# Motion Synchronous Composite Decoupling with Fewer Sensors on Multichannel Hydraulic Force Control for Aircraft Structural Loading Test System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis of the Loading Coupling

#### 2.1. Principle of Displacement Overlapping

**ω**can be given as

**F**represents the vector of loading force.

#### 2.2. Mass Concentration Method

_{i}. In light of the static equivalent principle, the distributed mass of a part can be transformed into the concentrated mass of both ends. The concentrated mass of an end is m

_{i}/2. Two contiguous concentrated mass points constitute one concentrated mass in loading point, whose mass is (m

_{i}+ m

_{i}

_{+ 1})/2. After the transformation of concentrated mass, the loading model of the system with deformation is represented in Figure 2b.

#### 2.3. Analysis of the Loading Coupling

## 3. Modeling of the Loading System

#### 3.1. Single Channel Loading System

#### 3.2. Multichannel Loading System

#### 3.3. Analysis of Loading Performance

## 4. The Motion Synchronous Composite Control Method

#### 4.1. The Principle of Motion Synchronous Composite Control Method

**F**can be obtained.

**G**is the transfer matrix of the Laplace.

_{i}is took as the new variables of the equation set. The above equations can be solved and $\mathrm{s}{F}_{i}\text{}$can be expressed as the linear combination of ${F}_{i}$ and ${u}_{ci}$. Then once again referring to the previous formula for ${u}_{c}$:

**C**is a constant vector about ${K}_{ij}$. This realizes the derivation of the decoupling control compensation signal by linear combination of the channel control signal and the output force signal.

#### 4.2. The Simulation of Motion Synchronous Composite Control Method

## 5. Experiment

## 6. Discussion

## 7. Conclusions

- The novel motion synchronous composite decoupling control method can realize decoupling in the case of linear loading with fewer sensors. Yet the traditional decoupling control method requires the addition of displacement, velocity, and acceleration sensors or high-order differentiation, which will increase the complexity of measurement system.
- The composite control method uses only the command signal and control signal to achieve multichannel decoupling under the condition of increasing the loading frequency. It is able to improve the dynamic tracking accuracy of the multichannel loading system. It is of great significance that this decouple method could guarantee control accuracy in the case where the test frequency is increased. The method is able to maintain accurate loading of the force at increasing frequency, so that the loading time can be shortened.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Loading model of the structural test. (

**a**) shows a simplified model of the airfoil. (

**b**) shows the deflection of the model at each loading point.

**Figure 12.**ANSYS simulation for cantilever beam and test bench. (

**a**) shows ANSYS simulation for cantilever beam. (

**b**) shows ANSYS simulation for test bench.

Symbol | Definition | Value and Unit |
---|---|---|

${Q}_{L}$ | total flow from servo valve | / |

${K}_{q}$ | flow gain of servo valve | 3 ${\mathrm{m}}^{2}$ |

${x}_{v}$ | servo valve spool displacement | / |

${K}_{c}$ | flow pressure coefficient of the servo valve | / |

${p}_{f}$ | load pressure of system | / |

A | effective area of the piston | 14.6$\text{}\times \text{}{10}^{-4}{\text{}\mathrm{m}}^{2}$ |

${x}_{d}$ | displacements of the piston rod | / |

V | total volume of the hydraulic cylinder | 4$\text{}\times \text{}{10}^{-6}{\text{}\mathrm{m}}^{3}$ |

E | elastic modulus | 7$\text{}\times \text{}{10}^{8}\text{}\mathrm{pa}$ |

${C}_{s}$ | comprehensive leakage coefficient | 4.7$\text{}\times \text{}{10}^{-13}{\text{}\mathrm{m}}^{5}/\left(\mathrm{N}\xb7\mathrm{s}\right)$ |

${M}_{a}$ | mass of the piston rod | / |

${B}_{a}$ | viscous damping coefficient | / |

${K}_{a}$ | stiffness coefficient of the force sensors | / |

${x}_{d}^{\prime}$ | displacement of the sensor’s lower surface | / |

${M}_{L}$ | the mass of the concentrated mass of load | 10 kg |

${B}_{L}$ | damping coefficient load | 1 $\mathrm{N}\xb7\mathrm{s}/\mathrm{m}$ |

${K}_{L}$ | stiffness coefficient of load | ${10}^{6}\text{}\mathrm{N}/\mathrm{m}$ |

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**MDPI and ACS Style**

Shang, Y.; Bai, N.; Jiao, L.; Yao, N.; Wu, S.; Jiao, Z.
Motion Synchronous Composite Decoupling with Fewer Sensors on Multichannel Hydraulic Force Control for Aircraft Structural Loading Test System. *Sensors* **2018**, *18*, 4050.
https://doi.org/10.3390/s18114050

**AMA Style**

Shang Y, Bai N, Jiao L, Yao N, Wu S, Jiao Z.
Motion Synchronous Composite Decoupling with Fewer Sensors on Multichannel Hydraulic Force Control for Aircraft Structural Loading Test System. *Sensors*. 2018; 18(11):4050.
https://doi.org/10.3390/s18114050

**Chicago/Turabian Style**

Shang, Yaoxing, Ning Bai, Lingzhi Jiao, Nan Yao, Shuai Wu, and Zongxia Jiao.
2018. "Motion Synchronous Composite Decoupling with Fewer Sensors on Multichannel Hydraulic Force Control for Aircraft Structural Loading Test System" *Sensors* 18, no. 11: 4050.
https://doi.org/10.3390/s18114050