# Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table

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## Abstract

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## 1. Introduction

- The high torque and flux ripples are minimized by replacing the conventional switching table with an intelligent one based on the ANN algorithm. The number of ripples in the flux, current, and torque can then be reduced.
- After the ripple’s reduction, the robustness and stability are addressed.
- Since the number of sectors is the most influential factor to overcome disturbance and system uncertainties, the number of sectors was increased from six to twelve, and a fuzzy logic speed controller was inserted.
- Eventually, a fast dynamic decoupled control that robustly responds to external disturbances and system uncertainties can be achieved.

## 2. Induction Motor State Space Mathematical Model

## 3. Direct Torque Control Basis

#### 3.1. Stator Flux and Torque Estimation

#### 3.2. Switching State Vector

## 4. Twelve-Sector DTC Algorithm

## 5. Fuzzy Logic Control for Speed Loop Regulation

#### 5.1. Fuzzification

#### 5.2. Knowledge Base and Inference Engine

#### 5.3. Defuzzification

## 6. Artificial Neural Network Switching Table for DTC Performance Improvement

#### 6.1. Artificial Neural Network Structure

#### 6.2. Artificial Neural Network Architecture

#### 6.3. The Proposed ANN Switching Table Architecture

## 7. Results and Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Power | 3 kW |

Mechanical speed | 1440 rpm |

Pole pairs number | 2 |

Frequency | 50 Hz |

Rated voltage | 220/380 V |

Rated current | 12.5/7.2 A |

Resistance of stator | 2.20 $\mathsf{\Omega}$ |

Resistance of rotor | 2.680 $\mathsf{\Omega}$ |

Inductance of stator | 0.2290 H |

Inductance of rotor | 0.2290 H |

Mutual inductance | 0.2170 H |

Moment of inertia | 0.0470 kg·m^{2} |

Coefficient of viscous friction | 0.0040 N·s/rad |

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**Figure 2.**Start-up and steady-state of the induction motor. (

**a**) Start-up: mechanical speed; (

**b**) start-up: electromagnetic torque.

**Figure 8.**Improvement of DTC performance: start-up and steady-state with load application. (

**a**) Basic DTC: mechanical speed, (

**b**) proposed DTC: mechanical speed, (

**c**) basic DTC: electromagnetic torque, (

**d**) proposed DTC: electromagnetic torque, (

**e**) basic DTC: stator flux linkage, (

**f**) proposed DTC: stator flux linkage, (

**g**) basic DTC: current of stator phase, (

**h**) proposed DTC: current of stator phase, (

**i**) basic DTC: circular trajectory of stator flux, (

**j**) proposed DTC: circular trajectory of stator flux, and (

**k**) basic DTC: sector selection, (

**l**) proposed DTC: sector selection.

**Figure 9.**THD improvement of electromagnetic torque, stator flux linkage, and stator phase current. (

**a**) Basic DTC: electromagnetic torque THD, (

**b**) proposed DTC: electromagnetic torque THD, (

**c**) basic DTC: flux of stator THD, (

**d**) proposed DTC: flux of stator THD, (

**e**) basic DTC: phase current THD, and (

**f**) proposed DTC: phase current THD.

$\mathsf{\Delta}{\mathit{\varphi}}_{\mathit{s}}$ | $\mathsf{\Delta}{\mathit{T}}_{\mathit{e}}$ | ${\mathit{S}}_{1}$ | ${\mathit{S}}_{2}$ | ${\mathit{S}}_{3}$ | ${\mathit{S}}_{4}$ | ${\mathit{S}}_{5}$ | ${\mathit{S}}_{6}$ |
---|---|---|---|---|---|---|---|

1 | 110 | 010 | 011 | 001 | 101 | 100 | |

1 | 0 | 111 | 000 | 111 | 000 | 111 | 000 |

−1 | 101 | 100 | 110 | 010 | 011 | 001 | |

1 | 010 | 011 | 001 | 101 | 100 | 110 | |

0 | 0 | 000 | 111 | 000 | 111 | 000 | 111 |

−1 | 001 | 101 | 100 | 110 | 010 | 011 |

$\mathsf{\Delta}{\mathit{\varphi}}_{\mathit{s}}$ | $\mathsf{\Delta}{\mathit{T}}_{\mathit{e}}$ | ${\mathit{S}}_{1}$ | ${\mathit{S}}_{2}$ | ${\mathit{S}}_{3}$ | ${\mathit{S}}_{4}$ | ${\mathit{S}}_{5}$ | ${\mathit{S}}_{6}$ | ${\mathit{S}}_{7}$ | ${\mathit{S}}_{8}$ | ${\mathit{S}}_{9}$ | ${\mathit{S}}_{10}$ | ${\mathit{S}}_{11}$ | ${\mathit{S}}_{12}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2 | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | |

1 | 1 | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ |

−1 | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | |

−2 | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | |

2 | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | |

0 | 1 | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ |

−1 | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | |

−2 | ${\overrightarrow{V}}_{5}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{6}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{1}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{2}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{3}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{4}$ | ${\overrightarrow{V}}_{5}$ |

${\mathit{\epsilon}}_{\mathit{\omega}}$ | NB | NM | NS | Z | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|

$\mathsf{\Delta}{\mathit{\epsilon}}_{\mathit{\omega}}$ | ||||||||

PB | Z | PS | PM | PB | PB | PB | PB | |

PM | NS | Z | PS | PM | PB | PB | PB | |

PS | NM | NS | Z | PS | PM | PB | PB | |

Z | NB | NM | NS | Z | PS | PM | PB | |

NS | NB | NB | NM | NS | Z | PS | PM | |

NM | NB | NB | NB | NM | NS | Z | PS | |

NB | NB | NB | NB | NB | NM | NS | Z |

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## Share and Cite

**MDPI and ACS Style**

Fahassa, C.; Zahraoui, Y.; Akherraz, M.; Kharrich, M.; Elattar, E.E.; Kamel, S.
Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table. *Mathematics* **2022**, *10*, 1357.
https://doi.org/10.3390/math10091357

**AMA Style**

Fahassa C, Zahraoui Y, Akherraz M, Kharrich M, Elattar EE, Kamel S.
Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table. *Mathematics*. 2022; 10(9):1357.
https://doi.org/10.3390/math10091357

**Chicago/Turabian Style**

Fahassa, Chaymae, Yassine Zahraoui, Mohammed Akherraz, Mohammed Kharrich, Ehab E. Elattar, and Salah Kamel.
2022. "Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table" *Mathematics* 10, no. 9: 1357.
https://doi.org/10.3390/math10091357