# A New Flux Linkage Estimation with Drift Cancellation Technique for Switched Reluctance Machines

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## Abstract

**:**

## 1. Introduction

## 2. Switched Reluctance Machine Modeling and Principles

## 3. Integration Drift

#### 3.1. Proposed Solution for the Drift Problem

#### 3.1.1. Resettable Integrator

#### 3.1.2. Low-Pass Filters

## 4. Proposed Drift Cancellation Method

#### Implementation Algorithm

## 5. Experimental Evaluation of the Proposed Algorithm

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SRM | Switched reluctance machines |

DTC | Direct torque control |

LMS | Least mean squares |

LPF | Low-pass filter |

HPF | High-pass filter |

PMSM | Permanent magnet synchronous machine |

IPMSM | Interior permanent magnet synchronous machine |

EKF | Extended Kalman Filter |

DAC | Digital–analog converter |

DCM | Direct current Motor |

HMI | Human–machine interface |

MAE | Mean absolute error |

MSE | Mean squared error |

${R}^{2}$ | R-squared factor |

RMSE | Root mean square error |

SSE | Sum of squared errors |

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**Figure 1.**Equivalent phase circuit of a switched reluctance machine (SRM) disregarding magnetic coupling and considering constant phase resistance.

**Figure 3.**Simulated sensed phase currents, voltages, and estimated flux linkages of a three-phase SRM with noise and calibration offset addition.

**Figure 5.**(

**a**) Simulation results of flux linkage estimation using low-pass filters (LPFs) with different cutoff frequencies; (

**b**) Details on waveforms.

Voltage Offset | Current Offset | Flux Linkage Drift (Wb.esp/s) |
---|---|---|

1 V | $0.1$ A | $1.017$ |

2 V | $0.2$ A | $1.99$ |

$-1$ V | $-0.1$ A | $-0.939$ |

$-2$ V | $-0.2$ A | $-1.923$ |

$\mathit{MAE}$ | $\mathit{MSE}$ | ${\mathit{R}}^{\mathbf{2}}$ | $\mathit{RMSE}$ | $\mathit{SSE}$ | |
---|---|---|---|---|---|

$\mathit{C}\mathbf{1}$ | $0.0849$ | $1.2208\phantom{\rule{4pt}{0ex}}{e}^{-6}$ | $0.9949$ | $0.0011$ | $0.2442$ |

$\mathit{C}\mathbf{2}$ | $0.3140$ | $1.6867\phantom{\rule{4pt}{0ex}}{e}^{-5}$ | $0.9472$ | $0.0041$ | $3.3733$ |

$\mathit{C}\mathbf{3}$ | $0.1391$ | $4.2060\phantom{\rule{4pt}{0ex}}{e}^{-6}$ | $0.9823$ | $0.0021$ | $0.4795$ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

de Paula, M.V.; dos Santos Barros, T.A. A New Flux Linkage Estimation with Drift Cancellation Technique for Switched Reluctance Machines. *Electronics* **2020**, *9*, 405.
https://doi.org/10.3390/electronics9030405

**AMA Style**

de Paula MV, dos Santos Barros TA. A New Flux Linkage Estimation with Drift Cancellation Technique for Switched Reluctance Machines. *Electronics*. 2020; 9(3):405.
https://doi.org/10.3390/electronics9030405

**Chicago/Turabian Style**

de Paula, Marcelo Vinícius, and Tárcio André dos Santos Barros. 2020. "A New Flux Linkage Estimation with Drift Cancellation Technique for Switched Reluctance Machines" *Electronics* 9, no. 3: 405.
https://doi.org/10.3390/electronics9030405