# Virtual Sensor Using a Super Twisting Algorithm Based Uniform Robust Exact Differentiator for Electric Vehicles

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## Abstract

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## 1. Introduction

#### 1.1. Electrified Powertrain

- Being unable to meet the road loads in all operating conditions;
- Aging (Reduced life span);
- Inefficient powertrain operations or high power loss.

#### 1.2. Related Work

#### 1.3. Major Contributions

## 2. EV-Based IPMSM Dynamics

#### 2.1. IPMSM Mathematical Modelling

## 3. Virtual Sensor Development Strategy

## 4. Simulation Experiments

#### 4.1. Simulator Design

#### 4.2. Estimating/Sensing of an Immeasurable Parameter

- Case 1:The PM flux linkage is estimated to be $0.33\phantom{\rule{2.84544pt}{0ex}}wb$ at a nominal temperature of 20 ${}^{\circ}$C. There is no change in stator resistance. The settling time remains less than 0.09 s and the convergence error remains close to zero.
- Case 2:As the operating temperature of IPMSM-based electrified powertrain increases to 35 ${}^{\circ}$C, the stator resistance value increases around $5\%$. Therefore, PM flux linkage decreases, and the decrease is estimated to $0.31\phantom{\rule{2.84544pt}{0ex}}wb$. The settling time remains less than 0.09 s, and the convergence error remains close to zero.
- Case 3:With the increase of operating temperature of IPMSM-based electrified powertrain to 50 ${}^{\circ}$C, the stator resistance value increases around $11\%$. The proposed virtual sensor is still able to detect decreased PM flux linkage. The estimated value from the figure can be seen to be $0.30\phantom{\rule{2.84544pt}{0ex}}wb$. The settling time still remains less than 0.09 s and the convergence error remains close to zero.
- Case 4:The stator resistance value increases $17\%$ with the increase of operating temperature of IPMSM-based electrified powertrain to 65 ${}^{\circ}$C. The PM flux linkage decreases, and the decrease is still correctly detected and estimated to be $0.29\phantom{\rule{2.84544pt}{0ex}}wb$. The settling time remains less than 0.09 s, and the convergence error remains close to zero.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

EV | Electric Vehicles |

OEMs | Original Equipment Manufacture |

PMSM | Permanent Magnet Synchronous Motor |

IPMSM | Interior Permanent Magnet Synchronous Motor |

SPMSM | Surface Mounted Permanent Magnet Synchronous Motor |

PM | Permanent Magnet |

SMO | Sliding Mode Observer |

HOSM | Higher Order Sliding Mode Observer |

STA | Super Twisting Algorithm |

URED | Uniform Robust Exact Differentiator |

WLTP | Worldwide harmonized Light vehicle Test Procedures |

${H}_{ci}$, ${B}_{r}$ | Intrinsic Coercivity and Remanence |

${I}_{f}$ | Field Current |

${L}_{s}$, ${L}_{f}$ | Stator and Mutual Inductance |

${L}_{ls}$ | Leakage Inductance |

${L}_{A}$, ${L}_{B}$ | Average value and Variation in value of magnetizing Inductance |

${V}_{ds},{V}_{qs}$ | Stator Voltages in d and q-axis in V |

${\psi}_{ds}$, ${\psi}_{qs}$ | Stator flux in d and q-frame in $Wb$ |

${i}_{ds}$, ${i}_{qs}$ | Stator currents in A |

${R}_{s}$ | Stator Resistance in $\Omega $ |

p | Poles pair |

$\theta $ | Angle between rotating and stationary reference frame |

${\theta}_{r}$ | Rotor position |

${\omega}_{m}$ | Rotor mechanical speed in $rad/s$ |

${L}_{ds}$, ${L}_{qs}$ | Inductances of stator in H |

${\psi}_{PM}$ | Permanent Magnet flux linkage at operating temperature in $Wb$ |

J | Moment of inertia in $kg/{m}^{2}$ |

${\tau}_{L}$ | Load torque in $Nm$ |

B | Viscous damping constant |

$BrT$ | Magnet remanence at operating temperature |

${T}_{0}$, T | Nominal and operating temperature |

${\psi}_{P{M}_{0}}$ | Permanent Magnet flux linkage at nominal temperature in $Wb$ |

A | Area passed by magnetic flux linkage at ${T}_{0}$ and T |

$\delta \left(T\right)$ | Difference between PM flux linkage at operating and nominal temperature |

$\alpha $ | Temperature coefficient of remanence, which is not constant but changes with temperature |

${F}_{r}$,${F}_{t}$ | Rolling and downgrade resistance force |

${F}_{v}$, ${F}_{a}$ | Viscous frictional and Aerodynamics drag force |

${F}_{te}$ | Tractive force |

${G}_{r}$ | Gear ratio |

${w}_{r}$ | Wheel radius |

m | Vehicle mass |

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**Figure 3.**Change of torque with respect to speed at temperature 20 ${}^{\circ}$C and 65 ${}^{\circ}$C.

**Figure 9.**Estimates PM flux linkage in $Wb$ against the reference at a nominal temperature of 20 ${}^{\circ}$C.

**Figure 14.**${\psi}_{PM}$ tracking error in $Wb$ against the reference at a nominal temperature of 20 ${}^{\circ}$C.

Parameters [Units] | Symbol | Value |
---|---|---|

Power [kW] | P | 3 |

Nominal Torque [Nm] | $\tau $ | 20 |

Stator Resistance [$\Omega $] | ${R}_{s}$ | 0.5 |

Inductance in q-axis [H] | ${L}_{q}$ | 0.005 |

Inductance in d-axis [H] | ${L}_{d}$ | 0.0035 |

Flux Linkage [Wb] | ${\psi}_{PM}$ | 0.33 |

Pole pairs | p | 3 |

Inertia [Kgm${}^{2}$] | J | 0.004 |

Viscous Damping | B | 0.0028 |

Vehicle Data | ||

Gear ratio | ${G}_{r}$ | 6 |

Wheel radius [m] | ${w}_{r}$ | 0.3 |

Vehicle mass [kg] | m | 750 |

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**MDPI and ACS Style**

Muazzam, H.; Ishak, M.K.; Hanif, A.; Uppal, A.A.; Bhatti, A.; Isa, N.A.M.
Virtual Sensor Using a Super Twisting Algorithm Based Uniform Robust Exact Differentiator for Electric Vehicles. *Energies* **2022**, *15*, 1773.
https://doi.org/10.3390/en15051773

**AMA Style**

Muazzam H, Ishak MK, Hanif A, Uppal AA, Bhatti A, Isa NAM.
Virtual Sensor Using a Super Twisting Algorithm Based Uniform Robust Exact Differentiator for Electric Vehicles. *Energies*. 2022; 15(5):1773.
https://doi.org/10.3390/en15051773

**Chicago/Turabian Style**

Muazzam, Hassam, Mohamad Khairi Ishak, Athar Hanif, Ali Arshad Uppal, AI Bhatti, and Nor Ashidi Mat Isa.
2022. "Virtual Sensor Using a Super Twisting Algorithm Based Uniform Robust Exact Differentiator for Electric Vehicles" *Energies* 15, no. 5: 1773.
https://doi.org/10.3390/en15051773