# An Efficient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Polymer Electrolyte Membrane Fuel Cell

_{2}and O

_{2}. In order to make a realistic expression derived from Equation (1), three main electric losses which could be classified as activation (${e}_{act}$), ohmic (${e}_{ohm}$) and concentration (${e}_{con}$) losses, are added to the Equation (1). Hence, a realistic PEMFC output voltage is expressed as Equation (2) [24,25].

#### 2.2. DC-DC Boost Converter

#### 2.3. Control Design

#### 2.3.1. PI Control

#### 2.3.2. Integral Fast Terminal Sliding Mode Control (IFTSMC)

#### 2.3.3. IFTSMC Stability Proof

#### 2.4. Digital Filter Design

#### 2.5. Description of the Test Bench

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PEMFC | polymer electrolyte membrane fuel cell |

PI | proportional-integral |

IFTSMC | integral fast terminal sliding mode control |

PEMFCs | proton exchange membrane fuel cells |

PWM | pulse width modulation |

PID | proportional-integral derivative |

FOPID | fractional-order proportional-integral-derivative |

TZTP | two-zero/three-pole |

PID-SSA | PID using slap swarm algorithm |

IRA | incremental resistance algorithm |

GAO | grey antlion optimizer |

GWM | grey wolf optimizer |

MBA | mine-blast algorithm |

FLC | fuzzy logic control |

P&O | perturb and observe |

FLC-PSO | fuzzy logic control based on particle swarm optimization |

ANFIS | adaptive neuro-fuzzy inference system |

SMC | sliding mode control |

HOSM-QC | high order sliding mode based on quasi-continuous algorithm |

HOSM-TA | high order sliding mode based on twisting algorithm |

HOSM-STA | high order sliding mode based on super-twisting algorithm |

TSMCs | terminal sliding mode controls |

DTSMC | distributed terminal sliding mode controller |

PFTC | proportional finite-time control |

PACC | proportional asymptotic convergent contro |

PIFTC | proportional-integral finite-time contro |

FTSMC | fast terminal sliding mode control |

ITSMC | integral terminal sliding mode control |

CLF | control Lyapunov function |

TDE | time delay estimation |

LHV | hydrogen lower heating value |

MOSFET | metal oxide semiconductor field effect transistor |

CCM | continuous-conduction-mode |

DCM | discontinuous-conduction-mode |

TSMC | terminal sliding mode |

DAC | digital to analog converter |

ADC | analog to digital converter |

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**Figure 10.**(

**a**): Boost converter output current; (

**b**): Boost converter output voltage; (

**c**): Boost converter output power.

Reference | Year | Controller | Converter | Features | Drawbacks |
---|---|---|---|---|---|

Ref. [12] | 2020 | PID | DC/DC buck and boost converters | - Easy to implement. - Low computational requirements. - The most common used in the industry. | - Sensitive when facing large load variation. - Inappropriate gains leads to the instability of the system. - Tuning the controller parameters is difficult. |

Ref. [13] | 2017 | FLC | DC/DC boost converter | - Easy to understand. - It simplifies implementation. - Similar to human reasoning. - Simple to extend by adding new rules. | - Human expertise is required to achieve a suitable accuracy - The system states have to be known. - It is not always accurate since the results are perceived as a guess. - Stability is not guaranteed. |

Ref. [14] | 2018 | BSTP | DC/DC boost converter | - Popular technique for high order systems. - Guaranteed stability design through Lyapunov function. - Uncertainties could be handled to a certain level. | - Complex Lyapunov function. - High design complexity - The exact mathematical model of the system is required - Sensitive to parameter variation. - Necessity of measuring all the state variables. |

Ref. [15] | 2019 | SMC | DC/DC boost converter | - Simple structure. - Easy parameter tuning. - Applicable for a wide range of nonlinear systems. - Robust to uncertainties and disturbances. - Stability is guaranteed. | - Excessive chattering effect. - Unguaranteed finite time convergence. - The trajectories are not robust against perturbations during the reaching phase. |

Ref. [17] Ref. [18] Ref. [19] | 2020 2020 2019 | QC TA STA | DC/DC boost converter | - Chattering reduction in comparison with SMC. - Finite time convergence. - Robust to parameter uncertainties and disturbances. | - Complex design. - Unable to use for first-order systems. - Precise and accurate response is not guaranteed. - Complex stability demonstration. |

Ref. [20] | 2017 | DTSMC | Voltage source converter | - Finite time convergence. - Capable of reducing the chattering. - Robust to parameter uncertainties and disturbances. | - Slow convergence speed. - Requires the knowledge of the system boundary uncertainties. - Convergence problem may occur in case if the system states move away from the equilibrium. - Problem of intrinsic singularity. |

Ref. [21] | 2016 | FTSMC | DC/AC inverter | - Finite time convergence. - Fast convergence rate. - Capable of reducing the chattering. - Robust to uncertainties and disturbances. | - Problem of intrinsic singularity. - Can not be applied to higher order systems. - The boundary information of system uncertainties is usually required to be known in advance. - Problem of intrinsic singularity. |

Ref. [22] | 2020 | ITSMC | AC/DC inverter | - Finite time convergence. - High tracking accuracy. - Robust to parameter uncertainties and disturbances. - Applicable to high order systems. | - Slow convergence rate. - Requires the knowledge of the system boundary uncertainties. - Problem of intrinsic singularity. |

FC50 Characteristics | Electrical Characteristics | ||
---|---|---|---|

Type of cell | Proton exchange membrane | Operating voltage | 2.5–9 V |

Cooling system | Ventilators | Operating current | 0–10 A |

Fuel type | Pure hydrogen | Rated. Output power | 40 Watt |

Dimensions W × H × D | 120 mm × 103 mm × 135 mm | Max. Output power | 50 Watt |

Weight | 1150 g | Open-circuit voltage | 9.0 V |

${H}_{2}$ Flow meter | ${H}_{2}$ Kit of 15 bar | ||

Precision | 0.8% of the quantified value | Inlet ${H}_{2}$ pressure | 1–15 bar |

Range of measuring | 10–1000 sml/min | Outlet ${H}_{2}$ pressure | 0.4–0.8 bar |

Thermal | ${H}_{2}$ Kit of 200 bar | ||

Operating temperature | +15– 50 ${}^{\circ}\mathrm{C}$ | Inlet ${H}_{2}$ pressure | 200 bar |

Max. Start temperature | + 45 ${}^{\circ}\mathrm{C}$ | Outlet ${H}_{2}$ pressure | 1–15 bar |

Fuel detector | ${H}_{2}$ Detector | ||

Recommended ${H}_{2}$ purity | 5 with $99.99\%$ | Type of sensors | ${H}_{2}$ 4% |

${H}_{2}$ input pressure | 0.4–8 bar (5.8–11.6 psig) | Measuring principle | 3 electrode sensor |

${H}_{2}$ consumption | Max. 700 sml/min (at $0{}^{\circ}\mathrm{C}$, 1013 bar) | Operating range | 0–4% |

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

Inductance | 6 μH |

Input capacitor | 1500 μF |

Output capacitor | 3000 μF |

Max. Switching frequency | 25,000 HZ |

Max. Input voltage | ${V}_{in}max$ = 60 V |

Max. Iput current | ${I}_{in}max$ = 30 A |

Max. Output voltage | ${V}_{out}max$ = 250 V |

Max. Output current | ${I}_{out}max$ = 30 A |

IFTSMC | PI |
---|---|

$p=1$ | ${K}_{cr}=0.04$ |

$q=3$ | ${P}_{cr}=12.08$ |

$\alpha =0.1$ | ${K}_{p}=0.02$ |

$\lambda =0.1$ | ${K}_{i}=10$ |

$k=0.5$ | − |

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**MDPI and ACS Style**

Silaa, M.Y.; Derbeli, M.; Barambones, O.; Napole, C.; Cheknane, A.; Gonzalez De Durana, J.M.
An Efficient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System. *Sustainability* **2021**, *13*, 2360.
https://doi.org/10.3390/su13042360

**AMA Style**

Silaa MY, Derbeli M, Barambones O, Napole C, Cheknane A, Gonzalez De Durana JM.
An Efficient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System. *Sustainability*. 2021; 13(4):2360.
https://doi.org/10.3390/su13042360

**Chicago/Turabian Style**

Silaa, Mohammed Yousri, Mohamed Derbeli, Oscar Barambones, Cristian Napole, Ali Cheknane, and José María Gonzalez De Durana.
2021. "An Efficient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System" *Sustainability* 13, no. 4: 2360.
https://doi.org/10.3390/su13042360