# Design and Stability Analysis of a Digital Automatic Power Control Based on a PI Controller for Laser Drivers

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## Abstract

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## 1. Introduction

## 2. Theoretical Design of the PI Controller

## 3. Numerical Results and Design Restriction

## 4. Experimental Setup

## 5. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison between the numerical controller and theoretical system response with operating parameters of $\eta {K}_{p}$ = 0.3, ${T}_{i}$ = 5${T}_{s}$, and ${y}_{sp}$ = 10 for (

**a**) system output. (

**b**) Zoom of differences between the theoretical and numerical output.

**Figure 4.**Numerical analysis of the system output for various total gains and ${y}_{0}$ = 4, ${T}_{i}$ = 5${T}_{s}$, and ${y}_{sp}$ = 10 as fixed system parameters.

**Figure 5.**Convergence analysis of the system output at the stability limit conditions (${T}_{i}={T}_{s}/2$, and $\eta {K}_{p}=1$) for numerical controllers by (

**a**) Riemann’s rule, (

**b**) the trapezoid method and (

**c**) Simpson’s rule and ${y}_{0}=2$, ${y}_{sp}=10$ as fixed parameters of the system.

**Figure 8.**The linear experimental relationship between the control signal (current supply) and signal actuator (potentiometer positions) at varying operating temperatures.

**Figure 9.**Calibration of trans-impedance amplifier signal from probing photodiode using emitted optical power measured with a Newport Model 840-C at varying operating temperatures.

**Figure 10.**Experimental laser diode emission curve for a ADL-65052TL at different operating temperatures.

**Figure 11.**Comparison of the experimental and theoretical output of the system for a total gain of ${\hat{K}}_{p}\approx $ 0.64 and an integral time of ${T}_{i}$ = 1 for an operating temperature of 20 °C.

**Figure 12.**Comparison of the theoretical and experimental control signal for a total gain of ${\hat{K}}_{p}\approx $ 0.64 and an integral time of ${T}_{i}$ = 1 for an operating temperature of 20 °C.

**Figure 13.**Theoretical and experimental responses of the system output on the stimulated emission zone for ${\hat{K}}_{p}\approx 0.64$ and ${T}_{i}=1$.

**Figure 14.**Theoretical and experimental control signals on the stimulated emission zone for ${\hat{K}}_{p}\approx 0.64$, ${T}_{i}=1$ and ${u}_{0}={T}_{i}\left(\right)open="("\; close=")">{I}_{th}/{K}_{p}-{y}_{sp}$.

**Figure 15.**Experimental response of the system for the constant theoretical output condition with system parameters defined by ${\hat{K}}_{p}\approx 0.64$, ${T}_{i}=1$ and ${u}_{0}={T}_{i}\left(\right)open="("\; close=")">{y}_{sp}+\eta {I}_{th}$.

**Figure 16.**Image of the laser inside the thermal vacuum chamber (NDT-4000, Nanomaster) during the performance test.

**Figure 17.**The laser was evaluated under space conditions. The reached pressure was $9\times {10}^{-7}$ Torr with the operating temperature varying at a rate of ∼0.9 °C/min. Performance testing was realized by using a thermal vacuum chamber (NDT-4000 from Nanomaster) to emulate the low-Earth orbit conditions. Subplot (

**a**) shows the temporal evolution of the output optical power (blue line) and the temperature (orange line) measured by a SHT31 temperature sensor attached close to the laser. Subplot (

**b**) shows a close-up of the region where the temperature and optical power are dropping from ∼21 °C to ∼17 °C and ∼3 mW ± 2%, respectively.

**Figure 18.**Robustness of the experimental system output (

**a**) for different $\eta {K}_{p}$ from 0.03 to 0.64, ${T}_{i}=1$ s and ${y}_{sp}=3.4$ mW, under thermal disturbances (

**b**).

**Table 1.**A comparison and summary of the main characteristics of the laser controllers cited in the article.

Manufacturer/Authors | Laser Operating Condition | Optical Power Instabilities | Features |
---|---|---|---|

Huang et al. [11] | constant temperature | 2% at maximum | APC, constant current control, constant temperature chamber, and Neural Based PI Controller for power stability. |

Temel et al. [14] | not reported | average of 1.2% | Temperature robust current driver circuit. |

Zhao et al. [15] | constant temperature | not reported | Constant-Current Driver Circuit, and high-precision Temperature Fuzzy PID Controller. |

Ilchev et al. [17] | not reported | not reported | Compact laser driver, current feedback control circuit, thermal protection for laser overheating. |

Zivojinovic et al. [19] | not reported | not applicable | APC, CMOS Integrated inverted driver circuit, designed and tested for communication systems (<100 MHz). |

Huan et al. [20] | not reported | not applicable | Fast APC, designed and tested for communication systems (<1.2 Gb/s). |

Our Laser Driver | different constant temperature during slow thermal instabilities | 0.40% at maximum, and average of 0.14% 1.3% at maximum, and average of 0.41% | APC, laser driver based on PI controller implemented in a low-cost SOC. |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pedreros, J.; Becerra, A.; Rojas, J.; Pavez, C.; Diaz, M.
Design and Stability Analysis of a Digital Automatic Power Control Based on a PI Controller for Laser Drivers. *Machines* **2023**, *11*, 516.
https://doi.org/10.3390/machines11050516

**AMA Style**

Pedreros J, Becerra A, Rojas J, Pavez C, Diaz M.
Design and Stability Analysis of a Digital Automatic Power Control Based on a PI Controller for Laser Drivers. *Machines*. 2023; 11(5):516.
https://doi.org/10.3390/machines11050516

**Chicago/Turabian Style**

Pedreros, Jose, Alex Becerra, Javier Rojas, Cristian Pavez, and Marcos Diaz.
2023. "Design and Stability Analysis of a Digital Automatic Power Control Based on a PI Controller for Laser Drivers" *Machines* 11, no. 5: 516.
https://doi.org/10.3390/machines11050516