# Application of Active Disturbance Rejection in a Bearingless Machine with Split-Winding

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## Abstract

**:**

## 1. Introduction

## 2. Split-Winding Bearingless Motor

#### Operation Principle

## 3. ADRC Control

## 4. Description of the System

#### 4.1. System Overview

#### 4.2. Split-Winding Bearingless Machine

#### 4.3. DSP TMS320F28335

#### 4.4. Control Algorithm Implementation

## 5. Experimental Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BIM | Bearingless Induction Machine |

ADRC | Active Disturbance Rejection Control |

LADRC | Linear Active Disturbance Rejection Control |

ESO | Extended State Observer |

LESO | Linear Extended State Observer |

NESO | Nonlinear Extended State Observer |

TD | Tracking Differentiator |

DSP | Digital Signal Processing |

PID | Proportional-Integral-Derivative |

PD | Proportional-Derivative |

PI | Proportional-Integral |

PWM | Pulse Width Modulation |

DC | Direct Current |

VSI | Voltage Source Inverter |

## References

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**Figure 1.**Spatial arrangement of the stator windings of a bearingless induction motor with split winding.

**Figure 4.**Stator of the bearingless induction motor with split-winding subjected to right-side radial force.

**Figure 14.**Steady state response of radial position control for the linear and nonlinear controllers in 3D. (

**a**) Linear ADRC. (

**b**) Nonlinear ADRC.

**Figure 15.**Response of radial position control under step setpoint changes for Linear ADRC. (

**a**) X-axis behavior with step setpoint changes applied. (

**b**) Y-axis behavior with step setpoint changes applied to X-axis. (

**c**) X-axis behavior with step setpoint changes applied to Y-axis. (

**d**) Y-axis behavior with step setpoint changes applied.

**Figure 16.**Response of radial position control under step setpoint changes for Nonlinear ADRC. (

**a**) X-axis behavior with step setpoint changes applied. (

**b**) Y-axis behavior with step setpoint changes applied to X-axis. (

**c**) X-axis behavior with step setpoint changes applied to Y-axis. (

**d**) Y-axis behavior with step setpoint changes applied.

**Figure 18.**Estimated states behavior for linear ADRC under radial load application. (

**a**) Linear ADRC—X-axis states. (

**b**) Linear ADRC—Y-axis states.

**Figure 19.**Estimated states behavior for nonlinear ADRC under radial load application. (

**a**) Nonlinear ADRC—X-axis states. (

**b**) Nonlinear ADRC—Y-axis states.

**Figure 20.**Generalized disturbance estimation and mean steady state error for X and Y axes to different values of radial load aligned with the X-axis. (

**a**) Generalized disturbance estimation (${z}_{3}$). (

**b**) Mean absolute error for X and Y axes.

**Figure 21.**Generalized disturbance estimation and mean steady state error for X and Y axes to different values of radial load aligned with the Y-axis. (

**a**) Generalized disturbance estimation (${z}_{3}$). (

**b**) Mean absolute error for X and Y axes.

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

Frequency | 60 Hz |

Poles number | 4 |

Supply voltage | $220/380$ V |

Current | $3.02/1.75$ A |

No-load current | $1.9$ A |

No-load power | 160 W |

Stator resistance per phase | $0.63$ Ohm |

**Table 2.**Mean values of the states estimated by the linear and nonlinear ESO before and after the radial load application.

Controller | State ${\mathit{z}}_{1}$ | State ${\mathit{z}}_{2}$ | State ${\mathit{z}}_{3}$ | |||
---|---|---|---|---|---|---|

Load Application | Before | After | Before | After | Before | After |

Linear ESO | $0.57$ | $0.64$ | $-0.32$ | $-0.33$ | $1.64$ | $-7$ |

Nonlinear ESO | $0.48$ | $0.48$ | $-1.34$ | $-2.6$ | $-1522$ | $-7909$ |

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## Share and Cite

**MDPI and ACS Style**

Teixeira, R.d.A.; da Silva, W.L.A.; Amaral, A.E.S.; Rodrigues, W.M.; Salazar, A.O.; Villarreal, E.R.L.
Application of Active Disturbance Rejection in a Bearingless Machine with Split-Winding. *Energies* **2023**, *16*, 3100.
https://doi.org/10.3390/en16073100

**AMA Style**

Teixeira RdA, da Silva WLA, Amaral AES, Rodrigues WM, Salazar AO, Villarreal ERL.
Application of Active Disturbance Rejection in a Bearingless Machine with Split-Winding. *Energies*. 2023; 16(7):3100.
https://doi.org/10.3390/en16073100

**Chicago/Turabian Style**

Teixeira, Rodrigo de Andrade, Werbet Luiz Almeida da Silva, Adson Emanuel Santos Amaral, Walter Martins Rodrigues, Andrés Ortiz Salazar, and Elmer Rolando Llanos Villarreal.
2023. "Application of Active Disturbance Rejection in a Bearingless Machine with Split-Winding" *Energies* 16, no. 7: 3100.
https://doi.org/10.3390/en16073100