# Model-Free Predictive Current Control of Synchronous Reluctance Motor Drives for Pump Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Background

#### Adaptive Model by Recursive Least Square Algorithm

## 3. Proposed Deadbeat Predictive Current Control

#### 3.1. Proposed Choice of Voltage Vector Module and Design Hints

#### 3.2. Proposed Optimisation Problem

#### 3.3. Algorithm for Finding the Optimal Solution

**GSS**) algorithm was adopted in this paper due to its simplicity and computational efficiency [30]. The solution of problem minimisation during each control period is given by

- $J\left(\phi \right(k+1\left)\right)$: the function that has to be minimised (i.e., Equation (10));
- lb: lower bound of the searching interval;
- ub: upper bound of the searching interval;
- $\u03f5$: termination tolerance for searching the solution;
- iter: maximum number of algorithm iterations for finding the solution.

## 4. Experimental Results and Discussion

#### 4.1. Design of Experiment: The Pump Load Emulator

#### 4.2. Pump Load Emulator Results

#### 4.3. Load Step Variations

#### 4.4. Effects of Different ${u}_{\mathrm{min}}$ Values

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

FS | Finite-Set |

CS | Continuous-Set |

PCC | Predictive Current Control |

PMSM | Permanent Magnet Synchronous Motor |

PWM | Pulse Width Modulator |

RLS | Recursive Least Square |

SynRM | Synchronous Reluctance Motor |

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**Figure 1.**Voltage plane area. The green area represents the feasible voltage vector region limited by the red-dot-dashed circles.

**Figure 2.**Example of cost function (10) for different voltage phase angle values.

**Figure 5.**Pump load emulation results of the motor under test SynRM${}_{1}$. Figures (

**a**,

**c**,

**e**) report the results of model-free FS-PCC [25]; Figures (

**b**,

**d**,

**f**) report the results of the proposed model-free PCC.

**Figure 6.**Pump load emulation results of the motor under test SynRM${}_{2}$. Figures (

**a**,

**c**,

**e**) report the results of model-free FS-PCC [25]; Figures (

**b**,

**d**,

**f**) report the results of the proposed model-free PCC.

**Figure 7.**Current controllers performances to rated current step reference variations at 30% ${\omega}_{n}$.

**Figure 8.**Current controllers performances to half-rated current step reference variations, SynRM${}_{2}$.

Parameter | Symbol | Unit | SynRM${}_{1}$ | SynRM${}_{2}$ |
---|---|---|---|---|

Resistance | R | $\mathrm{\Omega}$ | $4.6$ | $1.8$ |

d axis inductance (unsat.) | ${L}_{d}$ | $\mathrm{m}\mathrm{H}$ | 380 | 340 |

q axis inductance (unsat.) | ${L}_{q}$ | $\mathrm{m}\mathrm{H}$ | 85 | 60 |

Nominal current | ${I}_{n}$ | $\mathrm{A}$ | 4 | $5.6$ |

Nominal speed | ${\mathrm{\Omega}}_{n}$ | $\mathrm{rpm}$ | 1500 | 1500 |

Nominal power | ${P}_{n}$ | $\mathrm{W}$ | 1600 | 2200 |

Nominal torque | ${\tau}_{n}$ | $\mathrm{N}\mathrm{m}$ | $10.2$ | $14.0$ |

**Table 2.**Parameters of the virtual load emulator in (13).

Parameter | SynRM${}_{1}$ | SynRM${}_{2}$ |
---|---|---|

Static friction ${B}_{0}$ | $0.5542$ | $0.5542$ |

Ventilation friction ${B}_{1}$ | $9.1\times {10}^{-3}$ | $9.1\times {10}^{-3}$ |

Pump friction ${B}_{2}$ | $7.77\times {10}^{-4}$ | $11.65\times {10}^{-4}$ |

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**MDPI and ACS Style**

De Martin, I.D.; Pasqualotto, D.; Tinazzi, F.; Zigliotto, M. Model-Free Predictive Current Control of Synchronous Reluctance Motor Drives for Pump Applications. *Machines* **2021**, *9*, 217.
https://doi.org/10.3390/machines9100217

**AMA Style**

De Martin ID, Pasqualotto D, Tinazzi F, Zigliotto M. Model-Free Predictive Current Control of Synchronous Reluctance Motor Drives for Pump Applications. *Machines*. 2021; 9(10):217.
https://doi.org/10.3390/machines9100217

**Chicago/Turabian Style**

De Martin, Ismaele Diego, Dario Pasqualotto, Fabio Tinazzi, and Mauro Zigliotto. 2021. "Model-Free Predictive Current Control of Synchronous Reluctance Motor Drives for Pump Applications" *Machines* 9, no. 10: 217.
https://doi.org/10.3390/machines9100217