# Hierarchical Distributed Motion Control for Multiple Linear Switched Reluctance Machines

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. LSRM Modeling

#### 2.2. Network Topology and Graph Theory

## 3. Control Strategy

#### 3.1. Reference Signal Consensus Module

#### 3.2. Unit System Control

#### 3.3. Coordinated Tracking Control Module

#### 3.4. Stability Analysis

**Lemma**

**1.**

**Lemma**

**2.**

**Remark**

**1.**

## 4. Network Construction

#### 4.1. Simulation Analysis

#### 4.2. Experimental Setup

#### 4.3. Network Configuration

## 5. Experimental Results

#### 5.1. Control Performance under Two-level Tracking Control

#### 5.2. Performance under Lower-Level Tracking

#### 5.3. Performance under Independent Tracking

## 6. Conclusions and Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) control block diagram of the LSRMs network, (

**b**) simulation results of reference, and (

**c**) actual signals.

**Figure 8.**Dynamic position response waveforms: (

**a**) reference, (

**b**) actual and (

**c**) relative reference, and (

**d**) relative position signals under hierarchical synchronization.

**Figure 9.**Dynamic position response waveforms: (

**a**) actual, (

**b**) error, and (

**c**) relative position signals under low-level tracking synchronization.

**Figure 10.**Dynamic position response waveforms of relative signals under independent tracking control scheme.

Quantity | Value |
---|---|

Mass of moving platform | 3.8 kg |

Mass of stator | 5.0 kg |

Pole pitch | 12 mm |

Pole width | 6 mm |

Air gap length | 0.3 mm |

Phase resistance | 2 Ohm |

Number of turns | 200 |

Stack length | 50 mm |

Rated power | 250 W |

Voltage | 50 Volt |

Encoder resolution | 1 $\mathsf{\mu}$m |

Symbol | Value |
---|---|

$\alpha $ | 1 |

$\beta $ | 1 |

$\mu $ | $\left[\begin{array}{cccc}-1& -1& -1& 0\end{array}\right]$ |

$\lambda $ | $\left[\begin{array}{cccc}-1\pm i& -1\pm i& -1\pm i& -0.5\pm 0.866i\end{array}\right]$ |

LSRM | Reference Signal | Actual Signal | Error | Relative Reference | Relative Position |
---|---|---|---|---|---|

$i,j=0,1,2,3$ | ${r}_{i}-{y}_{i}$ | ${r}_{i}-{r}_{j}$ | ${y}_{i}-{y}_{j}$ | ||

0 | ${r}_{0}$ | ${y}_{0}$ | $erro{r}_{0}$ | $err{f}_{01}$ | $err{y}_{01}$ |

1 | ${r}_{1}$ | ${y}_{1}$ | $erro{r}_{1}$ | $err{f}_{02}$ | $err{y}_{02}$ |

2 | ${r}_{2}$ | ${y}_{2}$ | $erro{r}_{2}$ | $err{f}_{03}$ | $err{y}_{03}$ |

3 | ${r}_{3}$ | ${y}_{3}$ | $erro{r}_{3}$ | $err{f}_{12}$ | $err{y}_{12}$ |

$err{f}_{13}$ | $err{y}_{13}$ | ||||

$err{f}_{23}$ | $err{y}_{23}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, B.; Yuan, J.; Luo, J.; Wu, X.; Qiu, L.; Pan, J.F.
Hierarchical Distributed Motion Control for Multiple Linear Switched Reluctance Machines. *Energies* **2017**, *10*, 1426.
https://doi.org/10.3390/en10091426

**AMA Style**

Zhang B, Yuan J, Luo J, Wu X, Qiu L, Pan JF.
Hierarchical Distributed Motion Control for Multiple Linear Switched Reluctance Machines. *Energies*. 2017; 10(9):1426.
https://doi.org/10.3390/en10091426

**Chicago/Turabian Style**

Zhang, Bo, Jianping Yuan, Jianjun Luo, Xiaoyu Wu, Li Qiu, and J.F. Pan.
2017. "Hierarchical Distributed Motion Control for Multiple Linear Switched Reluctance Machines" *Energies* 10, no. 9: 1426.
https://doi.org/10.3390/en10091426