# Development of Model Predictive Controller for a Tail-Sitter VTOL UAV in Hover Flight

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. UAV System Configuration

#### 3.1. Aircraft Design

#### 3.2. Avionics and Propulsion System

## 4. Dynamic Modeling

#### 4.1. Coordinate System

#### 4.2. Dynamic Model of Vehicle

#### 4.3. Aerodynamic Model

#### 4.4. Actuator Model

## 5. Development of MPC Controllers

#### 5.1. Controller Structure

#### 5.2. Augmented Prediction Model

#### 5.2.1. Measured Disturbance

#### 5.2.2. Unmeasured Disturbance

#### 5.3. Model Linearization

#### 5.4. Objective Function

## 6. HIL Simulation

#### 6.1. HIL Simulation Structure

#### 6.2. Controller Parameters

#### 6.3. Simulation Results

#### 6.3.1. Step Path Tracking

#### 6.3.2. Circular Path Tracking with Wind

## 7. Flight Experiments

#### 7.1. Experiment Environment

#### 7.2. Experimental Results

#### 7.2.1. Hover with Wind Disturbance

#### 7.2.2. Circular Trajectory Following

## 8. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AOA | angle of attack |

CFD | computational fluid dynamics |

CG | center of gravity |

DAQ | data acquisition |

DOF | degree of freedom |

EOM | equations of motion |

ESC | electric speed controller |

FCC | federal communications commission |

HIL | hardware-in-the-loop |

LPE | local position estimator |

LQR | linear quadratic regulation |

MAC | mean aerodynamic chord |

MD | measured disturbance |

MPC | model predictive control |

NED | north-east-down |

PPT | PolyU Plus Tail-sitter |

QP | quadratic-programming |

RMSE | root mean square error |

UD | unmeasured disturbance |

UAV | unmanned aerial vehicle |

VLM | vortex lattice method |

VTOL | vertical takeoff and landing |

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**Figure 3.**The inertial coordinate ${\mathsf{\Gamma}}_{i}$ and body coordinate ${\mathsf{\Gamma}}_{b}$ of the UAV.

**Figure 5.**The experiment data and fitted curve of the motor-propeller system. (

**a**) thrust to throttle; (

**b**) torque to throttle.

**Figure 9.**Step path tracking results of attitude (

**left column**) and position (

**right column**) in HIL simulation.

**Figure 10.**Inclining spiral path tracking results of attitude (

**left column**) and position (

**right column**) with wind disturbance from 20–30 s in the HIL simulation.

**Figure 14.**Experimental results of attitude (

**left column**) and position (

**right column**) for hovering with the PID controller (the fan was turned on for 40–70 s).

**Figure 15.**Experimental results of attitude (

**left column**) and position (

**right column**) for hovering with the MPC controller (the fan was turned on for 40–70 s).

**Figure 16.**Experimental results of attitude (

**left column**) and position (

**right column**) for the UAV to follow a circular path with the MPC controller (the fan was turned on for 30–60 s).

Parameter | Value |
---|---|

${T}_{s}$ | 0.05 |

${H}_{p}$ | 40 |

${H}_{c}$ | 5 |

$\left|\mathbf{y}\right|$ constraint | ${[\mathrm{inf},\mathrm{inf},\mathrm{inf},20,20,20,\pi /6,\pi /6]}^{T}$ |

$\left|\mathbf{y}\right|$ scale factor | $\mathbf{I}$ |

$\left|\mathbf{u}\right|$ constraint | ${[\pi /6,\pi /6,10]}^{T}$ |

$\left|\mathbf{u}\right|$ scale factor | ${[1,1,15]}^{T}$ |

$\mathbf{Q}$ | $\mathrm{diag}\{8,8,5,5,2,2,10,8\}$ |

${\mathbf{R}}_{\mathbf{u}}$ | $\mathrm{diag}\{0,0,0\}$ |

${\mathbf{R}}_{\Delta \mathbf{u}}$ | $\mathrm{diag}\{10,4,10\}$ |

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**MDPI and ACS Style**

Li, B.; Zhou, W.; Sun, J.; Wen, C.-Y.; Chen, C.-K.
Development of Model Predictive Controller for a Tail-Sitter VTOL UAV in Hover Flight. *Sensors* **2018**, *18*, 2859.
https://doi.org/10.3390/s18092859

**AMA Style**

Li B, Zhou W, Sun J, Wen C-Y, Chen C-K.
Development of Model Predictive Controller for a Tail-Sitter VTOL UAV in Hover Flight. *Sensors*. 2018; 18(9):2859.
https://doi.org/10.3390/s18092859

**Chicago/Turabian Style**

Li, Boyang, Weifeng Zhou, Jingxuan Sun, Chih-Yung Wen, and Chih-Keng Chen.
2018. "Development of Model Predictive Controller for a Tail-Sitter VTOL UAV in Hover Flight" *Sensors* 18, no. 9: 2859.
https://doi.org/10.3390/s18092859