# Study on Unbalanced Magnetic Pulling Analysis and Its Control Method for Primary Helium Circulator of High-Temperature Gas-Cooled Reactor

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## Abstract

**:**

## 1. Introduction

## 2. The Mechanism of UMP in PHC-EP

#### 2.1. The Analysis of AMB in PHC-EP

#### 2.2. The Analysis of UMP in PHC-EP

#### 2.3. The Analysis of Multi-Frequency Vibration Characteristics

## 3. The Control Method for UMP

#### 3.1. Distributed ILC Algorithm

- (1)
- ${u}_{0}\left(t\right)$ is the initial control value. In this paper,$\text{}{u}_{0}\left(t\right)=0$.
- (2)
- ${\xi}_{ff}\left(k\right)$ is mainly used to improve the stability condition of the system with too fast convergence in the process of variable gain learning. It is also a kind of robust design method, to solve the problem that the identical initial conditions cannot be satisfied completely in each iteration. We set it here as the simplest inverse proportional function of$\text{}k$. Namely,$${\xi}_{ff}\left(k\right)=\frac{1}{k}$$This is an empirical approach, and it can be adjusted according to the speed of actual iteration. Further,$$\underset{k\to \infty}{\mathrm{lim}}\left(1-{\xi}_{ff}\left(k\right)\right)=1$$It can be seen from Equation (21) that as the number of iterations increases, ${u}_{k+1}\left(t\right)$ is more and more dependent on the previous$\text{}{u}_{k}\left(t\right)$.
- (3)
- ${\mathcal{L}}_{k}\left(k,t\right)$ is used to solve the problem that it is lack of real-time performance as a constant learning gain used in the algorithm; we choose a comprehensive exponential function based on $k$ and $t$ as the differential gain to achieve fast convergence of the system. Namely,$${\mathcal{L}}_{k}\left(k,t\right)={k}_{BC}\frac{1}{k}{e}^{\frac{t}{N}}$$$$\underset{k\to \infty}{\mathrm{lim}}{k}_{BC}\frac{1}{k}{e}^{\frac{t}{N}}=0$$

#### 3.2. Integrated Parallel Control Scheme

#### 3.3. Asynchronous Learning Mechanism Based on the Period of Rotation

- (1)
- The first step is to calculate the periodic component coefficients ${a}_{k}$ and ${b}_{k}$, and expressed as$$\{\begin{array}{c}{a}_{k}={\displaystyle {\displaystyle \sum}_{i=0}^{N-1}}{e}_{k}\left[i\right]\mathrm{cos}\left(\frac{4\pi i}{N}\right)\\ {b}_{k}={\displaystyle {\displaystyle \sum}_{i=0}^{N-1}}{e}_{k}\left[i\right]\mathrm{sin}\left(\frac{4\pi i}{N}\right)\end{array}$$
- (2)
- The second step is to synthesize periodic vibrations$\text{}\tilde{{e}_{k}}\left[i\right]$ as expressed below:$$\tilde{{e}_{k}}\left[i\right]|\begin{array}{c}N-1\\ i=0\end{array}=\frac{2}{N}\left({a}_{k}\mathrm{cos}\left(\frac{4\pi i}{N}\right)+{b}_{k}\mathrm{sin}\left(\frac{4\pi i}{N}\right)\right)$$$$\tilde{{e}_{k}}\left[i\right]|\begin{array}{c}N-1\\ i=0\end{array}={A}_{k}\mathrm{cos}(\frac{4\pi i}{N}-\theta )$$$$\{\begin{array}{c}{A}_{k}=\frac{2}{N}\sqrt{{a}_{k}{}^{2}+{b}_{k}{}^{2}}\\ tan\theta =\frac{{b}_{k}}{{a}_{k}}\end{array}$$

## 4. Experimental Research on Control Method

#### 4.1. Experimental System Design

#### 4.2. Experimental Results Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The structure of primary helium circulator (PHC) engineering prototype (PHC-EP) [12]. 1. Cooling fan; 2. upper auxiliary bearing; 3. axial thrust active magnetic bearing (AMB); 4. upper displacement sensor; 5. upper radial AMB; 6. asynchronous motor; 7. lower radial AMB; 8. lower displacement sensor; 9. lower auxiliary bearing; 10. rotor; 11. Wheel.

**Figure 7.**The integrated parallel control system of four radial directions in the AMB bench of PHC-EP.

**Figure 11.**The AMB rotor’s axis loci of the places’ installed displacement sensors with and without the ILC.

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

Rotor mass with impeller | 4 000 kg |

Rated speed | 4 000$\text{}r/m$ ($f\approx 66.7\text{}\mathrm{Hz}$) |

Motor Type | Three phase induction ($p=1$) |

AMB control method | Distributed control |

Operation mode | Constant speed |

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**MDPI and ACS Style**

Zheng, Y.; Mo, N.; Sun, Z.; Zhou, Y.; Shi, Z.
Study on Unbalanced Magnetic Pulling Analysis and Its Control Method for Primary Helium Circulator of High-Temperature Gas-Cooled Reactor. *Energies* **2019**, *12*, 3682.
https://doi.org/10.3390/en12193682

**AMA Style**

Zheng Y, Mo N, Sun Z, Zhou Y, Shi Z.
Study on Unbalanced Magnetic Pulling Analysis and Its Control Method for Primary Helium Circulator of High-Temperature Gas-Cooled Reactor. *Energies*. 2019; 12(19):3682.
https://doi.org/10.3390/en12193682

**Chicago/Turabian Style**

Zheng, Yangbo, Ni Mo, Zhe Sun, Yan Zhou, and Zhengang Shi.
2019. "Study on Unbalanced Magnetic Pulling Analysis and Its Control Method for Primary Helium Circulator of High-Temperature Gas-Cooled Reactor" *Energies* 12, no. 19: 3682.
https://doi.org/10.3390/en12193682