# Model-Predictive-Control-Based Reference Governor for Fuel Cells in Automotive Application Compared with Performance from a Real Vehicle

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## Abstract

**:**

## 1. Introduction

## 2. Vehicle as Validation Data Generator

#### Vehicle Control Strategy

- Tuning the controllers: it takes a lot of time, especially since decoupling has to be achieved and antiwindup schemes implemented. Further, the number of controllers to be tuned is high.
- Experimental work: to relate the requested power to the current, and then the current to all the other variables, the system has to be identified and a series of experiments with different levels of excitation at multiple operating points need to be conducted. This obviously includes a significant financial investment.
- Recalibration: in the case that a component is replaced (e.g., new compressor), the calibration process has to be repeated to some degree.

## 3. Methods

#### 3.1. Plant Model

#### 3.1.1. Cathode Submodel

#### 3.1.2. Anode Submodel

#### 3.1.3. GDL Submodel

#### 3.1.4. Power and Efficiency

#### 3.1.5. Surge and Choke Margin

#### 3.1.6. Plant Model Summary

#### 3.2. Prediction Model

#### 3.3. Successive Linearization

#### 3.4. MPC Formulation

#### 3.5. Objective Formulation

- System net power—the reference is taken from the vehicle in Section 2.
- System efficiency—the reference value is 1.
- Pressure difference across the membrane—the reference value is 200 mbar.
- Distance from optimal line in the compressor map—the reference value is 0.

#### 3.6. Constraints

## 4. Results and Discussion

#### 4.1. Simulation Results

#### 4.2. Benefits and Possible Applications of RG-MPC

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FC | Fuel cell |

PEM | Polymer electrolyte membrane |

MPC | Model predictive controller |

RG-MPC | Reference governor model predictive controller |

PI | Proportional-integral |

PID | Proportional-integral-derivative |

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**Figure 1.**Reference governor model predictive control (MPC) schematics. RG—reference governor; PI—proportional-integral.

**Figure 5.**Compressor map. The vicinity of the dashed line is chosen as the desired operation region.

**Figure 6.**Successive linearization concept. The system function

**f**(

**x**) is linearized around the state vector

**x**(t) at every time step. The linearized system is used to develop the MPC at that time step.

**Figure 10.**(

**a**) Pressure difference across the membrane, (

**b**) hydrogen inlet mass-flow, (

**c**) cathode backpressure valve.

**Figure 12.**Advantages of using the RG-MPC as a tool for generating optimization maps. PID—proportional-integral-derivative.

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**MDPI and ACS Style**

Vrlić, M.; Ritzberger, D.; Jakubek, S. Model-Predictive-Control-Based Reference Governor for Fuel Cells in Automotive Application Compared with Performance from a Real Vehicle. *Energies* **2021**, *14*, 2206.
https://doi.org/10.3390/en14082206

**AMA Style**

Vrlić M, Ritzberger D, Jakubek S. Model-Predictive-Control-Based Reference Governor for Fuel Cells in Automotive Application Compared with Performance from a Real Vehicle. *Energies*. 2021; 14(8):2206.
https://doi.org/10.3390/en14082206

**Chicago/Turabian Style**

Vrlić, Martin, Daniel Ritzberger, and Stefan Jakubek. 2021. "Model-Predictive-Control-Based Reference Governor for Fuel Cells in Automotive Application Compared with Performance from a Real Vehicle" *Energies* 14, no. 8: 2206.
https://doi.org/10.3390/en14082206