# Study of a Control Algorithm with the Disturbance of Massive Discharge on an Open Channel

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Construction of Hydraulic Simulation Model

#### 2.1. Governing Equation

**Z**is the water level of the section in m;

**B**is the width of the water-passing section in m;

**h**is the water depth of the section in m;

**Q**is the flow rate of the section in m

^{3}/s;

**x**is the space coordinate,

**t**is the time coordinate,

**q**is the inflow from the side of the channel per unit length, in m

^{3}/s;

**A**is the area of the water-passing section in m

^{2};

**g**is the acceleration due to gravity in m/s

^{2}; S

_{0}is channel specific drop,

**R**is the hydraulic gradient, in m; and

**S**is the friction-resistance ratio drop. The Equation is as follows:

_{f}#### 2.2. Inner Boundary Handling

^{3}/s;$\text{}{\mathit{C}}_{\mathit{d}}$ is the gate flow coefficient, $\mathit{u}$ is the gate opening, $\mathit{b}\text{}$is the bottom width of the gate, in m; and $\Delta \mathit{h}$ is the difference between the water level before and after the control gate, in m.

#### 2.3. Water Divider Generalization

## 3. Control Algorithm in the Case of Large Flow Diversion Disturbance

#### 3.1. Stepwise Storage Compensation Algorithm

#### Traditional Storage Compensation Algorithm

#### 3.2. Improved PID Control Algorithm

#### 3.2.1. Traditional PID Control Algorithm

#### 3.2.2. Improved PID Control Algorithm

#### 3.3. Storage Compensation Algorithm and Non-Linear PID Control Algorithm

## 4. Conclusions

^{3}/s to 20 m

^{3}/s in two hours (Figure 8). A tube head of the bleeder suddenly occurs after 24 h of the water disturbance event. The traditional storage quantity compensation algorithm and the coupling storage amount of compensation of the non-linear PID control algorithm of the two different algorithms respond to the canal pool overall water level disturbance and the middle pipe head bleeder from the large flow bleeder water distribution.

^{3}/s, and the upstream area has a fixed water depth boundary with a water depth of 3 m. The duration of the hydrodynamic simulation is 3 days, and the calculated time step is 3600 s. The boundary settings are shown in Figure 9.

#### 4.1. Analysis of Control Results of Traditional Storage Compensation Algorithm

^{3}/s to 20 m

^{3}/s over a 2 h period in the 24 h. To ensure the stability of the water level in front of the sluice when water diversion occurs, the channel pool can be regulated in advance with the method of storage volume compensation.

#### 4.2. Analysis of the Results of the Storage Compensation and Improved PID Coupling Control Algorithm

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Channel Number | Gate | Length (km) | Discharge (m^{3}/s) | Water Depth (m) | Outflow (m ^{3}/s) | Roughness | Canal Bottom Elevation | ||
---|---|---|---|---|---|---|---|---|---|

Up | Down | Up (m) | Down (m) | ||||||

1 | Guyunhe gate | Hutuohe Gate | 9.87 | 43 | 3.3 | 0 | 0.023 | 70.40 | 69.86 |

2 | Hutuohe Gate | Cihe Gate | 22.03 | 43 | 3.21 | 0 | 0.023 | 69.86 | 69.13 |

3 | Cihe Gate | Shahebei Gate | 15.21 | 43 | 3.03 | 0 | 0.023 | 69.13 | 68.36 |

4 | Shahebei Gate | Modaogou Gate | 19.73 | 13 | 3 | 20 | 0.023 | 68.36 | 66.70 |

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**MDPI and ACS Style**

Shen, J.; Kang, B.; Tao, Y.; Lin, F.; Song, X.
Study of a Control Algorithm with the Disturbance of Massive Discharge on an Open Channel. *Water* **2022**, *14*, 3252.
https://doi.org/10.3390/w14203252

**AMA Style**

Shen J, Kang B, Tao Y, Lin F, Song X.
Study of a Control Algorithm with the Disturbance of Massive Discharge on an Open Channel. *Water*. 2022; 14(20):3252.
https://doi.org/10.3390/w14203252

**Chicago/Turabian Style**

Shen, Jian, Bo Kang, Yuezan Tao, Fei Lin, and Xuegong Song.
2022. "Study of a Control Algorithm with the Disturbance of Massive Discharge on an Open Channel" *Water* 14, no. 20: 3252.
https://doi.org/10.3390/w14203252