# Analysis of Influence of Stratospheric Airship’s Key Parameter Perturbation on Motion Mode

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## Abstract

**:**

## 1. Introduction

^{3}as the research object, calculated the eigenvalues of the disturbed motion of the airship, and analyzed the influence of flight speed on the motion mode and kinetic characteristics of the airship; Yang et al. [12] systematically studied the motion modes of the stratospheric airship and provided the modal characteristics of longitudinal motion and lateral motion; Wang [13] revealed the influence of flight speed on the motion mode of an airship through analyzing the pole distribution and frequency characteristics of the airship at typical flight speeds. Liu [14] described the process of stratospheric airship mode calculation in detail and provided the correlation mechanism of flight speed change on airship motion mode; Miao [15] took the 1000 m

^{3}stratospheric verification airship as the research object, introduced the free motion characteristics of the airship at typical flight speeds, and simulated and analyzed the control response characteristics of the airship; Wang [16] introduced the motion mode characteristics of the V-shaped new concept stratospheric airship and calculated the motion mode of the airship under typical working conditions; Wang et al. [17] analyzed the characteristics of the longitudinal motion modes of the stratospheric airship from the perspective of stability and provided the modes sensitive to the longitudinal motion; Anshul et al. [18] conducted the trim and stability analysis of an airship with bifurcation techniques and provided the pole distribution diagram in different motion states; Wu et al. [19] analyzed and calculated the motion mode and dynamic characteristics of an airship driven by a new type of driving system with Matlab according to the characteristics of the “buoyant-slider” driven airship; Zhang [20] took GoodYear ZP4K as the research object, analyzed the characteristics of the longitudinal and lateral mode motion of the airship, and provided the generation mechanism of the pendulum motion mode; Liu [21] analyzed the influence of different motion models on the motion modes of airship under the conditions of straight and level flight at a constant speed and pointed out the root cause of the difference of motion modes. Yuan [22] proposed a control strategy combining model prediction, sliding mode control, and extended state observer for the space trajectory tracking of a stratospheric airship under state constraints, input saturation, and position disturbance and carried out a corresponding simulation analysis; Huang [23] analyzed the impact of external environmental changes on buoyant gas, airship mass, and internal and external pressure differences; Liu [24] proposed the corresponding dynamic model of a stratospheric airship according to the different description methods of aerodynamic parameters; Li [25] carried out dynamic modeling and a longitudinal stability analysis for a stratospheric airship with a double-hull configuration and gave the simulation results of pole distribution and handling characteristics; Gobiha [26] carried out dynamic modeling for an autonomous flying airship and used the established nonlinear 6 DOF model to simulate and evaluate the motion characteristics of the airship.

## 2. Overall Layout and Structure Parameters of Stratospheric Airship

## 3. Motion Model of Stratospheric Airship

#### 3.1. 6 DOF Nonlinear Model

- (1)
- Kinetic Equation

- (2)
- Kinematical Equation

#### 3.2. Linear Processing of Nonlinear Model

- (1)
- Longitudinal Motion Model Linearization

- (2)
- Horizontal Motion Model Linearization

## 4. Motion Mode of Stratospheric Airship

#### 4.1. Description of Motion Mode

#### 4.2. Characteristics of Motion Mode

- (1)
- Pitching Channel

- wherein ${\mathrm{A}}_{\mathrm{L}}=\left[\begin{array}{ccc}{\stackrel{-}{\mathrm{Z}}}^{\mathsf{\alpha}}& {\stackrel{-}{\mathrm{Z}}}^{\mathrm{q}}& {\stackrel{-}{\mathrm{Z}}}^{\mathsf{\theta}}\\ {\stackrel{-}{\mathrm{M}}}^{\mathsf{\alpha}}& {\stackrel{-}{\mathrm{M}}}^{\mathrm{q}}& {\stackrel{-}{\mathrm{M}}}^{\mathsf{\theta}}\\ 0& 1& 0\end{array}\right]$, ${\mathrm{m}}_{\mathrm{L}}=\left[\begin{array}{ccc}\left(\mathrm{m}+{\mathrm{m}}_{33}\right)\mathrm{s}& -\mathrm{m}{\mathrm{x}}_{\mathrm{G}}& 0\\ -\mathrm{m}{\mathrm{x}}_{\mathrm{G}}& \left({\mathrm{I}}_{\mathrm{y}}+{\mathrm{m}}_{55}\right)\mathrm{s}& 0\\ 0& 0& \mathrm{s}\end{array}\right]$
- wherein ${\mathrm{Z}}^{\mathsf{\alpha}}$ represents the derivative of normal aerodynamic coefficient; ${\mathrm{M}}^{\mathrm{q}}$ represents the derivative of pitch damping moment coefficient; ${\mathrm{M}}^{\mathsf{\theta}}$ represents the derivative of pitch attitude moment coefficient.

- (2)
- Yaw Channel

- wherein ${\mathrm{A}}_{\mathrm{S}}=\left[\begin{array}{cc}{\stackrel{-}{\mathrm{Y}}}^{\mathsf{\beta}}& {\stackrel{-}{\mathrm{Y}}}^{\mathrm{r}}\\ {\stackrel{-}{\mathrm{N}}}^{\mathsf{\beta}}& {\stackrel{-}{\mathrm{N}}}^{\mathrm{r}}\end{array}\right]$, ${\mathrm{m}}_{\mathrm{S}}=\left[\begin{array}{cc}\mathrm{m}+{\mathrm{m}}_{22}& \mathrm{m}{\mathrm{x}}_{\mathrm{G}}\\ \mathrm{m}{\mathrm{x}}_{\mathrm{G}}& {\mathrm{I}}_{\mathrm{z}}+{\mathrm{m}}_{66}\end{array}\right]$.
- wherein ${\mathrm{Y}}^{\mathsf{\beta}}$ represents the derivative of lateral aerodynamic coefficient; ${\mathrm{N}}^{\mathsf{\beta}}$ represents the derivative of the yaw aerodynamic stabilization coefficient; ${\mathrm{Y}}^{\mathrm{r}}$ and ${\mathrm{N}}^{\mathrm{r}}$ respectively represent the derivatives of yaw damping force and damping force moment coefficients.

- (3)
- Analysis of Difference between Pitch Motion Mode and Yaw Motion Mode

## 5. Influence of Key Parameter Perturbation on Motion Mode

#### 5.1. Moment of Aerodynamic Stabilization

- (1)
- Pitching Channel

- (2)
- Yaw Channel

#### 5.2. Location of Mass Center

#### 5.2.1. Axial Location

- (1)
- Pitching Channel

- (2)
- Yaw Channel

#### 5.2.2. Vertical Location

#### 5.3. Location of Buoyant Center

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Curve of Influence of Moment of Aerodynamic Stabilization on Pitching Channel Motion Mode: (

**a**) frequency change curves of the first-order inertial damping mode under the perturbation of the pitch aerodynamic stability moment (

**b**) damping and frequency change curves of the second-order oscillation convergence mode under the perturbation of the pitch aerodynamic stability moment.

**Figure 5.**Bode Plot and Deviation Curve of Pitching Channel in Perturbation State of Moment of Pitching Aerodynamic Stabilization: (

**a**) Bode plot of the pitching channel in the perturbation state of the pitch aerodynamic stability moment, (

**b**) amplitude frequency and phase frequency deviation curves of the pitching channel in the perturbation state of the pitch aerodynamic stability moment.

**Figure 6.**Curve of Influence of Moment Perturbation of Yaw Aerodynamic Stabilization on Pitching Channel Motion Mode: (

**a**) frequency characteristic curve of the yaw channel motion mode under the perturbation of the yaw aerodynamic stability moment, (

**b**) damping characteristic curve of the yaw channel motion mode under the perturbation of the yaw aerodynamic stability moment.

**Figure 7.**Bode Plot and Deviation Curve of Yaw Channel in Perturbation State of Moment of Yaw Aerodynamic Stabilization: (

**a**) Bode plot of the yaw channel in the perturbation state of the yaw aerodynamic stability moment, (

**b**) amplitude frequency and phase frequency deviation curves of the yaw channel in the perturbation state of the yaw aerodynamic stability moment.

**Figure 8.**Bode Plot and Deviation Curve of Axial Mass Center Perturbation for Pitching Channel: (

**a**) Bode diagram of the pitch channel under the state of perturbation of the pitch axial position, (

**b**) amplitude frequency and phase frequency error curves of the pitch channel under the state of perturbation of the axial position.

**Figure 9.**Curve of Influence of Axial Mass Center Perturbation on Pitching Channel Motion Mode: (

**a**) Bode plot of the pitching channel with axial location perturbation of the mass center, (

**b**) amplitude frequency and phase frequency deviation curves of the pitching channel with axial location perturbation of the mass center.

**Figure 11.**Curve of Influence of Vertical Mass Center Perturbation on Motion Mode of Pitching Channel: (

**a**) frequency characteristic curve of the first-order inertia damping mode of the pitching channel affected by the vertical perturbation of the mass center, (

**b**) damping and frequency characteristic curves of the second-order oscillation convergence mode of the pitching channel affected by the vertical perturbation of the mass center.

**Figure 12.**Curve of Influence of Vertical Buoyant Center Perturbation on Motion Mode of Pitching Channel: (

**a**) frequency characteristic curve of the first-order inertia damping mode of the pitching channel affected by the vertical perturbation of the buoyant center, (

**b**) damping and frequency characteristic curves of the pendulum motion mode of the pitching channel affected by the vertical perturbation of the buoyant center.

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

Mass [kg] | 11,800 |

Length [m] | 138 |

Diameter [m] | 35 |

Volume [m^{3}] | 134,037 |

Flight altitude [km] | 20 |

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**MDPI and ACS Style**

Tang, J.; Bai, S.; Xie, W.; Wu, J.; Jiang, H.; Sun, Y.
Analysis of Influence of Stratospheric Airship’s Key Parameter Perturbation on Motion Mode. *Aerospace* **2023**, *10*, 329.
https://doi.org/10.3390/aerospace10040329

**AMA Style**

Tang J, Bai S, Xie W, Wu J, Jiang H, Sun Y.
Analysis of Influence of Stratospheric Airship’s Key Parameter Perturbation on Motion Mode. *Aerospace*. 2023; 10(4):329.
https://doi.org/10.3390/aerospace10040329

**Chicago/Turabian Style**

Tang, Jiwei, Shilong Bai, Weicheng Xie, Junjie Wu, Hanjie Jiang, and Yuxuan Sun.
2023. "Analysis of Influence of Stratospheric Airship’s Key Parameter Perturbation on Motion Mode" *Aerospace* 10, no. 4: 329.
https://doi.org/10.3390/aerospace10040329