# Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances

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## Abstract

**:**

## 1. Introduction

## 2. Unmanned Helicopter Models

**Assumption**

**1**

**.**The disturbance aerodynamic forces and aerodynamic moments satisfy $\left|\right|{\dot{\mathit{d}}}_{1}\left(t\right)\left|\right|<{D}_{1},\left|\right|{\dot{\mathit{d}}}_{2}\left(t\right)\left|\right|<{D}_{2}$, where ${D}_{1}$ and ${D}_{2}$ denotes the unknown boundary.

**Lemma**

**1**

**.**For any constant $\u03f5>0$ and the appropriate dimensional vectors or matrices $\mathit{X}$ and $\mathit{Y}$, the following inequality holds:

**Lemma**

**2**

**.**For any constant ${k}_{b}$ and real variable $z\left(t\right)$, the following inequality holds while $z\left(t\right)<{k}_{b}$:

## 3. Flight-Tracking Controller Design

#### 3.1. System Transformation

#### 3.2. Nonlinear Disturbance Observer Design

#### 3.3. State-Constrained Backstepping Controller Design

**Remark**

**1.**

**Remark**

**2.**

## 4. Stability Analysis

**Theorem**

**1.**

**Proof.**

## 5. Numerical Simulation

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Parameter (Unit) | Parameter Description | Parameter (Unit) | Parameter Description |
---|---|---|---|

$m=8$ kg | quality of the helicopter | ${J}_{xx}=0.26\phantom{\rule{3.33333pt}{0ex}}\mathrm{kg}\xb7{\mathrm{m}}^{2}$ | moment of rotation |

${J}_{yy}=0.35\phantom{\rule{3.33333pt}{0ex}}\mathrm{kg}\xb7{\mathrm{m}}^{2}$ | moment of rotation | ${J}_{zz}=0.29\phantom{\rule{3.33333pt}{0ex}}\mathrm{kg}\xb7{\mathrm{m}}^{2}$ | moment of rotation |

${C}_{ma}=107\phantom{\rule{3.33333pt}{0ex}}(\mathrm{N}\xb7\mathrm{m}/\mathrm{rad})$ | pitch moment intensity factor | ${C}_{mb}=199\phantom{\rule{3.33333pt}{0ex}}(\mathrm{N}\xb7\mathrm{m}/\mathrm{rad})$ | rolling moment intensity factor |

${C}_{MQ}=0.0044\phantom{\rule{3.33333pt}{0ex}}(\mathrm{M}\xb7{\mathrm{N}}^{-\frac{1}{2}})$ | main rotor torque factor | ${D}_{MQ}=0.6304\phantom{\rule{3.33333pt}{0ex}}(\mathrm{M}\xb7{\mathrm{N}}^{-\frac{1}{2}})$ | main rotor torque factor |

${x}_{m}=0$ m | distance between the center of the main rotor and the x-axis of the helicopter’s center of gravity | ${z}_{m}=0.284$ m | distance between the center of the main rotor and the z-axis of the helicopter’s center of gravity |

${x}_{t}=0.915$ m | distance between the center of the tail and the x-axis of the helicopter’s center of gravity | ${z}_{t}=0.104$ m | distance between the center of the tail and the z-axis of the helicopter’s center of gravity |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Huang, Y.; Liu, H.; Li, D.
Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances. *Aerospace* **2023**, *10*, 471.
https://doi.org/10.3390/aerospace10050471

**AMA Style**

Li Y, Huang Y, Liu H, Li D.
Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances. *Aerospace*. 2023; 10(5):471.
https://doi.org/10.3390/aerospace10050471

**Chicago/Turabian Style**

Li, Yankai, Yulong Huang, Han Liu, and Dongping Li.
2023. "Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances" *Aerospace* 10, no. 5: 471.
https://doi.org/10.3390/aerospace10050471