# Design and Implementation of Predictive Controllers for a 36-Slot 12-Pole Outer-Rotor SPMSM/SPMSG System with Energy Recovery

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model of SPMSMs

## 3. Predictive Speed-Loop Controller Design

## 4. Predictive Current-Loop Controller Design

## 5. SPMSM Drive System

- (a)
- Constant-torque region

- (b)
- Constant-power region

- (c)
- Maximum torque/volt control region

- (d)
- Implementation

## 6. Implementation

^{2}, and a viscous coefficient of 0.005 N·m·s/rad. When the indoor exercise bicycle is ridden from a virtual upland to a lowland, the motor of the indoor exercise bicycle is accelerated. Then, the relays are connected to the inverter, which uses the energy from the battery set to drive the SPMSM, which adds extra torque to the indoor exercise bicycle to make the ride feel more realistic. However, when the rider of the indoor bicycle is riding from a virtual lowland to an upland, the motor of the indoor exercise bicycle is decelerated. The relays are connected to the 3-phase rectifier to transfer the SPMSG energy to the capacitor of the DC-link. After that, a buck-converter is used to convert the DC-link capacitor voltage to near 25 V, which provides for regenerative resistance. Then, the SPMSM converter transforms its energy into the regenerative resistance. In order to store and save the recovered energy, a charger is implemented to use the regenerated energy to charge the 24-V battery set.

## 7. Experimental Results

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The d-q axis current curves. The line from 0 to A is MTPA control, and the line from A to B is Flux-weakening control.

**Figure 7.**Flux-weakening and MTPV control. (

**a**) d-q axis current curve, (

**b**) flux-weakening control, (

**c**) MTPV control.

**Figure 9.**Photographs of the SPMSM drive system. (

**a**) motor (

**b**) encoder, motor, and coupling connector.

**Figure 12.**Measured sinusoidal responses using different controllers at 200 r/min. (

**a**) speeds, (

**b**) errors.

**Figure 13.**Measured triangular responses using different controllers at 200 r/min. (

**a**) speeds, (

**b**) errors.

**Figure 19.**Measured responses at 300 r/min without flux-weakening control. (

**a**) speeds, (

**b**) currents.

**Figure 21.**Measured speed responses at 350 r/min with maximum torque/voltage control. (

**a**) speeds, (

**b**) torque-speed curve.

**Figure 23.**Speed responses with varied parameters $2{r}_{s}$, $0.5{L}_{d}$, $0.5{L}_{q}$, and $2J$ at 50 r/min. (

**a**) speeds. (

**b**) proposed predictive controller. (

**c**) PI errors.

Conditions | Specifications | PI Controllers | Predictive Controllers |
---|---|---|---|

200 r/min step-input command | Rise time | 1 s | 0.4 s |

Settling time | 1.4 s | 0.8 s | |

Steady-state errors | ±2 r/min | ±1 r/min | |

200 r/min adding a 2N-m load | Recovery time | 0.5 s | 0.2 s |

Maximum speed drop | 31 r/min | 20 r/min | |

200 r/min sinusoidal speed command | Maximum speed error | 44 r/min | 22 r/min |

$\sqrt{\frac{{\displaystyle \sum _{k=1}^{n}{\omega}_{error}^{2}(k)}}{n}}$ | 194 r/min | 94 r/min | |

200 r/min triangular speed command | Maximum speed error | 37 r/min | 28 r/min |

$\sqrt{\frac{{\displaystyle \sum _{k=1}^{n}{\omega}_{error}^{2}(k)}}{n}}$ | 188 r/min | 134 r/min |

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**MDPI and ACS Style**

Liu, T.-H.; Lu, W.-R.; Cheng, S.-H. Design and Implementation of Predictive Controllers for a 36-Slot 12-Pole Outer-Rotor SPMSM/SPMSG System with Energy Recovery. *Energies* **2023**, *16*, 2845.
https://doi.org/10.3390/en16062845

**AMA Style**

Liu T-H, Lu W-R, Cheng S-H. Design and Implementation of Predictive Controllers for a 36-Slot 12-Pole Outer-Rotor SPMSM/SPMSG System with Energy Recovery. *Energies*. 2023; 16(6):2845.
https://doi.org/10.3390/en16062845

**Chicago/Turabian Style**

Liu, Tian-Hua, Wen-Rui Lu, and Sheng-Hsien Cheng. 2023. "Design and Implementation of Predictive Controllers for a 36-Slot 12-Pole Outer-Rotor SPMSM/SPMSG System with Energy Recovery" *Energies* 16, no. 6: 2845.
https://doi.org/10.3390/en16062845