# Operator-Based Triboelectric Nanogenerator Power Management and Output Voltage Control

^{*}

## Abstract

**:**

## 1. Introduction

^{−2}, volume power density 15 MW m

^{−3}, and instantaneous conversion efficiency approximately $70\%$ [2]. TENGs have garnered significant attention due to their high efficiency, cost-effectiveness, and adaptability, making them suitable for a wide range of applications [3,4].

## 2. TENG Modeling

#### 2.1. TENG Model and Analysis of Its Circuit Equation

^{−2}, which allows the TENG to generate a significant amount of charge during mechanical motion.

#### 2.2. TENG Simulation Model and Analysis of Its Circuit Equation

## 3. Proposed TENG’s System and Control

#### 3.1. TENG’s System

#### 3.1.1. TENG’s PMU with Storage Capacitor Array

#### 3.1.2. TENG’s DC-DC Converter Structure

#### 3.2. TENG’s System Control

#### 3.2.1. Operator-Based TENG System Decomposition

- -
- A implements the mapping from output y to feedback b. Here, b is constructed as $\frac{1}{10}}w$, residing in the same space as w, yielding (29).
- -
- ${B}^{-1}$ implements the mapping from error e to input u. Given that b is structured in the same space as w, e is also designed to reside in this space, specifically $e={\displaystyle \frac{9}{10}}w$, resulting in (30). The construction of B is represented as per the formula, facilitating the mapping from u to e.

#### 3.2.2. Plant Tracking Designed for Reference

#### 3.2.3. Plant Suppression Designed for Uncertainty

## 4. Simulation and Verification

#### 4.1. Simulation of TENG Model

#### 4.2. Simulation of Tracking for Reference

#### 4.3. Simulation of Suppression for Uncertainty

## 5. Conclusions

- The buck model in DCM is a nonlinear system model with parameters including inductance, capacitance, duty cycle, input voltage, and output voltage. The multi-parameter nature of the model suggests that the control algorithms will be complex, leading to the need for research on output tracking and disturbance suppression based on this model.
- This paper applies the RCF method to the buck model, resulting in a simplified tracking compensator. Based on this, a more complex disturbance suppression algorithm is developed using operator theory and validated through simulations, with favorable results. In practical applications, as shown in Figure 18, $P+\Delta P$ represents the actual buck circuit, while other parts of the algorithm are based on the buck model (including parameters). By sampling the output voltage and input voltage parameters of $P+\Delta P$, the algorithm can compute the duty signal. This is because the algorithm has already accounted for the effects of device parameter fluctuations (disturbance sources) within the buck circuit, eliminating the need to focus on parameter variations. This design is characterized by its low dependency on the controlled object and high feasibility.
- Given that TENGs are low-energy-output systems, future research should focus on how to effectively leverage the system’s self-power capability to run the algorithm (based on the controller) while minimizing energy loss and improving the system’s energy utilization efficiency.

- Parasitic parameters and model reconstruction: The mathematical model of the buck converter circuit will be reconstructed to include parasitic parameters of key components such as diodes, inductors, capacitors, resistors, and switches. The uncertainty sources will be expanded to encompass these parasitic parameters. Suppression of such uncertainties will be achieved through compensator design based on operator theory.
- Storage capacitor array model: The design and validation of the storage capacitor array model will be further refined. Testing will be conducted on an experimental platform integrated with the TENG system to ensure that the model accurately reflects real-world performance.
- Comprehensive system modeling: A detailed mathematical model of the external mechanical vibration source for the TENG will be developed and integrated with the TENG and power system models to create a comprehensive system. Research will focus on the efficient conversion of mechanical vibration energy into electrical energy based on this integrated model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**The TENG’s storage capacitor voltage waveform increases when charged (where capacitor value is 220 uF). (

**a**) Capacitor voltage increase with time; unit: seconds. (

**b**) Capacitor voltage increase with time; unit: 0.05 s. (

**c**) Rectified current from TENG with time; unit: seconds. (

**d**) Rectified current from TENG with time; unit: 0.05 s.

**Figure 12.**Buck converter DCM in a PWM period. (

**a**) The definitions of ${D}_{a}$, ${D}_{b}$, and ${D}_{c}$’s intervals according to the current state. (

**b**) ${D}_{a}$, ${D}_{b}$, and ${D}_{c}$’s intervals expressed in a PWM period. (

**c**) The circuit states of ${D}_{a}$, ${D}_{b}$, and ${D}_{c}$.

**Figure 20.**TENG’s $RC$ ($C=10\phantom{\rule{0.166667em}{0ex}}$uf, $R=10\phantom{\rule{0.166667em}{0ex}}$k$\Omega $, $R=100\phantom{\rule{0.166667em}{0ex}}$k$\Omega $) load with rectifier simulation verification.

**Figure 21.**TENG’s $RC$ ($C=10\phantom{\rule{0.166667em}{0ex}}$uf, $C=100\phantom{\rule{0.166667em}{0ex}}$uf, $R=100\phantom{\rule{0.166667em}{0ex}}$k$\Omega $) load with rectifier simulation verification.

**Figure 22.**Tracking Vref as $4\phantom{\rule{0.166667em}{0ex}}V$. (

**a**) is input voltage source with fluctuation between 10 V and 40 V. (

**b**) is the output voltage (${V}_{out}$) without tracking control. (

**c**) is the ${V}_{out}$ with tracking control.

**Figure 24.**Tracking Vref as $3\phantom{\rule{0.166667em}{0ex}}$V, $4\phantom{\rule{0.166667em}{0ex}}$V, $5\phantom{\rule{0.166667em}{0ex}}$V.

**Figure 26.**Output voltage with $L\pm \Delta L\phantom{\rule{3.33333pt}{0ex}}\left(2\mathrm{uH}\right)$.

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

Dielectric thickness | ${d}_{1}$ | 125 um |

Air dielectric constant | ${\u03f5}_{0}$ | 8.85 $\ast \phantom{\rule{0.166667em}{0ex}}{10}^{-12}\phantom{\rule{0.166667em}{0ex}}$ F/m |

Relative dielectric constant | ${\u03f5}_{1}$ | 3.4 |

Effective dielectric thickness | ${d}_{0}$ | ${d}_{0}={d}_{1}/{\u03f5}_{1}=36.76\phantom{\rule{0.166667em}{0ex}}$um |

Width of dielectric | W | $0.25\phantom{\rule{0.166667em}{0ex}}$m |

Length of dielectric | L | $0.25\phantom{\rule{0.166667em}{0ex}}$m |

Area of dielectric | S | $S=W\ast L=0.0625\phantom{\rule{0.166667em}{0ex}}$m^{2} |

Surface triboelectric charge density | $\sigma $ | 140 uCm^{−2} |

Maximum separation distance | ${x}_{max}$ | 0.002 m |

Average velocity of mechanical motion | v | 0.133 ms^{−1} |

1 | State Definition |
---|---|

Discharge state | Storage capacitor is used as power source for DC-DC converter |

Charge state | Storage capacitor is charged by TENG |

Isolation state | Storage capacitor is not charged and not used as power source |

2 | Condition Definition |

Condition 1 | ${V}_{c}<{V}_{c}\left(min\right)$ and TENG is busy |

Condition 2 | ${V}_{c}\ge {V}_{c}\left(max\right)$ and power source is vacancy |

Condition 3 | ${V}_{c}<{V}_{c}\left(min\right)$ and TENG is idle |

Condition 4 | ${V}_{c}\ge {V}_{c}\left(max\right)$ and power source is vacancy |

Condition 5 | ${V}_{c}\ge {V}_{c}\left(max\right)$ and power source is available |

Condition 6 | ${V}_{c}<{V}_{c}\left(min\right)$ and TENG is idle |

ine Condition 7 | ${V}_{c}<{V}_{c}\left(max\right)$ |

Condition 8 | Power source is available and TENG is busy |

Condition 9 | ${V}_{c}\ge {V}_{c}\left(min\right)$ |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Inductor value | ${L}_{b}$ | 5 | uH |

Capacitor value | ${C}_{b}$ | 1 | uF |

Period of PWM | ${T}_{s}$ | 1 | us |

Resistor load | ${R}_{load}$ | 100 K | $\Omega $ |

Voltage of output | ${V}_{out}$ | 4 | V |

Voltage of input | ${V}_{in}$ | See Figure 13 | V |

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**MDPI and ACS Style**

Liu, C.; Shimane, R.; Deng, M.
Operator-Based Triboelectric Nanogenerator Power Management and Output Voltage Control. *Micromachines* **2024**, *15*, 1114.
https://doi.org/10.3390/mi15091114

**AMA Style**

Liu C, Shimane R, Deng M.
Operator-Based Triboelectric Nanogenerator Power Management and Output Voltage Control. *Micromachines*. 2024; 15(9):1114.
https://doi.org/10.3390/mi15091114

**Chicago/Turabian Style**

Liu, Chengyao, Ryusei Shimane, and Mingcong Deng.
2024. "Operator-Based Triboelectric Nanogenerator Power Management and Output Voltage Control" *Micromachines* 15, no. 9: 1114.
https://doi.org/10.3390/mi15091114