# Study of Gust Calculation and Gust Alleviation: Simulations and Wind Tunnel Tests

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Gust Calculation Method

## 3. Wind Tunnel Test of Gust Calculation

#### 3.1. Gust Generator Design

#### 3.2. Gust Sensor and Plunging–Pitching Motion Device

#### 3.3. Sensors Signals Fusion Method

#### 3.4. Analysis of Gust Calculation Test Results

## 4. Influence of Sensor Characteristics on Gust Calculation and Gust Alleviation

#### 4.1. Mathematical Model Building

- (1)
- State-space model

- (2)
- Feedforward controller design

#### 4.2. Model Description

#### 4.3. Influence of Sensor Delay on Gust Calculation and Gust Alleviation

#### 4.4. Influence of Sensor Measurement Error on Gust Calculation and Gust Alleviation

## 5. Wind Tunnel Test of Gust Alleviation

#### 5.1. Test Model

#### 5.2. Measurement and Control System

- (1)
- Overall structure

- (2)
- Stability augmentation system

- (3)
- Gust alleviation system

#### 5.3. Analysis of Gust Alleviation Test Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${\mathit{C}}_{\xi \xi}$ | Damping matrix | $\mathit{F}$ | Generalized aerodynamic matrix |

$f$ | Gust frequency | $H$ | Aircraft height |

$J$ | Root mean square of the calculated gust AOA | $K$ | Control system gain |

${\mathit{K}}_{\xi \xi}$ | Stiffness matrix | $L$ | Gust scale |

${\mathbf{L}}_{bg}$ | Coordinate transformation matrix | $\mathit{M}$ | Mass matrix |

$\mathit{q}$ | Generalized displacement matrix | $q$ | Pitch rate |

$\mathit{Q}$ | Generalized aerodynamic influence coefficient matrix | $r$ | Yaw rate |

${u}_{c}$ | Command output by control system | $V$ | Flight speed |

${\mathbf{V}}_{a}$ | Airspeed vector | ${\mathbf{V}}_{g}$ | Ground speed vector |

${\mathbf{V}}_{w}$ | Wind speed of the changing wind field | ${\mathbf{V}}_{wg}$ | Gust velocity vector |

${w}_{g}$ | Gusts velocity value | ${w}_{m}$ | Gust amplitude |

${x}_{AOA}$ | Distance from center of gravity to AOA sensor | ${x}_{AOS}$ | Distance from center of gravity to AOS sensor |

$\alpha $ | Angle of attack | ${\alpha}_{wg}$ | Gust angle |

$\beta $ | Angle of sideslip | ${\beta}_{wg}$ | Angle of sideslip due to gust |

$\delta $ | Control surface deflection angle | $\omega $ | Angle frequency |

$\eta $ | Gust alleviation rate | $\theta $ | Pitch angle |

$\lambda $ | Cross-correlation function | $\rho $ | Air density |

$\varphi $ | Roll angle | $\psi $ | Yaw angle |

${\sigma}_{c}$ | Maximum gust response value with control | ${\sigma}_{o}$ | Maximum gust response value without control |

$\tau $ | Time delay |

## Abbreviations

AOA | Angle of attack |

AOS | Angle of sideslip |

CCS | Combined control system |

FBCS | Feedback control system |

FFCS | Feedforward control system |

GAS | Gust alleviation system |

GLA | Gust load alleviation |

SAS | Stability augmentation system |

TDSN | Time delay step number |

WRBM | Wing root bending moment |

WTA | Wingtip acceleration |

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**Figure 19.**Aircraft model installed in wind tunnel. (

**a**) Rear view of model and (

**b**) front view of model.

Modal Name of Aircraft | Modal Frequency (Hz) | |
---|---|---|

Experimental Value | Theoretical Value | |

Plunging mode | -- | 0.0 |

Pitching mode | -- | 0.0 |

First-order bending | 2.13 | 2.14 |

Second-order bending | 5.39 | 5.49 |

TDSN | WTA | WRBM | ||||
---|---|---|---|---|---|---|

Open-Loop (g) | Closed-Loop (g) | Alleviation Rate (%) | Open-Loop (g) | Closed-Loop (g) | Alleviation Rate (%) | |

0 | 0.45 | 0.24 | 46.67 | 26.39 | 14.36 | 45.59 |

3 | 0.30 | 33.33 | 15.83 | 40.02 | ||

6 | 0.37 | 17.78 | 18.60 | 29.52 | ||

9 | 0.44 | 2.22 | 22.29 | 15.54 | ||

12 | 0.49 | −8.89 | 26.48 | −0.34 | ||

15 | 0.53 | −17.78 | 30.79 | −16.67 |

Response | Alleviation Rate (%) | ||
---|---|---|---|

FFCS | FBCS | CCS | |

WRBM | 39.12 | 33.54 | 65.31 |

WTA | 65.47 | 37.91 | 67.89 |

Pitch rate | 41.14 | 46.30 | 70.13 |

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**MDPI and ACS Style**

Zhou, Y.; Wu, Z.; Yang, C.
Study of Gust Calculation and Gust Alleviation: Simulations and Wind Tunnel Tests. *Aerospace* **2023**, *10*, 139.
https://doi.org/10.3390/aerospace10020139

**AMA Style**

Zhou Y, Wu Z, Yang C.
Study of Gust Calculation and Gust Alleviation: Simulations and Wind Tunnel Tests. *Aerospace*. 2023; 10(2):139.
https://doi.org/10.3390/aerospace10020139

**Chicago/Turabian Style**

Zhou, Yitao, Zhigang Wu, and Chao Yang.
2023. "Study of Gust Calculation and Gust Alleviation: Simulations and Wind Tunnel Tests" *Aerospace* 10, no. 2: 139.
https://doi.org/10.3390/aerospace10020139