4 . G4s denotes the fault detection flag of fault type F4 when the short-circuit of the complete limb happens due to the occurrence of fault F4 . G4 y shows the fault diagnosis flag of the six switches T1 to T6 under the fault condition of F4 , where y = 1, 2, . . . , 6. From the experimental results in Fig. 16(c) and (d), the fault diagnosis time are approximately 0.0008 and 0.0006 s, respectively. It can be

learnt that the fault diagnosis time of lower switch short-circuit fault is less than 0.0008 s. After the diagnosis of the fault, fault isolation measure is taken to disconnect the unexpected conducting phase in order to avoid the secondary fault. Similarly, the diagnosis processes of upper switch T1 short-circuit fault are shown in Fig. 15(e), (f) and 16(e), (f). Also, the fault diagnosis time is less than 0.0008 s. Fig. 17 shows the transient state of motor input voltage, dclink current, and faulty phase current when the fault of each type happens. The shadow areas show the faulty state. It can be learnt from Fig. 17(f) and (g) that the overcurrent process of dclink current caused by the short-circuit fault of three-phase full bridge is very short. The high magnitude of the phase current under fault shown in Fig. 17(b), (e)–(h) which may cause secondary fault are protected by effective measures. The proposed fault diagnosis method with protective circuit is verified to be effective to achieve fast and exact diagnosis.

VIII. CONCLUSION In this paper, a method for online inverter fault diagnosis of motor inverter composed of a buck converter and a threephase full bridge is proposed. The voltage observers based on the system model of buck converter and three-phase full bridge are developed to estimate the buck converter output voltage and motor input voltage, respectively. Thus, the residual voltage errors can be calculated to detect the fault type. Also, the corresponding fault features are extracted to identify the faulty


switch. The open-circuit fault and short-circuit fault in both buck converter and three-phase full bridge can be diagnosed rapidly and effectively by the proposed method. Simulated and experimental results verify the validity of the proposed fault diagnosis method. REFERENCES [1] J. Fang and Y. Ren, “High-precision control for a single-gimbal magnetically suspended control moment gyro based on inverse system method,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 4331–4342, Sep. 2011. [2] S. Zheng and B. Han, “Investigations of an integrated angular velocity measurement and attitude control system for spacecraft using magnetically suspended double-gimbal CMGs,” Adv. Space Res., vol. 51, pp. 2216– 2228, 2013. [3] S. Jung, J. Park, H. Kim, K. Cho, and M. Youn, “An MRAS-based diagnosis of open-circuit fault in PWM voltage-source inverters for PM synchronous motor drive systems,” IEEE Trans. Power Electron., vol. 28, no. 5, pp. 2514–2526, May 2013. [4] J. Fang, W. Li, and H. Li, “Self-compensation of the commutation angle based on dc-link current for high-speed brushless DC motors with low inductance,” IEEE Trans. Power Electron., vol. 29, no. 1, pp. 428–439, Jan. 2014. [5] R. Ravaud, G. Lemarquand, and V. Lemarquand, “Ironless permanent magnet motors: Three-dimensional analytical calculation,” in Proc. IEEE Int. Elect. Mach. Drives Conf., May 2009, pp. 947–952. [6] H. Zhu and J. Zou, “Temperature rise calculation and test of the wheel motor for satellite in vacuum,” in Proc. 8th Int. Conf. Elect. Mach. Syst., Sep. 2005, vol. 1, pp. 695–698. [7] J. Fang, X. Zhou, and G. Liu, “Instantaneous torque control of small inductance brushless DC motor,” IEEE Trans. Power Electron., vol. 27, no. 12, pp. 4952–4964, Dec. 2012. [8] F. Antritter, P. Maurer, and J. Reger, “Flatness based control of buck converter driven dc motor,” in Proc. 4th IFAC Symp. Mechatron. Syst., 2006, vol. 4, pp. 36–41. [9] J. Linares-Flores and H. Sira-Ramirez, “DC motor velocity control through a dc-to-dc power converter,” in Proc. 43rd Conf. Decision Control, 2004, vol. 5, pp. 5297–5302. [10] M. M. Peretz and S. Ben-Yaakov, “Time-domain design of digital compensators for PWM DC-DC converters,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 284–293, Jan. 2012. [11] S. Iwasaki, R. P. Deodhar, Y. Liu, A. Pride, Z. Q. Zhu, and J. J. Bremner, “Influence of PWM on the proximity loss in permanent-magnet brushless ac machines,” IEEE Trans. Ind. Appl., vol. 45, no. 4, pp. 1359–1367, Jul./Aug. 2009. [12] Y. S. Lai and Y. K. Lin, “A unified approach to zero-crossing point detection of back EMF for brushless DC motor drives without current and Hall sensors,” IEEE Trans. Power Electron., vol. 26, no. 6, pp. 1704–1713, Jun. 2011. [13] N. Milivojevic, M. Krishnamurthy, A. Emadi, and I. Stamenkovic, “Theory and implementation of a simple digital control strategy for brushless DC generators,” IEEE Trans. Power Electron., vol. 26, no. 11, pp. 3345– 3356, Nov. 2011. [14] B.-G. Park, K.-J. Lee, R.-Y. Kim, T.-S. Kim, J.-S. Ryu, and D.-S. Hyun, “Simple fault diagnosis based on operating characteristic of brushless direct-current motor drives,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1586–1593, May 2011. [15] P. Duan, K. Xie, L. Zhang, and X. Rong, “Open-switch fault diagnosis and system reconfiguration of doubly fed wind power converter used in a microgrid,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 816–821, Mar. 2011. [16] J. O. Estima and A. J. Marques Cardoso, “A novel diagnostic method for single power switch open-circuit faults in voltage-fed PWM motor drives,” in Proc. Int. Symp. Power Electron., Elect. Drives, Autom. Motion, 2010, pp. 535–540. [17] R. L. de Araujo Ribeiro, C. B. Jacobina, E. R. Cabral da Silva, and A. M. N. Lima, “Fault detection of open-switch damage in voltage-fed PWM motor drive systems,” IEEE Trans. Power Electron., vol. 18, no. 2, pp. 587–593, Mar. 2003. [18] N. M. A. Freire, J. O. Estima, and A. J. Marques Cardoso, “Open-circuit fault diagnosis in PMSG drives for wind turbine applications,” IEEE Trans. Ind. Electron., vol. 60, no. 9, pp. 3957–3967, Sep. 2013. [19] N. M. A. Freire, J. O. Estima, and A. J. Marques Cardoso, “A voltagebased approach without extra hardware for open-circuit fault diagnosis in closed-loop PWM AC regenerative drives,” IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 4960–4970, Sep. 2014.

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[20] Q. An, L. Sun, K. Zhao, and L. Sun, “Switching function model-based fast-diagnostic method of open-switch faults in inverters without sensors,” IEEE Trans. Power Electron., vol. 26, no. 1, pp. 119–126, Jan. 2011. [21] M. Shahbazi, M. Zolghadri, P. Poure, and S. Saadate, “Fast detection of open-switch faults with reduced sensor count for a fault-tolerant threephase converter,” in Proc. 2nd Power Electron., Drive Syst. Technol. Conf., 2011, pp. 546–550. [22] D. U. Campos-Delgado and D. R. Espinoza-Trejo, “An observer-based diagnosis scheme for single and simultaneous open-switch faults in induction motor drives,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 671–679, Feb. 2011. [23] D. R. Espinoza-Trejo, D. U. Campos-Delgado, E. Barcenas, and F. J. Martınez-Lopez, “Robust fault diagnosis scheme for open-circuit faults in voltage source inverters feeding induction motors by using non-linear proportional-integral observers,” IET Power Electron., vol. 5, no. 7, pp. 1204–1216, 2012. [24] S. Shao, P. W. Wheeler, J. C. Clare, and A. J. Watson, “Fault detection for modular multilevel converters based on sliding mode observer,” IEEE Trans. Power Electron., vol. 28, no. 11, pp. 4867–4872, Nov. 2013. [25] A. B. Youssef, S. K. E. Khil, and I. Slama-Belkhodja, “State observerbased sensor fault detection and isolation, and fault tolerant control of a single-phase PWM rectifier for electric railway traction,” IEEE Trans. Power Electron., vol. 28, no. 12, pp. 5842–5853, Dec. 2013. [26] F. Zidani, D. Diallo, M. E. H. Benbouzid, and R. Na¨ıt-Sa¨ıd, “A fuzzybased approach for the diagnosis of fault modes in a voltage-fed PWM inverter induction motor drive,” IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 586–593, Feb. 2008. [27] M. A. Awadallah and M. M. Morcos, “Automatic diagnosis and location of open-switch fault in brushless dc motor drives using wavelets and neurofuzzy systems,” IEEE Trans. Energy Convers., vol. 21, no. 1, pp. 104–111, Mar. 2006. [28] Y. Murphey, M. Abul Masrur, Z. Chen, and B. Zhang, “Model-based fault diagnosis in electric drives using machine learning,” IEEE/ASME Trans. Mechatron., vol. 11, no. 3, pp. 290–303, Jun. 2006. [29] M. Aktas and V. Turkmenoglu, “Wavelet-based switching faults detection in direct torque control induction motor drives,” IET Sci. Meas. Technol., vol. 4, no. 6, pp. 303–310, 2010. [30] J. O. Estima and A. J. Marques Cardoso, “Impact of inverter faults in the overall performance of permanent magnet synchronous motor drives,” in Proc. IEEE Int. Elect. Mach. Drives Conf., 2009, pp. 1319–1325. [31] D. U. Campos-Delgado, J. A. Pecina-Sánchez, D. R. Espinoza-Trejo, and E. R. Arce-Santana, “Diagnosis of open-switch faults in variable speed drives by stator current analysis and pattern recognition,” IET Electr. Power Appl., vol. 7, no. 6, pp. 509–522, Jul. 2013. [32] F. Meinguet, P. Sandulescu, X. Kestelyn, and E. Semail, “A method for fault detection and isolation based on the processing of multiple diagnostic indices: Application to inverter faults in AC drives,” IEEE Trans. Veh. Technol., vol. 62, no. 3, pp. 995–1009, Mar. 2013. [33] J. Fang, H. Li, and B. Han, “Torque ripple reduction in BLDC torque motor with nonideal back EMF,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4630–4637, Nov. 2012. Jiancheng Fang (M’11) received the B.S. degree from Shandong University of Technology, Jinan, China, in 1983, the M.S. degree from Xi’an Jiaotong University, Xi’an, China, in 1988, and the Ph.D. degree from Southeast University, Nanjing, China, in 1996. He is the Dean of the School of Instrumentation Science and Optoelectronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China. He has authored or coauthored more than 150 papers and four books. He has been granted 35 Chinese invention patents as the first inventor. His current research interests include the attitude control system technology of spacecraft, novel inertial instrument and equipment technology, inertial navigation, and integrated navigation technologies of aerial vehicles. Dr. Fang has the special appointment professorship with the title of “Cheung Kong Scholar,” which has been jointly established by the Ministry of Education of China and the Li Ka Shing Foundation. He is in the first group of Principal Scientists of the National Laboratory for Aeronautics and Astronautics of China. He received the first class National Science and Technology Progress Award of China as the third contributor in 2006, the first class National Invention Award of China as the first inventor, and the second class National Science and Technology Progress Award of China as the first contributor in 2007.

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Wenzhuo Li received the B.S. degree from China Agricultural University, Beijing, China, in 2008. She is currently working toward the Ph.D. degree in the College of Instrumentation Science and OptoElectronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China. She is currently a Research Member with Fundamental Science on Novel Inertial Instrument and Navigation System Technology Laboratory, Beijing University of Aeronautics and Astronautics. Her research interests include motor control system, faulttolerant drives and sensorless drive of a brushless dc motor.

Haitao Li was born in Shandong, China, in 1979. He received the B.S. and M.S. degrees from Shandong University, Jinan, China, in 2002 and 2005, respectively, and the Ph.D. degree from the Beijing University of Aeronautics and Astronautics, Beijing, China, in 2009. He is currently a Research Member with Fundamental Science on Novel Inertial Instrument and Navigation System Technology Laboratory, School of Instrumentation Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, China. His main research interests include magnetically suspended control moment gyro and its nonlinear control.


Xiangbo Xu was born in Shandong, China, in 1982. He received the B.S. degree from Shandong University, Jinan, China, in 2006, the M.S. and Ph.D. degrees from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2009 and 2014. He is currently an Academician with the School of Technology, Beijing Forestry University, Beijing, China. His research interests include precise control of motor servo system, active control and vibration suppression of active magnetic bearing.