# The Driving Waveform Design Method of Power-Law Fluid Piezoelectric Printing Based on Iterative Learning Control

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## Abstract

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## 1. Introduction

## 2. Model Modification and Parameter Estimation

_{e}(t) is the driving waveform, e is the conversion coefficient of the inverse piezoelectric effects [18], ${\rho}_{0}$ is the origin density, c is the sound velocity in fluid, and ${l}_{p}\pi \left[{V}_{e}{\left(t\right)}^{2}{e}^{2}-2{r}_{0}{V}_{e}\left(t\right)e\right]$ is the volume change $\Delta V$. Equation (1) means the driving waveform is a part of a system state parameter, making it not convenient to design the controlling method. The model needs to be modified, and it is necessary to convert the driving waveform into system state variables such as electric current or voltage. The change in pipe diameter caused by the driving waveform is so tiny that the volume change $\Delta V$ could be simplified as follows:

## 3. Iterative Learning Method

## 4. Results and Discussion

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 5.**Viscosities of xanthan gum solution and DI water. The measured values are marked by symbols. The fitting curves are marked by solid lines.

**Figure 10.**Comparison of xanthan gum solution CFD result and experimental result at the condition of the origin driving waveform.

**Figure 13.**Comparison of xanthan gum solution CFD result and experimental result at the condition of the modified driving waveform.

Length (mm) | ${\mathit{l}}_{1}$ | ${\mathit{l}}_{2}$ | ${\mathit{l}}_{3}$ | ${\mathit{l}}_{4}$ | ${\mathit{r}}_{0}$ | ${\mathit{r}}_{\mathit{a}}$ |
---|---|---|---|---|---|---|

8.87 | 8.2 | 4.71 | 1 | 0.235 | 0.04 |

${\mathit{V}}_{\mathit{a}}\left(\mathbf{v}\right)$ | ${\mathit{t}}_{\mathit{u}}\left(\mathsf{\mu}\mathbf{s}\right)$ | ${\mathit{t}}_{\mathit{w}}\left(\mathsf{\mu}\mathbf{s}\right)$ | ${\mathit{t}}_{\mathit{d}}\left(\mathsf{\mu}\mathbf{s}\right)$ | |
---|---|---|---|---|

$\mathrm{xanthan}\text{}\mathrm{gum}\text{}0.2\text{}\mathrm{g}/\mathrm{L}$ | 26 | 3 | 18 | 3 |

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**MDPI and ACS Style**

Peng, J.; Huang, J.; Wang, J.; Meng, F.; Gong, H.; Ping, B.
The Driving Waveform Design Method of Power-Law Fluid Piezoelectric Printing Based on Iterative Learning Control. *Sensors* **2022**, *22*, 935.
https://doi.org/10.3390/s22030935

**AMA Style**

Peng J, Huang J, Wang J, Meng F, Gong H, Ping B.
The Driving Waveform Design Method of Power-Law Fluid Piezoelectric Printing Based on Iterative Learning Control. *Sensors*. 2022; 22(3):935.
https://doi.org/10.3390/s22030935

**Chicago/Turabian Style**

Peng, Ju, Jin Huang, Jianjun Wang, Fanbo Meng, Hongxiao Gong, and Bu Ping.
2022. "The Driving Waveform Design Method of Power-Law Fluid Piezoelectric Printing Based on Iterative Learning Control" *Sensors* 22, no. 3: 935.
https://doi.org/10.3390/s22030935