# Hybrid Quasi-Optimal PID-SDRE Quadrotor Control

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## Abstract

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## 1. Introduction

- Development of a flight controller for quad tilt-wing UAV that during its transition flight (with the change of wing angle) will be able to deal with high nonlinearity in this situation and provide drone stability [10];
- Development of a suboptimal integral sliding mode trajectory tracking anti-interference controller based on the state-dependent Riccati equation [11];
- Development of non-linear controllers for cargo UAVs to obtain precise robot flight and efficient reduction of load oscillations by exploiting the natural coupling between horizontal UAV movement and payload oscillation [12].

- Optimal attitude stabilization and control with finite time;
- An increasing precise attitude control method;
- Elimination of the PID stabilizer and the tuning problem.

## 2. Quadrotor Model

## 3. Control System Design

#### 3.1. PID-SDRE Attitude Controller

- PID controller without SDRE stabilizer;
- SDRE feedback compensator neglecting PID stabilizer.

#### 3.2. P-PID Attitude Controller

#### 3.3. Finite-Time SDRE Stabilizer

## 4. Experimental Results

#### 4.1. UAV Used in Simulation Experiments

- Take-off mass: 13 kg,
- Max. flight time: 40 min,
- Flight range: 4.5 kg,
- Optimal flight speed: 30 km/h,
- Max. flight speed: 60 km/h.

#### 4.2. Simulation Experiments

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BF | Body Frame |

EF | Earth Frame |

EKF | Extended Kalman Filter |

GPS | Global Positioning System |

INS | Inertial Navigation System |

NED | North-East-Down |

PID | Proportional–Integral–Derivative Controller |

QTW UAV | Quad Tilt-Wing Unmanned Aerial Vehicle |

SDC | State-Dependent Coefficient |

SDRE | State-Dependent Riccati Equation |

UAV | Unmanned Aerial Vehicle |

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**MDPI and ACS Style**

Giernacki, W.; Stępień, S.; Chodnicki, M.; Wróblewska, A.
Hybrid Quasi-Optimal PID-SDRE Quadrotor Control. *Energies* **2022**, *15*, 4312.
https://doi.org/10.3390/en15124312

**AMA Style**

Giernacki W, Stępień S, Chodnicki M, Wróblewska A.
Hybrid Quasi-Optimal PID-SDRE Quadrotor Control. *Energies*. 2022; 15(12):4312.
https://doi.org/10.3390/en15124312

**Chicago/Turabian Style**

Giernacki, Wojciech, Sławomir Stępień, Marcin Chodnicki, and Agnieszka Wróblewska.
2022. "Hybrid Quasi-Optimal PID-SDRE Quadrotor Control" *Energies* 15, no. 12: 4312.
https://doi.org/10.3390/en15124312