# Adaptive Nonlinear Control of Salient-Pole PMSM for Hybrid Electric Vehicle Applications: Theory and Experiments

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## Abstract

**:**

## 1. Introduction

_{d}, which may degrade the machine performance. Another adaptive model reference system technique for speed estimation is used in [18] for the sensorless speed control of SP-PMSMs with space-vector pulse-width modulation. The stable and efficient estimation of the rotor speed is guaranteed by the simultaneous identification of the parameters of the SP-PMSM.

^{®}/Simulink

^{®}and experimental tests with a DS 1202 MicroLabBox show that the adaptive controller meets the desired performance requirements.

## 2. SP-PMSM Mathematic Model

- Controlling the signals ${x}_{1}$ and ${x}_{3}$ to their references;
- Estimating the non-measurable parameters of a SP-PMSM, such us $f$ and $J$;
- Estimating the load torque ${C}_{r}$.

## 3. Adaptive Nonlinear Control

#### 3.1. Adaptive Backstepping Design

#### 3.2. Current-Controller Design Technique

#### 3.3. Speed-Controller Design Technique

**Proposition 1.**

- Closed-loop system is GAS;
- Current d-axis regulation is set to zero;
- Perfect tracking of motor speed ${x}_{3}$ is set to its reference;
- Non-measurable parameters of the SP-PMSM such as f and J are estimated;
- Load torque C
_{r}is estimated.

**Proof.**

^{®}/Simulink

^{®}in the next section.

## 4. Numerical Simulation

^{®}/Simulink

^{®}software, the SP-PMSM control-simulation bench is created, as shown in Figure 1.

#### 4.1. Speed Change

_{r}are constants $\left({C}_{r}=5Nm\right)$.

_{q}and ${i}_{d}$. The current i

_{q}comes to confirm our interpretation, because $p.\sqrt{\frac{3}{2}}{\psi}_{sf}.{i}_{q}=f.\Omega +{C}_{r},$ where $p,{\psi}_{sf}$ and ${C}_{r}$ are constants. Hence, a large variation in $\Omega $ generates a small variation in ${i}_{q}$. Therefore, this gap represents the mechanical losses of the SP-PMSM. The current ${i}_{d}$ is always set to zero to remove the effect of the torque ${i}_{d}$ × ${i}_{q}$ in Equation (3).

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- The proposed control guarantees perfect vehicle speed tracking to its reference;
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- The closed-loop system is stable with respect to the variation in the reference speed.

#### 4.2. Inertia Change

_{r}, the friction f and the reference velocity constant.

_{q}remains constant. It depends on the load torque, which means that the variation in SP-PMSM power is almost zero.

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- The perfect tracking of the vehicle speed to its reference;
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- The estimation of inertia J by this controller helps to ensure the stability and robustness of the system;
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- The moment of inertia J depends on the mass but not on the speed.

#### 4.3. Friction Change

_{r}and the reference speed. Thereafter, we will see the effect of friction on the vehicle speed.

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- The perfect tracking of the vehicle speed to its reference;
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- The estimation of friction f by this controller helps to ensure the stability and robustness of the system;
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- The variation in friction due to the aging of the machine or in cases where the maintenance schedule of the machine is not maintained.

#### 4.4. Torque Change

_{r}on the vehicle speed.

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- The perfect tracking of the vehicle speed to its reference;
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- The estimation of C
_{r}by this controller helps to ensure the stability and robustness of the system.

## 5. Experimental Results

^{®}software. The test bench consists essentially of:

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- Three metal hydride canisters from Heliocentris with storage capacities of 800 NL of hydrogen;
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- A Ballard Nexa 1200 fuel-cell module with its monitoring software;
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- A power supply from BK Precision.
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- A MicroLabBox-dSPACE DS1202 with Control Desk
^{®}software plugged into a Pentium 4 personal computer. - -
- A salient-pole permanent-magnet synchronous motor;
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- A DC power supply;
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- A DC/AC converter;
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- A DC/DC converter;
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- A Hall-Effect current sensor;
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- A voltage sensor;
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- A digital scope;
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- A magnetic powder brake;
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- An encoder position sensor;
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- A torque sensor.

#### 5.1. Speed Change

#### 5.2. Torque Change

## 6. Conclusions

_{r}and internal parameters (inertia and friction) of the SP-PMSM. Finally, according to the formal analysis, simulation and experimental results, it is shown that the obtained nonlinear adaptive controller ensures objectives such as:

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- The perfect tracking of the vehicle speed to its reference;
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- The high stability of the closed-loop system;
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- The estimation of non-measurable parameters of the SP-PMSM such as f and J;
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- The estimation of the load torque Cr.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The SP-PMSM and control-system schematic diagram. Where V

_{s}= R x

_{3}: Vehicle Speed (m/s); R = 0.29 m: Radius of the point’s trajectory (m).

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

Stator resistance R_{s} | 0.56 Ω |

Number of pole pairs p | 3 |

Rotation inertia J | 0.0021 kg.m^{2} |

Flux of permanent magnet ψ_{sf} | 0.82 Wb |

Inductance L_{d} | 0.048 H |

Inductance L_{q} | 0.064 H |

Viscous damping f | 0.0001 Nm/rd.s^{−1} |

Rated voltage | 320 V |

Rated power | 2 kW |

Rated speed | 1800 r/mn |

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

Output power | 1200 W |

Output current | max. 55 A |

Nominal voltage | 24 V |

Output voltage | 0–32 V |

Input voltage | 16–45 V |

Operational temperature | −10–55 °C |

Efficiency | >96% |

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

Rated power | 1200 W |

Rated current | 52 A |

Rated voltage | 24 V |

Output voltage | 20–36 V |

Operational temperature | 5–40 °C |

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

Output power | 2016 W |

Output current | max. 42 A |

Output voltage | 48 V |

Input voltage | 24 V |

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

Rated power | 1000 W |

Rated current | 25.7 A |

Rated voltage | 48 V |

Rated speed | 1000 r/min |

Rated torque | 10 N.m |

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

Rated power | 2000 W |

Rated voltage | 48 V |

Continuous current | 60 A |

Peak current | 150 A |

Working frequency | 16.6 kHz |

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

c_{1} | 20 |

c_{2} | 2000 |

c_{3} | 200 |

γ_{1} | 0.003 |

γ_{2} | 0.005 |

γ_{3} | 0.007 |

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**MDPI and ACS Style**

El Fakir, C.; El Idrissi, Z.; Lassioui, A.; Belhaj, F.Z.; Gaouzi, K.; El Fadil, H.; Rachid, A.
Adaptive Nonlinear Control of Salient-Pole PMSM for Hybrid Electric Vehicle Applications: Theory and Experiments. *World Electr. Veh. J.* **2023**, *14*, 30.
https://doi.org/10.3390/wevj14020030

**AMA Style**

El Fakir C, El Idrissi Z, Lassioui A, Belhaj FZ, Gaouzi K, El Fadil H, Rachid A.
Adaptive Nonlinear Control of Salient-Pole PMSM for Hybrid Electric Vehicle Applications: Theory and Experiments. *World Electric Vehicle Journal*. 2023; 14(2):30.
https://doi.org/10.3390/wevj14020030

**Chicago/Turabian Style**

El Fakir, Chaimae, Zakariae El Idrissi, Abdellah Lassioui, Fatima Zahra Belhaj, Khawla Gaouzi, Hassan El Fadil, and Aziz Rachid.
2023. "Adaptive Nonlinear Control of Salient-Pole PMSM for Hybrid Electric Vehicle Applications: Theory and Experiments" *World Electric Vehicle Journal* 14, no. 2: 30.
https://doi.org/10.3390/wevj14020030