# Novel Approach to Fault-Tolerant Control of Inter-Turn Short Circuits in Permanent Magnet Synchronous Motors for UAV Propellers

^{*}

## Abstract

**:**

## 1. Introduction

_{2}-emissions, lower noise, a higher efficiency, a reduced thermal signature (crucial for military applications), and simplified maintenance. However, several reliability and safety issues are still open, especially for long-endurance UAVs flying in unsegregated airspaces.

- Take-off weight: from 35 to 50 kg;
- Endurance: >6 h;
- Range: >3 km;
- Take-off system: pneumatic launcher;
- Landing system: parachute and airbags;
- Propulsion system: Permanent Magnet Synchronous Motor (PMSM) powering a twin-blade fixed-pitch propeller;
- Innovative sensing systems:
- ○
- Synthetic aperture radar, to support surveillance missions in adverse environmental conditions;
- ○
- Sense-and-avoid system, integrating a camera with a miniaturised radar, to support autonomous flight capabilities in emergency conditions.

## 2. Materials and Methods

#### 2.1. System Description

- An electromechanical section, with:
- ○
- Three-phase surface-mounted PMSM with phase windings in Y-connection;
- ○
- Twin-blade fixed-pitch propeller [41];
- ○
- Mechanical coupling joint.

- An Electronic Control Unit (ECU), including:
- ○
- CONtrol/MONitoring (CON/MON) module, for the implementation of the closed-loop control and health-monitoring functions;
- ○
- Four-leg converter;
- ○
- Three current sensors (CSa, CSb, CSc), one per each motor phase;
- ○
- One Angular Position Sensor (APS), measuring the motor angle;
- ○
- A Power Supply Unit (PSU), converting the power input coming from the UAV electrical power storage system to all components and sensors;
- ○
- Data and power connectors for the interface with the Flight Control Computer (FCC) and the UAV electrical system.

#### 2.2. Model of the Aero-Mechanical Section

#### 2.3. Model of the PMSM with ITSC Fault

## 3. Fault-Tolerant Control System

#### 3.1. FDI Algorithm Conceptualization

- An ITSC fault can be detected by measuring the difference between the lengths of major and minor axes of the ellipse;
- An ITSC fault can be isolated by measuring the inclination of the major axis of the ellipse.

- The difference between the lengths of major and minor axes of the ellipse provides a symptom about the ITSC extension (fault detection);
- The inclination of the major axis of the ellipse provides a symptom about the ITSC location (fault isolation).

#### 3.2. FDI Algorithm Design and Implementation

#### 3.3. Fault Accommodation Algorithm

- From the planar reference $\left({n}_{f},{b}_{f},{c}_{f}\right)$ to a planar reference frame $({\alpha}_{f},{\beta}_{f},{\mathit{\gamma}}_{f})$, in which the ${\alpha}_{f}$ axis has an opposite direction w.r.t. the neutral current axis ${n}_{f}$;
- From the planar reference $({\alpha}_{f},{\beta}_{f},{\mathit{\gamma}}_{f})$ to a planar rotating frame $({d}_{f},{q}_{f},{z}_{f})$ that maintains the same commands after the isolation (${i}_{d}{}_{f}={i}_{d}^{*}$ and ${i}_{q}{}_{f}={i}_{q}^{*})$.

## 4. Results and Discussion

#### 4.1. Failure Transient Characterization

^{−6}s integration step. It is worth noting that the choice of a fixed-step solver is not strictly related to the objectives of this work (in which the model is used for “off-line” simulations testing the FTC), but it has been selected for the next step of the project, when the FTC system will be implemented in the ECU boards via the automatic MATLAB compiler and executed in “real-time”.

#### 4.2. FDI Parameters Definition

- Simulation 1: cruise speed hold,
- Simulation 2: maximum speed ramp demand.

#### 4.3. Critical Comparison with Other ITSC FDI Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**.**It is worth noting that the matrix $\u2102$ is singular, and $\mathbb{S}$ is also singular if all data points lie exactly on an ellipse. Because of that, the computation of eigenvalues is numerically unstable and it can produce wrong results (as infinite or complex numbers). To overcome the drawback, Halìř [52] suggested to partition the $\u2102$ and $\mathbb{S}$ matrices. The constraint matrix is defined as:

## Appendix B

Definition | Symbol | Value | Unit |
---|---|---|---|

Cruise speed | ${\dot{\theta}}_{p}$_{|cruise} | 5800 | rpm |

Cruise power | P_{p|cruise} | 1100 | W |

Climb speed | ${\dot{\theta}}_{p}$_{|climb} | 7400 | rpm |

Climb power | P_{p|climb} | 3238 | W |

Definition | Symbol | Value | Unit |
---|---|---|---|

Stator phase resistance | R | 0.025 | Ω |

Stator phase inductance single module | L | 1 × 10^{−5} | H |

Pole pairs number | n_{d} | 5 | - |

Total turns number per phase | N | 36 | - |

Torque constant | k_{t} | 0.12 | Nm/A |

Back-electromotive force constant | k_{e} | 0.036 | V/(rad/s) |

Permanent magnet flux linkage | λ_{m} | 0.008 | Wb |

Maximum current (continuous duty cycle) | I_{sat} | 80 | A |

Voltage supply | V_{DC} | 36 | V |

Rotor inertia | J_{em} | 8.2 × 10^{−3} | kg·m^{2} |

Propeller diameter | D_{p} | 0.5588 | m |

Propeller inertia | J_{p} | 1.62 × 10^{−2} | kg·m^{2} |

Joint stiffness | K_{gb} | 1.598 × 10^{3} | Nm/rad |

Joint damping | C_{gb t} | 0.2545 | Nm/(rad/s) |

Insulation resistance coefficient | k_{Rf} | 11 | - |

Maximum cogging torque | Q_{cmax} | 0.036 | Nm |

Harmonic index of the cogging disturbances | n_{h} | 12 | - |

Definition | Symbol | Value | Unit |
---|---|---|---|

Control frequency | ${f}_{CL}$ | $20$ | $\mathrm{kHz}$ |

Ellipse measurement points | $n$ | $40$ | $-$ |

Sampling frequency $(={f}_{CL}/n)$ | ${f}_{FDI}$ | $500$ | $\mathrm{Hz}$ |

Detection index threshold | ${\epsilon}_{d}{}_{th}$ | $0.6$ | $\mathrm{A}$ |

Isolation index threshold | ${\epsilon}_{i}{}_{th}$ | $60$ | $\mathrm{deg}$ |

Fault counter threshold | ${n}_{th}$ | $20$ | $-$ |

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**Figure 4.**Full electric propulsion system: (

**a**) mechanical scheme; (

**b**) three-phase PMSM schematics with shorted turns in phase a (one pole pair and accessible neutral point).

**Figure 5.**Decomposition of the current phasor in the Clarke plane into positive- and negative-sequence components.

**Figure 6.**Inclination of the ellipse major axis (

**a**) and ellipses axis ratio (

**b**) under ITSC faults of different extensions and locations.

**Figure 8.**Reference frame transformation: (

**a**) normal Clarke–Park transformation, (

**b**) new transformation with phase a isolated.

**Figure 10.**Propeller speed tracking with ITSC ($\mu =0.5$) on phase a at t = 150 ms: (

**a**) stationary and (

**b**) unsteady operations.

**Figure 11.**Normalized motor torque with ITSC ($\mu =0.5$) on phase a at t = 150 ms: (

**a**) stationary (${Q}_{{m}_{max}}\approx 12\mathrm{Nm}$) and (

**b**) unsteady operations (${Q}_{{m}_{max}}\approx 15\mathrm{Nm}$).

**Figure 12.**Normalized phase currents with ITSC ($\mu =0.5$) on phase a at t = 150 ms (${I}_{sat}=80\mathrm{A}$): (

**a**) stationary (

**b**) unsteady operations.

**Figure 13.**Current phasor trajectory in Clarke space with ITSC ($\mu =0.5$) on phase a (${I}_{sat}=80\mathrm{A}$): (

**a**) stationary (

**b**) unsteady operations.

**Figure 14.**Ellipse parameters with ITSC ($\mu =0.5$) on phase a at t = 40 ms: (

**a**) stationary (

**b**) unsteady operations.

**Figure 15.**Propeller speed demands imposed for FDI design simulations (ITSC with $\mu =0.1$ at t = 150 ms).

Isolated Phase (w) | x | y | m |
---|---|---|---|

a | b | c | 0 |

b | c | a | 2 |

c | a | c | 1 |

Acronym | Method |
---|---|

C1 | Able to detect the faulty phase. |

C2 | Insensitive to operating loads. |

C3 | Robust against speed changes. |

C4 | Robust against current waveform. |

C5 | Minimum number of detected shorted turns. |

C6 | Electrical periods for FDI (latency time). |

C7 | Real-time computation. |

C8 | Tuning simplicity. |

Method | |||||
---|---|---|---|---|---|

Capability | M1 | M2 | M3 | M4 | M5 |

C1 | Yes | No | No | Yes | Yes |

C2 | No | No | Yes | No | Yes |

C3 | No | Yes | No | Not provided | Yes |

C4 | Not provided | Not provided | Not provided | Not provided | Yes |

C5 | 2 | 1 | 4 | 1 | 4 |

C6 | Not provided | Not provided | Not provided | 10 (200 ms) | 20 (40 ms) |

C7 | No | No | No | Yes | Yes |

C8 | Yes | No | Yes | No | Yes |

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**MDPI and ACS Style**

Suti, A.; Di Rito, G.; Galatolo, R.
Novel Approach to Fault-Tolerant Control of Inter-Turn Short Circuits in Permanent Magnet Synchronous Motors for UAV Propellers. *Aerospace* **2022**, *9*, 401.
https://doi.org/10.3390/aerospace9080401

**AMA Style**

Suti A, Di Rito G, Galatolo R.
Novel Approach to Fault-Tolerant Control of Inter-Turn Short Circuits in Permanent Magnet Synchronous Motors for UAV Propellers. *Aerospace*. 2022; 9(8):401.
https://doi.org/10.3390/aerospace9080401

**Chicago/Turabian Style**

Suti, Aleksander, Gianpietro Di Rito, and Roberto Galatolo.
2022. "Novel Approach to Fault-Tolerant Control of Inter-Turn Short Circuits in Permanent Magnet Synchronous Motors for UAV Propellers" *Aerospace* 9, no. 8: 401.
https://doi.org/10.3390/aerospace9080401