Disambiguation of Uniform Demagnetization Fault From Position Sensor Fault in FOC PMSM Applications

Electrification of higher torque density applications in the transportation sector and robotics sector are primarily met with permanent magnet synchronous machines (PMSMs), attributing to their unique properties. However, wide operating temperatures, field weakening controls, and low-quality magnets, lead to uniform demagnetization of rotor magnets. Demagnetization in torque control applications reduce the effective output torque as the output torque is proportional to rotor flux level. Detection of such rotor demagnetization is essential and only second to few key faults from the system perspective. However, static position sensor offset error (SPSOE) is a fault mode that may mask itself as a demagnetization fault. Though the demagnetization fault is irreversible, the SPSOE is remediable avoiding sustained-severe degradation of system performance. The false positive nature of demagnetization detection and the SPSOE are discussed in detail in the paper, and a disambiguation strategy is proposed and successfully implemented. Simulation and experimental results are presented to validate the effectiveness of the proposed strategy.

aerospace industry through electrification. Ground as well 23 as aerospace transportation application subsystems such as 24 propulsion/powertrain, steering, power generation, thermal 25 management and air conditioning systems are being con-26 verted to electric. Numerous other industries such as robotics, 27 The associate editor coordinating the review of this manuscript and approving it for publication was Feifei Bu . manufacturing and consumer products are also rapidly grow-28 ing in size, fueled by the mechatronic systems integrated 29 with AI. Among the machines popular for electromechanical 30 energy conversion, permanent magnet synchronous machines 31 (PMSMs) have proven to be advantageous. Despite the cost of 32 rare earth magnets, the higher torque density, compact design, 33 better thermal characteristics, and simple, high dynamic con-34 trol have become the factors favoring PMSMs. 35 Electric machines used in powertrain, aerospace propul-36 sion, power generation units, and steering systems are sub-37 jected to high temperature conditions, high currents and 38 field weakening control to achieve higher speeds without 39 increasing the DC link voltage. Field weakening enables 40 PMSMs to operate at higher speeds without sacrificing 41 their high torque capability at low speed. However, sub-42 jecting a PMSM to high temperatures and field weaken-43 ing for a prolonged period, demagnetizes the rotor magnets 44 to a certain degree [1], [2], [3]. Additionally, manufacturing 45 defects may also contribute to accelerating the demagnetiza-46 tion process [4].
The key contribution of this paper stems from the fact tro motive force (Induced EMF or back EMF) profile of a 66 machine as the induced EMF is a function of speed and flux 67 linkage (1). Figure 1 illustrates an example of how demag-

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In this scenario a uniform demagnetization effect is consid-80 ered as all magnets on the rotor are subjected to the opposing 81 flux generated by the stator used for field weakening. There-82 fore, it is assumed that the flux linkage coefficient is reduced 83 introducing a reduction in the induced EMF amplitude as 84 in (2). The DC offset (e 0 ) and the higher order harmonics 85 are assumed to be negligible during the considered uniform 86 demagnetization scenario.λ r m is the flux linkage constant 87 amplitude after demagnetization. 88 E as (θ r ) =λ r m ω r sin(θ r ) ≈ λ r m ω r sin(θ r ) − λ r m ω r sin(θ r )

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(2) 90 where, ω r represents the motor speed. Reduced flux link-91 age constant implies that the machines torque constant 92 has also reduced, resulting in lower torque output at the 93 same regulated current in torque-controlled applications. 94 In speed-control applications, the higher currents injected 95 by the controller increases the system losses leading to ele-96 vated operating temperatures, promoting demagnetization. 97 Therefore, detecting significant amount of uniform demagne-98 tization is essential to sustain system performance. The organization of the paper is as follows. Introduc-110 tory section states the problem and summarizes the existing 111 body of work on demagnetization detection. More impor-112 tantly, their inability to distinguishing a PSOE presented. 113 Section II through IV explains how the false-positive may 114 occur in the demagnetization detection strategy. A detailed 115 analysis has been provided and the phenomenon is illustrated 116 through simulation and experimental results. Particularly, 117 section III provides experimental and simulation results and 118 section IV details the demagnetization detection algorithm. 119 Sections V and VI cover the disambiguation strategy and 120 present the analysis, simulation, and experimental results. 121 Particularly, section V discusses how the PSOE causes false 122 positives in demagnetization detection algorithm and pro-123 poses a disambiguation strategy. Section VI concludes the 124 paper with final remarks.

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Demagnetization detection in PMSMs have been studied 126 by number of researchers and are discussed here to empha-127 size the significance of the research presented in this paper. 128 The focus of this paper is to disambiguate between PSOE 129 and uniform demagnetization through a signal analysis-130 based approach. Therefore, finite element analysis (FEA) 131 of motor demagnetization is not considered in this body of 132 work. To provide a comprehensive analysis, we have cited 133 references that include FEA results under demagnetization 134 faults. The authors of [5] propose a real-time demagnetization 135 tance matrix. The demagnetization assessment is made based 137 on a first order approximation of the demagnetization char-138 acteristics under varying parameter levels such as current 139 references, resulting in a temperature estimate. Zhao et al. 140 in [6] propose an adaptive linear neuron model reference

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The approach is using a signal injected through the d-axis zation diagnosis in [10], [11], [12], and [13]. Asymmetric  Further, frequency domain spectrum generation requires high 179 computational power, which may not be available on con-180 sumer applications. Authors of [17] and [18] propose search  detection is discussed in [19]. A convolutional neural net-     However, in the situation where uniform demagnetization 249 has occurred, the rotor reference frame voltages applied to 250 the motor are given by (9). Note that true motor currents Rotor reference frame voltages shown in (8) can be calcu-264 lated given the motor parameters, motor speed and reference 265 currents. The difference between the voltages applied to the 266 motor and the voltages computed based on the model will 267 emphasize the voltage difference induced by the demagne-268 tization as in (10). These voltage errors are represented by 269 V r qs_err and V r ds_err .
Speed normalized quadrature axis voltage error as shown 273 in (11) Prior to experimental validation, MATLAB Simulink based 286 simulations were conducted to validate the proposed strat-287 egy. The system used for the simulation study closely 288 models the experimental setup to be discussed in part b, 289 below. The PMSM is operated in torque control mode, while 290 the mechanical system speed is maintained constant by a 291 dynamometer.
292 Figure 4 illustrates the effect of varying uniform demag-293 netization on rotor reference frame voltage errors discussed 294 in (10). Simulations results in figure 4 are at varying uniform 295 demagnetization levels, while the speed is held constant. Sim-296 ulation data was collected under six different speed settings. 297 First subplot depicts the quadrature axis current which is 298 regulated at 1 A. Second subplot is representing the variation 299 of flux linkage coefficient, at each level of demagnetization. 300 Third and fourth subplots indicate the behavior of the rotor 301 reference frame voltage errors at each operating condition (as 302 in (10)). The results clearly show that increased demagnetiza-303 tion under torque control operation has an influence on V r qs_err 304 in the steady state but no effect on V r ds_err . This reveals the 305 important result that a uniform demagnetization effect only 306 reflects on the quadrature axis voltage, and that it has no effect 307 on the direct axis voltage.

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Experimental validation of the proposed method is presented 329 here. The experimental setup is depicted in figure 6 followed 330 by the parameters of the PMSM in Table 1. The PMSM 331 is coupled to a DC machine through an in-line torque sen-332 sor. Both machines are controlled with dSPACE DS1104 333 R&D platform shown. The PMSM is operated in field ori-334 ented controlled torque mode, whereas the DC machine is 335 speed regulated. The demagnetization detection as well as 336 the demagnetization effect emulation was also implemented 337 on the same dSPACE platform. dSPACE systems is a rapid 338 prototyping platform facilitated by Matlab Simulink based 339 auto coding. The underlying DSP is a MPC8240 processor 340 with PPC 603e core operating at 250 MHz clock.

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According to (11), under uniform demagnetization,λ r m < 342 λ r m . Therefore, V r qs_m < V r qs . V r qs is a computed value based 343 on motor parameters, current references and motor speed, 344 according to (8) to be compared with the applied voltage 345 in rotor reference frame, which is V r qs_m . However, demag-346 netizing a machine is permanent and makes the machine 347 useless for future research. Hence, for the purpose of algo-348 rithm validation, uniform demagnetization was emulated by 349 achieving V r qs_m < V r qs condition through modifying the λ r m 350 value to be larger than the nominal value. For dynamometer 351 testing, this was deemed acceptable as the faulty motor is 352 acting as the torque regulator and the dynamometer (DC 353 motor) is regulating speed, which matches the torque on the 354 faulty PMSM.   rent levels. The look-up table implementation is shown in 400 figure 10.

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The reference current used by the FOC algorithm was used 402 as the input to the look up table to prevent additional noise 403 from influencing the demagnetization detection algorithm. 404 Results after the current based compensation are shown in 405 figure 9. It is evident that the results with current based 406 compensation show no variation of voltage error with varying 407 current.

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The updated uniform demagnetization detection algorithm 409 is provided in the block diagram below (Figure 10). The block 410 diagram also includes transient blocking and a threshold com-411 pared with q-axis voltage error to trigger a uniform demag-412 netization fault flag. The transient blocking filter bandwidth 413 has been set to 10% of the current regular bandwidth, which 414 is 100 rads −1 in this experiment. The fault trigger threshold 415 has been set to detect a demagnetization of 5% or more. Since 416 the voltage error is normalized with respect to speed and λ r m 417 the quantity compared with the fault threshold is the amount 418 of change in uniform demagnetization. Simulation results and 419 experimental results under varying conditions are discussed 420 in the next section.
θ r and θ e are true motor rotor position and measured rotor 493 position respectively. K s is the forward reference frame trans-494 formation and K s is the inverse reference frame transforma-495 tion. The resulting closed loop system transfer function due 496 to PSOE under dynamic conditions is represented by (15).
The above result maybe further reduced by considering 500 the steady state response of the system for a step input (1/s), 501 resulting in (16) and (17) Above result concludes that PSOE has direct influence on 507 q-axis voltage, d-axis voltage, and voltage error terms that are 508 used for uniform demagnetization detection.

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To summarize, as shown in figure 16, uniform demagneti-510 zation only affects q-axis voltage equation. However, PSOE 511 effects both q-and d-axis voltage equations (from a motor 512 point of view). Hence, we show that V r qs_err is affected by 513 both uniform demagnetization fault and PSOE. But V r ds_err 514 is only affected by PSOE. FOC controlled PMSMs require 515 rotor position information for optimal stator field orientation 516 and commutation. However, as discussed in [21], [22], and 517 [23], position sensor measurement may contain a DC offset 518 (PSOE: position sensor offset error) and/or harmonic content. 519 Of these, the PSOE has a significant impact on system torque 520 output, along with the potential to cause a false positive in 521 demagnetization detection approach(s). Experimental result 522 below supports the above argument. Figure 17 illustrates the 523 behavior of V r qs_err and V r ds_err discussed in (10) and (17) 524 during a varying PSOE at different speeds. The varying PSOE 525 value is shown in the first subplot of figure 17. The effect 526 is only amplified at higher speed as seen by the increasing 527 voltage error amplitudes in subplot 3 and 4. As discussed next 528 this characteristic serves as a means to disambiguate the two 529 faults.

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The effect of PSOE on the uniform demagnetization detec-531 tion method is shown in figures 11 (simulation) and 18 532     is method is summarized in Table 2. The direct axis voltage 554 error is filtered and compared with a set threshold for the 555 second flag. Therefore, when a PSOE is introduced to the 556 system, both demagnetization detection flag and PSOE fault 557 flag will be set. Fault disambiguation algorithm in flow chart 558 form is shown in figure 20.