# Brain Emotional Learning Control Based on Radial Basis Function for Permanent Magnet Synchronous Motor

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Vector Control System for PMSM

_{r}and the actual speed n is used as the input of the speed PI regulator. The currents i

_{d}and i

_{q}of the dq axis are obtained by coordinate transformation of the collected three-phase currents i

_{a}, i

_{b}, and i

_{c}. Set i

_{d}* to zero and subtract i

_{d}as the input to the current regulator 2. The output of the speed PI regulator is i

_{q}* and its difference from i

_{q}is added to the current regulator 1. The outputs u

_{d}and u

_{q}of the two current regulators are converted by coordinates as inputs to the SVPWM generator to generate six drive signals that control the inverter to provide drive voltage to the PMSM. For such a closed-loop control system, when the speed fluctuates, the control signal will also change so that the speed is stable near the given value.

_{d}, u

_{q}, i

_{d}, i

_{q}, L

_{d}, and L

_{q}are, respectively, the stator voltage, inductance, and current of the dq axis, R is the stator resistance, ${\omega}_{\mathrm{e}}$ is the rotor electrical angle, and ${\psi}_{f}$ is the flux linkage of the PMSM.

## 3. Improved Brain Emotional Learning Control

#### 3.1. Conventional BELC

_{r}, the feedback speed as n, and the input error of brain emotional learning control as e = n

_{r}− n.

_{1}, k

_{2}, k

_{3}, k

_{4}, and k

_{5}are adjustable coefficients.

_{i}are the weights of node A

_{i}.

_{i}of each node in real time when the output is less than the emotional implication signal and keep the same when the output is greater than the emotional implication signal.

_{i}is the weight of each node in the orbital cortex.

_{i}are

#### 3.2. RBF-Based Brain Emotional Learning Control

_{j}is the Gaussian kernel function

**C**indicates the center vector of the j-th network node while b

_{j}_{j}denotes the node width

_{m}(k) is the predictive value of the identifier output of the RBF neural network.

**W**of the RBF neural network, the center vector

**C**, and the basis width vector

_{j}**B**are updated using the gradient descent method. The weights

**W**are updated as follows

**B**is updated as

**C**is updated as follows

_{j}_{3}, k

_{4}, and k

_{5}are adjusted online according to the sensitivity calculated by the RBF neural network.

_{i}and signal REW are obtained. The SI

_{i}and REW signals are acquired following the adjustment of the sensory input and emotional implication functions. Subsequently, these signals undergo supervised learning in accordance with (4)–(10). Finally, the output of the RBF-based BELC controller is obtained as E. The RBF neural network serves the purpose of parameter optimization for the coefficients of the emotional implication functions k

_{3}, k

_{4}, and k

_{5}. In the RBF-based BELC control, the RBF neural network is constructed following (11)–(19), with its inputs being (20)–(22). Additionally, Equations (24) and (25) are used for online tuning of the coefficients of the emotional implication functions k

_{3}, k

_{4}, and k

_{5}, resulting in the optimal output of the RBF-based BELC controller. The aim of this is to improve the control of the PMSM speed by the RBF-based BELC controller.

## 4. Simulation Verification

## 5. Experimental Verification

#### 5.1. Experimental Setup

#### 5.2. Comparative Performance Test of Speed Control

#### 5.3. Comparative Performance Test of Torque Control

#### 5.4. Comparative Performance Test of Current Control

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Comparison of current under three control strategies: (

**a**) PI, (

**b**) BELC, (

**c**) RBF-based BELC.

Parameters | Unit | Numerical Value |
---|---|---|

Power rating | kW | 1.5 |

Rated speed | rpm | 1500 |

Rated current | A | 10 |

Polar logarithm | - | 4 |

Rotational inertia | kg·m^{2} | 0.00194 |

Rated torque | N·m | 10 |

Stator resistance | Ω | 1.29 |

d-axis inductance | mH | 2.53 |

q-axis inductance | mH | 2.53 |

Indexes | RBF-Based BELC | BELC | PI |
---|---|---|---|

Time of speed reaching stability (ms) | 8.2 | 18 | 22 |

Maximum speed error after stabilization (rpm) | 0.1 | 0.1 | 0.5 |

Speed overshoot (%) | 0 | 2.125 | 6.875 |

Speed drop after sudden loading (rpm) | 6 | 8 | 19 |

Speed recovery time after sudden loading (ms) | 7.1 | 9.3 | 8.6 |

Parameters | RBF-Based BELC | BELC | PI |
---|---|---|---|

Speed overshoot at start-up (%) | 2.75 | 7.25 | 19.25 |

Speed drop of sudden loading (%) | 1.75 | 2.5 | 4 |

Speed rise of abrupt no-load (%) | 2.5 | 6.5 | 10.25 |

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**MDPI and ACS Style**

Li, W.; Li, B.; Liang, S.; Xiao, H.
Brain Emotional Learning Control Based on Radial Basis Function for Permanent Magnet Synchronous Motor. *Electronics* **2023**, *12*, 4748.
https://doi.org/10.3390/electronics12234748

**AMA Style**

Li W, Li B, Liang S, Xiao H.
Brain Emotional Learning Control Based on Radial Basis Function for Permanent Magnet Synchronous Motor. *Electronics*. 2023; 12(23):4748.
https://doi.org/10.3390/electronics12234748

**Chicago/Turabian Style**

Li, Wenjuan, Boyang Li, Shuwei Liang, and Han Xiao.
2023. "Brain Emotional Learning Control Based on Radial Basis Function for Permanent Magnet Synchronous Motor" *Electronics* 12, no. 23: 4748.
https://doi.org/10.3390/electronics12234748