# Low-Cost Implementation of an Adaptive Neural Network Controller for a Drive with an Elastic Shaft

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Plant and the Controller

**x**—the input vector, ${\mu}_{j}$—the center vector of the j-th neuron, $\left|\right|\xb7\left|\right|$—euclidean distance, ${\sigma}_{j}$—the width of the activation function. The output of the RBF neural network can then be calculated as:

## 3. Simulation Results

## 4. Low-Cost Implementation of the Control Algorithm

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DAC | Digital-to-Analog Converter |

DSP | Digital Signal Processor |

e | error signal |

FPGA | Field Programmable Gate Array |

GPIO | General-Purpose Input/Output |

HMI | Human–Machine Interface |

HIL | Hardware-in-the-Loop |

${m}_{e}$ | electromagnetic torque |

${m}_{L}$ | load torque |

${m}_{s}$ | torsional torque |

ppr | pulses per revolution |

p.u. | per unit |

PWM | Pulse Width Modulation |

RBF | Radial Basis Function |

RBFNN | Radial Basis Function Neural Network |

rpm | revolutions per minute |

${T}_{1}$ | time constant of the motor machine |

${T}_{2}$ | time constant of the load machine |

${T}_{c}$ | time constant of the shaft |

${T}_{mod}$ | reference speed time constant |

w | weights of a neural network |

$\gamma $ | learning rate of center and widths of neurons |

$\xi $ | damping coefficient |

$\eta $ | learning rate of weights of the neural network |

$\mu $ | center of the neuron |

$\sigma $ | width of the neuron |

${\omega}_{0}$ | resonant frequency of the system |

${\omega}_{1}$ | speed of the motor |

${\omega}_{2}$ | speed of the load |

${\omega}_{refm}$ | model reference speed |

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**Figure 2.**The control structure with the adaptive RBFNN speed controller applied to the two-mass drive.

**Figure 4.**Operation of the drive under nominal conditions—electromagnetic (${m}_{e}$) and torsional (${m}_{s}$) torques.

**Figure 5.**Operation of the drive with an increase in the inertia of the load machine (${T}_{2}=2{T}_{2n}$) (

**a**), with a zoom (

**b**).

**Figure 6.**Change in the adaptive parameters of the RBF neural network: weights (

**a**), centers (

**b**), widths (

**c**).

**Figure 7.**Impact of initial weights randomization: complete simulation (

**a**), initial part of the simulations (

**b**).

**Figure 8.**Influence of initial widths randomization (of radial activation functions) (

**a**), close-up of the beginning of the simulation (

**b**).

**Figure 9.**Effect of initial centers randomization (of radial activation functions) (

**a**), close-up for the beginning of the simulation (

**b**).

**Figure 10.**Different values of weight-related learning rate $\eta $ (

**a**), zoom of a selected part of simulation (

**b**).

**Figure 11.**Impact of the center-width-related learning rate $\gamma $ (

**a**), zoom of a selected part of simulation (

**b**).

**Figure 12.**Comparison of the load speed for different reference signal filters (

**a**), zoom of the selected part of simulation (

**b**).

**Figure 16.**Rotational speed of the load machine achieved with the proposed control structure—experimental results.

Parameter | Discovery Board | dSpace DS1103 |
---|---|---|

Microprocessor | Single-core CortexM4F @ 168 MHz | Single-core PowerPC 750GX @ 1 GHz |

RAM size | 192 kB | 32 MB |

Analog-to-Digital converter | 3 × 12 bit | 16 × 16 bit |

Digital-to-Analog converter | 2 × 12 bit | 8 × 16 bit |

Serial port | 4 × UART | 1 × UART |

GPIO ports | 75 | 32 |

Timers | 12 × 16 bit + 2 × 32 bit | 2 × 32 bit + 1 × 64 bit |

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**MDPI and ACS Style**

Malarczyk, M.; Zychlewicz, M.; Stanislawski, R.; Kaminski, M.
Low-Cost Implementation of an Adaptive Neural Network Controller for a Drive with an Elastic Shaft. *Signals* **2023**, *4*, 56-72.
https://doi.org/10.3390/signals4010003

**AMA Style**

Malarczyk M, Zychlewicz M, Stanislawski R, Kaminski M.
Low-Cost Implementation of an Adaptive Neural Network Controller for a Drive with an Elastic Shaft. *Signals*. 2023; 4(1):56-72.
https://doi.org/10.3390/signals4010003

**Chicago/Turabian Style**

Malarczyk, Mateusz, Mateusz Zychlewicz, Radoslaw Stanislawski, and Marcin Kaminski.
2023. "Low-Cost Implementation of an Adaptive Neural Network Controller for a Drive with an Elastic Shaft" *Signals* 4, no. 1: 56-72.
https://doi.org/10.3390/signals4010003