# Signal-Based Position Sensor Fault Diagnosis Applied to PMSM Drives for Fault-Tolerant Operation in Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Position Sensor Fault Prognosis

#### 2.1. Effect of Position Sensor Faults

#### 2.2. Position Sensor Failure Detection

_{s}) and stator inductance (L

_{s}) at different load levels of 100%, 50%, and 0% in the absence of a sensor fault. Parameter variations are introduced by changing the parameters in the SPMSM model as ${\mathrm{R}}_{\mathrm{s}}={\mathrm{R}}_{\mathrm{s}\_0}+\u2206{\mathrm{R}}_{\mathrm{s}}$ and ${\mathrm{L}}_{\mathrm{s}}={\mathrm{L}}_{\mathrm{s}\_0}+\u2206{\mathrm{L}}_{\mathrm{s}}$, where subindex 0 represents rated values, and $\u2206{\mathrm{R}}_{\mathrm{s}}$ and $\u2206{\mathrm{L}}_{\mathrm{s}}$ represent changes in stator resistances and inductances, respectively. Moreover, the FDIS is tested for delay variation (T

_{d}) at different speed levels of 100%, 50%, 10%, and 1% without a sensor fault. Maximum speed residual values at steady-state are acquired with each parameter variation and delay length, and are denoted by ${\mathsf{\u0190}}_{\mathrm{r}\_\mathrm{m}\mathrm{a}\mathrm{x}}$.

_{s}and L

_{s}, as shown in Figure 3a,b, respectively. Even in healthy sensor conditions, variations in both parameters have a negligible effect on fault residuals. Therefore, to prevent false fault detection, the threshold level (${\mathsf{\omega}}_{\mathrm{t}\mathrm{h}}$) is set sufficiently high. As shown in Figure 3c, residual sensitivity is low at very low speeds, but as the delay length increases, residual level increases. Instead of setting different thresholds for low and high speeds, the delay length at low speeds is varied for a wide speed range of fault detection. In our case, because T

_{s}= $0.05\mathrm{m}\mathrm{s}$, a delay length of 3 suffices; T

_{d}= 3T

_{s}. Hence, the overall speed threshold for the simulation model is chosen to be ${\mathsf{\omega}}_{\mathrm{t}\mathrm{h}}=0.53$.

_{q}).

## 3. Modeling of Vehicle Dynamics and PMSM

#### 3.1. Modeling of Vehicle Dynamics

#### 3.2. Modeling of PMSM

## 4. Modeling and Designing Position Sensor FTC

_{p}, K

_{i}> 0, and e(τ) = $\left\{\begin{array}{c}{\mathsf{\omega}}_{\mathrm{e}\_\mathrm{r}\mathrm{e}\mathrm{f}}-{\mathsf{\omega}}_{{\mathrm{e}}_{\mathrm{e}\mathrm{s}\mathrm{t}}},\mathrm{i}\mathrm{f}{\mathrm{F}}_{\mathrm{q}}=1\\ {\mathsf{\omega}}_{\mathrm{e}\_\mathrm{r}\mathrm{e}\mathrm{f}}-{\mathsf{\omega}}_{\mathrm{e}},\mathrm{i}\mathrm{f}{\mathrm{F}}_{\mathrm{q}}=0\end{array}\right.$.

_{p}and K

_{i}to reduce the speed tracking error e(τ), and appropriate anti-windup mechanisms are important to ensure that the system can respond effectively to changes without becoming saturated. The observer estimates the position state based on current sensor measurements. Assuming the system is healthy during its initial drive operation, the observer’s finite-time convergence will lead to the post-fault decoupling between the controller and observer which ensures stability of the control system.

#### 4.1. Flux Observer-Based Sensorless Operation

#### 4.2. Sliding Mode Observer-Based Sensorless Operation

## 5. Simulated FTC Performance Evolution for EVs

_{p}= 200, K

_{i}= 100, respectively. The flux observer HPF frequency is set at 5.1863 Hz. The Table 1 and Table 2 list the parameters for the SPMSM and two-wheeler vehicle, respectively.

## 6. FTC Experimental Verification

_{p}= 200, K

_{i}= 100, respectively. The HPF frequency of the flux observer is 3.1 Hz. The controller settings for the speed control loop are K

_{p}= 0.001, K

_{i}= 0.05, and for the current control loop are K

_{p}= 0.87, K

_{i}= 1500. The experimental laboratory prototype setup is shown in Figure 13.

_{v}is mass of the vehicle; ρ

_{a}is the density of air; C

_{d}is the coefficient of drag; and A

_{f}is the frontal area of the vehicle.

_{s}and L

_{s}).

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Maximum residual values under parameter variation. (

**a**) Stator resistance variation at various load levels. (

**b**) Stator inductance variation at various load levels. (

**c**) Delay length variation at various speed levels.

**Figure 9.**Vehicle disturbance profile. (

**a**) Sine road profile with an irregular surface. (

**b**) Uneven road profile with class-D road roughness. (

**c**) Wind speed profile with disturbance.

**Figure 10.**FTC under a sine-wave road profile with disturbance, varying wind speed, and position sensor fault at time = 16 s. (

**a**) Fault residual and its threshold and flag. (

**b**) Speed reference and actual motor speed. (

**c**) Motor speed error. (

**d**) Motor torque. (

**e**) Position traveled.

**Figure 11.**FTC under uneven road profile with class-D roughness, varying wind speed, and position sensor fault at time = 17 s. (

**a**) Fault residual and its threshold and flag. (

**b**) Speed reference and actual motor speed. (

**c**) Motor speed error. (

**d**) Motor torque. (

**e**) Position traveled.

**Figure 14.**Detection of position sensor fault in a constant speed profile, and position sensor fault at time = 0.5 s. (

**a**) Speed residual and its threshold and flag. (

**b**) Actual and reference speeds for flux observer. (

**c**) Actual and reference speeds for sliding mode observer.

**Figure 15.**Detection of position sensor faults in a ramped speed profile, and position sensor fault at time = 2 s. (

**a**) Speed residual and its threshold. (

**b**) Actual and reference speeds for flux observer. (

**c**) Actual and reference speeds for sliding mode observer.

**Figure 16.**Experiments with parameter variations at 600 r.p.m and position sensor fault at time = 0.5 s (a) for flux observer and (b) for sliding mode observer.

Parameter | Value | Parameter | Value |
---|---|---|---|

Flux linkage | 0.016412 V.s | Pole pairs | 4 |

Stator inductance | 0.06995 mH | Stator resistance | 0.85 ohm |

Max motor speed | 6000 r/min | DC link voltage | 48 V |

Peak current | 85 A | Rated torque | 7 Nm |

Power | 3 kW | Peak torque | 25 Nm |

Parameter | Value | Parameter | Value |
---|---|---|---|

Weight (M_{v}) | 120 kg | Frontal area (A_{f}) | 0.86 m^{2} |

Wheel radius (r) | 0.16 m | Air density (ρ_{a}) | 1.2 kg/m^{3} |

Rolling resistance coef. (C_{r}) | 0.01 | Drag coef. (C_{d}) | 0.2 |

Velocity (ν) | 70 Kmph | Gearbox ratio (i_{tr}) | 3.5 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Flux linkage | 0.0409 V/Hz | Pole pairs | 4 |

Stator inductance | 0.1569 mH | Stator resistance | 0.36 ohm |

Max motor speed | 6000 r/min | DC link voltage | 24 V |

Peak current | 7.1 A | Rated torque | 0.2754 Nm |

Parameter | Value | Parameter | Value |
---|---|---|---|

Weight (M_{v}) | 2 kg | Frontal area (A_{f}) | 0.15 m^{2} |

Wheel radius (r) | 0.16 m | Air density (ρ_{a}) | 1.2 kg/m^{3} |

Motor speed (ω_{m}) | from the encoder angle | Drag coef. (C_{d}) | 0.2 |

Velocity (ν) | 70 Kmph | Gearbox ratio (i_{tr}) | 3.5 |

Feature | FO | SMO |
---|---|---|

Complexity of DSP implementation | Lower | Higher |

PI controller needed for position estimation | No | Yes |

DSP execution time | Lower | Higher |

Rotor position error | Low | Low |

Maximum steady-state speed error | Low | Low |

References | Fault Detection Time | Fault Detection Range | Remarks |
---|---|---|---|

[2] | Not specified for the given result | Medium to high speed | The algorithm is dependent on the estimated quantity and fixed threshold |

[8] | Not specified for the given result | Medium to high speed | The algorithm is dependent on the estimated quantity and fixed threshold |

[10] | 2.2 ms | Medium to high speed | The algorithm is dependent on the estimated quantity and adaptive threshold |

[15] | Not specified for the given result | Low to high speed | The algorithm is dependent on the estimated quantity |

[6] | 3 ms | Low to high speed | The algorithm is independent of the estimated quantity and adaptive threshold |

Proposed Scheme | 0.05–0.15 ms | Low to high speed | The algorithm is independent of the estimated quantity and fixed threshold |

References | FTC Technique | FTC Performance | Remarks |
---|---|---|---|

[7] | PI regulator with adaptive EKF as position observer applied to PMSM | No speed undershoot during fault, no speed oscillation after fault, and wide-speed tracking | Complex design and difficult hardware implementation |

[2] | PI regulator with HOSM as position observer applied to PMSM | Speed undershoot during fault, no speed oscillation after fault, and wide-speed tracking | Complex observer gain design and easy hardware implementation |

[15] | PI regulator with BEMF observer with I-F control applied to PMSM | Speed undershoot during fault, small speed oscillation after fault, and wide-speed tracking performance have not been studied | Simple design and easy hardware implementation |

[8] | Torque and hysteresis current controllers with SMO as position observer applied to SRM | Speed undershoot during fault, no speed oscillation after fault, and wide-speed tracking performance have not been studied | Simple design and no practical testing has been carried out |

Proposed Technique | (a) PI regulator with Flux Observer as position observer applied to PMSM | No speed undershoot during fault, small speed oscillation after fault, and wide-speed tracking | Simple design and easy hardware implementation |

(b) PI regulator with SMO-QPLLL as position observer applied to PMSM | No speed undershoot during fault, no speed oscillation after fault, and wide-speed tracking | Simple design and easy hardware implementation |

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**MDPI and ACS Style**

Saha, S.; Kar, U.
Signal-Based Position Sensor Fault Diagnosis Applied to PMSM Drives for Fault-Tolerant Operation in Electric Vehicles. *World Electr. Veh. J.* **2023**, *14*, 123.
https://doi.org/10.3390/wevj14050123

**AMA Style**

Saha S, Kar U.
Signal-Based Position Sensor Fault Diagnosis Applied to PMSM Drives for Fault-Tolerant Operation in Electric Vehicles. *World Electric Vehicle Journal*. 2023; 14(5):123.
https://doi.org/10.3390/wevj14050123

**Chicago/Turabian Style**

Saha, Sankhadip, and Urmila Kar.
2023. "Signal-Based Position Sensor Fault Diagnosis Applied to PMSM Drives for Fault-Tolerant Operation in Electric Vehicles" *World Electric Vehicle Journal* 14, no. 5: 123.
https://doi.org/10.3390/wevj14050123