# Multidimensional Interpolation Decoupling Strategy for CD Basis Weight of Papermaking Process

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}was implemented in an actual project in a paper mill.

## 1. Introduction

## 2. Experimental

#### 2.1. Materials

#### 2.2. Measuring Method of the Process Data

## 3. Modeling and Block Decomposition of CD Control System

#### 3.1. Modeling of CD Control System

#### 3.2. Identification of Coupling Matrix

#### 3.3. Block and Decomposition Control of Coupling Matrix

#### 3.3.1. Coupling Matrix Blocking

#### 3.3.2. Decomposition Algorithm Control

## 4. Interpolation Decoupling Strategy for CD Control System

## 5. Results of Simulation and Application

^{2}was implemented in an actual project of a paper mill.

^{2}, and the allowable basis weight fluctuation range is $\pm 7$ g/m

^{2}. In order to reduce the pulp consumption in the paper production process, the actual project stabilizes the paper basis weight at 133 g/m

^{2}for automatic control. Based on the criterion of equal basis weight in each region, the following model is established.

^{2}, the dilution valves are controlled by the S7-300 PLC. When the working condition is stable, a monitoring picture of a certain period is shown in Figure 21, and 50 scanning points are measured randomly. The basis weight deviation curve is shown in Figure 22. It can be seen that the fluctuation deviation is small, so that the algorithm is proven to be very practical.

## 6. Conclusions

## Supplementary Materials

Supplementary File 1## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Time | $\mathbf{Control}\text{}\mathbf{Input}\text{}{\mathit{u}}_{1}$ | $\mathbf{Control}\text{}\mathbf{Input}\text{}{\mathit{u}}_{2}$ | $\cdots $ | $\mathbf{Control}\text{}\mathbf{Input}\text{}{\mathit{u}}_{\mathit{q}-1}$ | $\mathbf{Control}\text{}\mathbf{Input}\text{}{\mathit{u}}_{\mathit{q}}$ |
---|---|---|---|---|---|

$t$ | ${\left[{u}_{1,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{p,}0,\cdots ,0\right]}^{T}$ | $\cdots $ | ${\left[{u}_{1,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{p,}0,\cdots ,0\right]}^{T}$ |

$t+1$ | ${\left[0,{u}_{2,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{p+1,}0,\cdots ,0\right]}^{T}$ | $\cdots $ | ${\left[0,{u}_{2,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{p+1,}0,\cdots ,0\right]}^{T}$ |

$\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ |

$t+p+1$ | ${\left[0,\cdots ,0,{u}_{p,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{2p+1}\right]}^{T}$ | $\cdots $ | ${\left[0,\cdots ,0,{u}_{p,}0,\cdots ,0\right]}^{T}$ | ${\left[0,\cdots ,0,{u}_{2p+1}\right]}^{T}$ |

$\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ |

$t+2p+1$ | ${\left[0,\cdots ,0,{u}_{2p+1}\right]}^{T}$ | ${\left[{u}_{1,}0,\cdots ,0\right]}^{T}$ | $\cdots $ | ${\left[0,\cdots ,0,{u}_{2p+1}\right]}^{T}$ | ${\left[{u}_{1,}0,\cdots ,0\right]}^{T}$ |

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**MDPI and ACS Style**

Shan, W.; Liu, B. Multidimensional Interpolation Decoupling Strategy for CD Basis Weight of Papermaking Process. *Symmetry* **2020**, *12*, 149.
https://doi.org/10.3390/sym12010149

**AMA Style**

Shan W, Liu B. Multidimensional Interpolation Decoupling Strategy for CD Basis Weight of Papermaking Process. *Symmetry*. 2020; 12(1):149.
https://doi.org/10.3390/sym12010149

**Chicago/Turabian Style**

Shan, Wenjuan, and Bing Liu. 2020. "Multidimensional Interpolation Decoupling Strategy for CD Basis Weight of Papermaking Process" *Symmetry* 12, no. 1: 149.
https://doi.org/10.3390/sym12010149