# Different Control Techniques of Permanent Magnet Synchronous Motor with Fuzzy Logic for Electric Vehicles: Analysis, Modelling, and Comparison

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## Abstract

**:**

## 1. Introduction

_{2}emissions, sulfur oxides, and nitrogen oxides. Policies aim to reach carbon neutrality in this sector by 2050 as part of the ecological and energy transition [1]. Fuel cell electric vehicles (FCEVs), battery electric vehicles (BEVs), and hybrid electric vehicles (HEVs) are considered key solutions to current environmental problems. BEVs are purely electric vehicles powered solely by batteries; they offer many advantages, such as zero emissions, optimal performances, independence from oil, and a quiet and smooth operation with little environmental noise [2,3]. The automotive industry and the scientific community attach great importance to the development of electric vehicles (EVs), focusing on key aspects of their performances. Ongoing research aims to improve the energy source of EVs, their structure, and their electrical drive system, which is a major area of interest for automotive manufacturers and researchers. The propulsion system of an EV consists mainly of an electric motor, a controller, a battery stack, and power converters. To ensure the propulsion of EVs, there are several types of electric motors, such as direct current (DC) motors, induction motors (IM), variable reluctance motors (VRM), and permanent magnet synchronous motors (PMSM) [4,5].

## 2. System Configuration and Modeling

#### 2.1. Mathematical Model of the Electric Vehicle

_{roll}), aerodynamic drag force (F

_{aero}), slope force (F

_{slope}), and acceleration force (F

_{acc}), as depicted in Figure 2. The total traction force (F

_{t}) that is necessary to drive the vehicle can be expressed as follows [32,33]:

#### 2.1.1. Rolling Resistance Force

_{ro}are the vehicle total mass, the gravity acceleration and the coefficients of rolling resistance, respectively.

#### 2.1.2. Aerodynamic Drag

#### 2.1.3. Slope Force

#### 2.1.4. Acceleration Force

_{m}is the rotational inertia coefficient, γ is the vehicle acceleration.

_{t}) is the sum of all these forces and can be given by:

#### 2.2. Voltage Source Inverter Model

_{dc}) and the switching signals define the output phase voltages of VSI, as expressed in Equation (9) [34,35].

#### 2.3. Permanent Magnet Synchronous Motor Model

#### 2.4. Battery Model

## 3. Control Topologies

#### 3.1. Direct Torque Control (DTC)

_{ϕs}and H

_{Te}denote the output signals of the stator flux and electromagnetic torque hysteresis comparators, respectively, and N

_{i}and V

_{i}represent the ith sector and the voltage vector. After selecting the optimal voltage vector, it is applied to the 2L-VSI to minimize the flux and torque errors. The stator flux can be estimated as given in [11,39]:

#### 3.2. Fuzzy Direct Torque Control (FDTC)

#### 3.2.1. Fuzzification

**For torque error**. The torque error ($e{T}_{e}$) can be classified into three linguistic variables: “Negative” (N), “Zero” (Z) and “Positive” (P). These variables are inspired by the behavior of a three-level hysteresis comparator. As illustrated in Figure 7a, the variable Z is represented by a triangular MF, while L and H are represented by trapezoidal MFs.**For stator flux error**. The stator flux error ($e{\varphi}_{s}$) can be classified into two linguistic variables “Negative” (N) and “Positive” (P) inspired from the behavior of the two-level hysteresis comparator. As shown in Figure 7b, the L and H variables are represented by two trapezoidal MFs.**For stator flux angle**. The stator flux angle (${\theta}_{s}$) can be divided into six linguistic variables (${\theta}_{1}$ to ${\theta}_{6}$) inspired by the six sectors of the sector selector. As shown in Figure 7c, the six variables are represented by isosceles triangular MFs.

#### 3.2.2. Fuzzy Control Rules

#### 3.2.3. Defuzzification

_{i}(i: 0,…7) at the output of FLC is converted into switching signals (S

_{a}, S

_{b}, S

_{c}) using the Boolean expression (0 or 1) given by [10]. The resulting fuzzy direct torque control scheme for PMSM in EV systems is presented in Figure 8, and the surfaces of the fuzzy logic controller are shown in Figure 9.

#### 3.3. Model Predictive Direct Torque Control (MPDTC)

#### 3.3.1. Current, Flux and Torque Predictions

#### 3.3.2. Cost Function Minimization

#### 3.3.3. Time Delay Compensation

#### 3.4. Fuzzy Logic Speed Control

_{e}*), as illustrated in Figure 12. Scaling factors are utilized at the input and output of the FLC to adjust its sensitivity while maintaining its structure [43,44]. The speed error (e) and its derivative (de) are normalized before being fed into the FLC, and are expressed as follows:

## 4. Simulation Results and Discussion

#### 4.1. Comparison between Different Control Techniques

^{−4}km/h, which is lower than that of the conventional DTC, which is about 2.2 × 10

^{−4}km/h, and that of the FDTC, which is about 1.1 × 10

^{−4}km/h, presenting an improvement of 77.27% and 50.54% compared to the DTC and FDTC techniques, respectively. In short, these results show that the MPDTC technique offers better speed control performance for the electric vehicle during the NYCC cycle.

#### 4.2. Dynamic Performance of the Battery for DTC, FDTC and MPDTC

## 5. Real-Time Platform Using RT-LAB

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Mamdani-type membership functions (

**a**) stator flux error input; (

**b**) electromagnetic torque error input; (

**c**) stator flux angle input; (

**d**) stator voltage vectors output.

**Figure 9.**Fuzzy logic controller surfaces (

**a**) stator flux angle, torque error, and voltage vectors; (

**b**) stator flux angle, stator flux error, and voltage vectors; (

**c**) stator flux error, torque error, and voltage vectors.

**Figure 13.**Membership functions for (

**a**) speed error; (

**b**) derivative speed error; (

**c**) reference torque.

**Figure 15.**Electromagnetic torque of the PMSM under different control techniques with NYCC driving cycle.

**Figure 16.**Stator flux responses of the PMSM under different control techniques with NYCC driving cycle.

**Figure 18.**Performance evolution of the different techniques at various speed values (

**a**) Torque ripples; (

**b**) Flux ripples; (

**c**) Speed ripples.

**Figure 21.**Li-ion battery performance with DTC technique (

**a**) voltage; (

**b**) current; (

**c**) state of charge, and covered distance.

**Figure 22.**Li-ion battery performance with FDTC technique (

**a**) voltage; (

**b**) current; (

**c**) state of charge, and covered distance.

**Figure 23.**Li-ion battery performance with MPDTC technique (

**a**) voltage; (

**b**) current; (

**c**) state of charge and covered distance.

**Figure 26.**Steady-state analysis at low speed with different techniques (

**a**) DTC; (

**b**) FDTC; (

**c**) MPDTC.

Parameters | Values | Units |
---|---|---|

Vehicle total mass $\left(m\right)$ | 1325 | kg |

Air density (${\rho}_{air}$) | 1.20 | kg/m² |

Frontal area (${A}_{f}$) | 2.57 | m² |

Tire radius (r) | 0.30 | m |

Drag coefficient (${C}_{d}$) | 0.30 | - |

Gear ratio (G) | 5.20 | - |

$({\mathit{S}}_{\mathit{a}}$$,{\mathit{S}}_{\mathit{b}}$$,{\mathit{S}}_{\mathit{c}})$ | Voltage Vectors V | $({\mathit{S}}_{\mathit{a}}$$,{\mathit{S}}_{\mathit{b}}$$,{\mathit{S}}_{\mathit{c}})$ | Voltage Vectors V |
---|---|---|---|

(0, 0, 0) | ${V}_{0}=0$ | (0, 1, 1) | ${V}_{4}=-\frac{2}{3}{V}_{dc}$ |

(1, 0, 0) | ${V}_{1}=\frac{2}{3}{V}_{dc}$ | (0, 0, 1) | ${V}_{5}=-\frac{1}{3}{V}_{dc}-j\frac{\sqrt{3}}{3}{V}_{dc}$ |

(1, 1, 0) | ${V}_{2}=\frac{1}{3}{V}_{dc}+j\frac{\sqrt{3}}{3}{V}_{dc}$ | (1, 0, 1) | ${V}_{6}=\frac{1}{3}{V}_{dc}-j\frac{\sqrt{3}}{3}{V}_{dc}$ |

(0, 1, 0) | ${V}_{3}=-\frac{1}{3}{V}_{dc}+j\frac{\sqrt{3}}{3}{V}_{dc}$ | (1, 1, 1) | ${V}_{7}=0$ |

Parameters | Values | Units |
---|---|---|

Rated power (${P}_{r}$) | 50 | kW |

Stator resistance (${R}_{s}$) | 6.5 | mΩ |

Stator inductance (${L}_{sd}$, ${L}_{sq}$) | 8.35 | mH |

PM magnet flux (${\varphi}_{f}$) | 0.1757 | Wb |

Number of pole pairs (p) | 4 | - |

Motor inertia (J) | 0.089 | kg.m² |

Viscous damping (f) | 0.005 | N.s/m |

H_{Te} | H_{ϕS} | Sector N | |||||
---|---|---|---|---|---|---|---|

N_{1} | N_{2} | N_{3} | N_{4} | N_{5} | N_{6} | ||

1 | 1 | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} | V_{2} |

0 | V_{2} | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} | |

0 | 1 | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} |

0 | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | |

−1 | 1 | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} | V_{5} |

0 | V_{5} | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} |

eT_{e} | eϕ_{S} | Angle θ | |||||
---|---|---|---|---|---|---|---|

θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{5} | θ_{6} | ||

P | P | V_{2} | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} |

N | V_{3} | V_{4} | V_{5} | V_{6} | V_{1} | V_{2} | |

Z | P | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} |

N | V_{0} | V_{7} | V_{0} | V_{7} | V_{0} | V_{7} | |

N | P | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} | V_{5} |

N | V_{5} | V_{6} | V_{1} | V_{2} | V_{3} | V_{4} |

de | e | |||||||

NB | NM | NS | ZE | PS | PM | PB | ||

NB | NB | NB | NB | NB | NM | NS | EZ | |

NM | NB | NB | NB | NM | NS | EZ | PS | |

NS | NB | NB | NM | NS | EZ | PS | PM | |

ZE | NB | NM | NS | EZ | PS | PM | PB | |

PS | NM | NS | EZ | PS | PM | PB | PB | |

PM | NS | EZ | PS | V_{5} | PB | PB | PB | |

PB | EZ | PS | PM | PB | PB | PB | PB |

**Table 7.**Performances of the different control techniques in terms of torque ripples, flux ripples, speed ripples and THD.

Performances | DTC | FDTC | MPDTC | Improvement (%) MPDTC Compared to FDTC | Improvement (%) MPDTC Compared to DTC |
---|---|---|---|---|---|

Torque ripples (N.m) | 2.40 | 1.90 | 0.65 | 65.78 | 72.92 |

Flux ripples (Wb) | 0.004 | 0.002 | 0.001 | 50 | 75.00 |

Speed ripples (km/h) | 0.00022 | 0.00011 | 0.00005 | 50.54 | 77.27 |

THD (%) | 6.64 | 5.28 | 3.37 | 36.17 | 49.24 |

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## Share and Cite

**MDPI and ACS Style**

Kakouche, K.; Oubelaid, A.; Mezani, S.; Rekioua, D.; Rekioua, T. Different Control Techniques of Permanent Magnet Synchronous Motor with Fuzzy Logic for Electric Vehicles: Analysis, Modelling, and Comparison. *Energies* **2023**, *16*, 3116.
https://doi.org/10.3390/en16073116

**AMA Style**

Kakouche K, Oubelaid A, Mezani S, Rekioua D, Rekioua T. Different Control Techniques of Permanent Magnet Synchronous Motor with Fuzzy Logic for Electric Vehicles: Analysis, Modelling, and Comparison. *Energies*. 2023; 16(7):3116.
https://doi.org/10.3390/en16073116

**Chicago/Turabian Style**

Kakouche, Khoudir, Adel Oubelaid, Smail Mezani, Djamila Rekioua, and Toufik Rekioua. 2023. "Different Control Techniques of Permanent Magnet Synchronous Motor with Fuzzy Logic for Electric Vehicles: Analysis, Modelling, and Comparison" *Energies* 16, no. 7: 3116.
https://doi.org/10.3390/en16073116