# Design and Verification of Short-Distance Landing Control System for a One-Third-Scale Unmanned Supersonic Experimental Airplane

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## Abstract

**:**

## 1. Introduction

## 2. New Landing Control Design Method

#### 2.1. Design Policy

#### 2.2. Longitudinal Conrol System Configuration

#### 2.3. Glideslope Controller

#### 2.4. Flare Controller

#### 2.5. Designe Procedure

- Identify the aerodynamic and physical characteristics via measurement or estimation from the analytical methods.
- Design target performance from mission requirement or acceptable load at touch down.
- Determine ${K}_{\mathrm{L}}$, ${K}_{\mathrm{D}},$ and ${D}_{0}$ as in Equations (2) and (3) by introducing the aerodynamic characteristics and the physical characteristics of UAV.
- Determine ${\alpha}_{\mathrm{M}\mathrm{A}\mathrm{X}}$ and ${\alpha}_{\mathrm{G}\mathrm{S}}$ from aerodynamic characteristics and the physical characteristics of UAV.
- Design ${\Gamma}_{\mathrm{G}\mathrm{S}}$ using Equation (4) by introducing the parameters determined in previous step.
- Design $\tau $ using Equation (20) by introducing the parameters determined in previous step.
- Design control systems which configure the longitudinal control system shown in Figure 3 to meet the target performance.

#### 2.5.1. Determine ${\alpha}_{GS}$ and ${\alpha}_{MAX}$

#### 2.5.2. Design ${\Gamma}_{GS}$ and $\mathsf{\tau}$

#### 2.5.3. Control System Design

## 3. Design

#### 3.1. Specifications of a One-Third-Scale Oowashi

#### 3.2. Target Performance

#### 3.3. Design result

## 4. Simulation

#### 4.1. Simulation Cases

#### 4.2. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$a$ | acceleration, m/s^{2} |

$D$ | drag, N |

$g$ | gravitational acceleration, m/ s^{2} |

$h$ | height, m |

${K}_{\mathrm{L}}$ | lift per unit AoA, N/rad |

${K}_{\mathrm{D}}$ | drag per unit AoA, N/rad^{2} |

$L$ | lift, N |

$\mathrm{m}$ | mass, kg |

$T$ | thrust, N |

$t$ | time from flare start, s |

$V$ | velocity, m/s |

$\alpha $ | angle of attack, rad |

$\gamma $ | error of path angle, rad |

$\Gamma $ | path angle, rad |

$\mathsf{\theta}$ | pitch angle, rad |

$\tau $ | flare time constant, s |

Subscripts | |

f | flare |

fs | flare start |

GS | glideslope |

target | target performance |

MAX | maximum |

min | minimum |

## References

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**Figure 6.**Estimated AoA versus flare time for one-third-scale Oowashi using Equation (19) at $\tau =1.5$.

Items | Value |
---|---|

Mass | 4 kg |

Length | 1.5 m |

${\alpha}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}}$ | 16 deg. |

Average cord | 0.4 m |

Wingspan | 0.8 m |

Longitudinal | Lateral | ||
---|---|---|---|

Items | Value | Items | Value |

${{C}_{\mathrm{x}}}_{\mathrm{u}}$ | −0.1340 | ${{C}_{\mathrm{y}}}_{\mathsf{\beta}}$ | −0.0083 |

${{C}_{\mathrm{x}}}_{\mathsf{\alpha}}$ | 0.0390 | ${{C}_{\mathrm{y}}}_{\mathrm{p}}$ | 0 |

${{C}_{\mathrm{z}}}_{\mathrm{u}}$ | 0 | ${{C}_{\mathrm{y}}}_{{\mathsf{\delta}}_{\mathrm{r}}}$ | 0.1483 |

${{C}_{\mathrm{z}}}_{\mathsf{\alpha}}$ | −3.1139 | ${{C}_{\mathrm{y}}}_{\mathrm{r}}$ | 0.6062 |

${{C}_{\mathrm{z}}}_{{\mathsf{\delta}}_{\mathrm{e}}}$ | −0.5076 | ${{C}_{\mathrm{l}}}_{\mathsf{\beta}}$ | −0.1031 |

${{C}_{\mathrm{z}}}_{\mathrm{q}}$ | 0 | ${{C}_{\mathrm{l}}}_{{\mathsf{\delta}}_{\mathrm{a}}}$ | 0.0605 |

${{C}_{\mathrm{m}}}_{\mathrm{u}}$ | 0 | ${{C}_{\mathrm{l}}}_{{\mathsf{\delta}}_{\mathrm{r}}}$ | 0.0152 |

${{C}_{\mathrm{m}}}_{\mathsf{\alpha}}$ | −1.7120 | ${{C}_{\mathrm{l}}}_{\mathrm{p}}$ | −0.2194 |

${{C}_{\mathrm{m}}}_{{\mathsf{\delta}}_{\mathrm{e}}}$ | −1.3121 | ${{C}_{\mathrm{l}}}_{\mathrm{r}}$ | 0.0802 |

${{C}_{\mathrm{m}}}_{\mathrm{q}}$ | −5.0348 | ${{C}_{\mathrm{n}}}_{\mathsf{\beta}}$ | 0.2077 |

${{C}_{\mathrm{m}}}_{\dot{\mathsf{\alpha}}}$ | −3.4185 | ${{C}_{\mathrm{n}}}_{{\mathsf{\delta}}_{\mathrm{a}}}$ | 0.0685 |

${{C}_{\mathrm{n}}}_{{\mathsf{\delta}}_{\mathrm{r}}}$ | −0.1152 | ||

${{C}_{\mathrm{n}}}_{\mathrm{p}}$ | −0.0107 | ||

${{C}_{\mathrm{n}}}_{\mathrm{r}}$ | −0.4804 |

Items | Value |
---|---|

Sink rate at touchdown | <1 m/s |

Landing distance | <400 m |

Velocity at touch down | 25 ± 1 m/s |

Items | Value |
---|---|

${K}_{\mathrm{D}}$ | 271 N/(rad^{2}) |

${D}_{0}$ | 12.5 N |

${T}_{\mathrm{G}\mathrm{S}}$ | 12.5 N |

${K}_{\mathrm{L}}$ | 253 N/rad |

V | 25 m/s |

${\alpha}_{\mathrm{G}\mathrm{S}}$ | 10 deg. |

Items | Value |
---|---|

${\Gamma}_{\mathrm{G}\mathrm{S}}$ | 12 deg. |

$\tau $ | 1.5 s |

Items | Value |
---|---|

Height of glideslope start | 60 m |

Initial speed | 25 m/s |

Case | ${\mathit{\Gamma}}_{\mathbf{G}\mathbf{S}}$ | $\mathit{\tau}$ |
---|---|---|

1 | 3 deg. | 3 s |

2 | 12 deg. | 1.5 s |

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## Share and Cite

**MDPI and ACS Style**

Hyokawa, S.; Ueba, M. Design and Verification of Short-Distance Landing Control System for a One-Third-Scale Unmanned Supersonic Experimental Airplane. *Aerospace* **2023**, *10*, 334.
https://doi.org/10.3390/aerospace10040334

**AMA Style**

Hyokawa S, Ueba M. Design and Verification of Short-Distance Landing Control System for a One-Third-Scale Unmanned Supersonic Experimental Airplane. *Aerospace*. 2023; 10(4):334.
https://doi.org/10.3390/aerospace10040334

**Chicago/Turabian Style**

Hyokawa, Satoshi, and Masazumi Ueba. 2023. "Design and Verification of Short-Distance Landing Control System for a One-Third-Scale Unmanned Supersonic Experimental Airplane" *Aerospace* 10, no. 4: 334.
https://doi.org/10.3390/aerospace10040334