High-Performance Tracking for Proton Exchange Membrane Fuel Cell System PEMFC Using Model Predictive Control
Abstract
:1. Introduction
2. Materials and Methods
2.1. Hardware Description
- PEM FC50: The technical data of the PEM FC50 are described in Table 2. The fuel stack is supplied by hydrogen through a metal hydride storage cylinder 60 SL, which is connected to the manometer that decreases the pressure. The stack contains 10 cells stacked in series and generates a rated power of 40 W.
- DC–DC boost converter: The power converter used in the test bench is constructed by the TEP-192-Research Group of Huelva University. Unlike the commercial converters, this boost converter offers a PWM control input where the controller could be designed via the user. It is characterized by an IGBT transistor with an input switching frequency equal to 20 kHz; the maximum input voltage and current are, respectively, equal to 60 V and 30 A with an accuracy of ; while, the maximum output voltage and current are around 250 V and 30 A.
- MicroLabBox dSPACE DS1202: The dSPACE-DS1202 is an effective device for fast control systems due to its high performance when turning the theoretical design into a real-time experiment. The device includes more than 100 various type of input/output channels with a dual core processor and independent co-processor that manages host PC communication. By adding the library of real-time implementation (RTI) in a Simulink–Matlab interface, it allows the use of the basic toolboxes in order to configure all the I/O sensors as well as the PWM signal required for controlling the system. Then, a generated C code will be sent to the MicroLabBox by the RTI when compiling the Simulink model. Hence, a PWM pulse is produced using the converted code given by the MicroLabBox. The control desk software is used for creating an interface with the graphical user interface (GUI), which allows to visualize and observe the online evolution of the obtained signals with clear figures that make the online evaluation of the different parameter changes easier and faster.
- Electronic programmable load: The characteristics of the electronic programmable load used in this work are described in Table 3. The experimental tests were carried out under an abrupt change of the load resistance through an electronic programmable load BK 8500B. The latter is used instead of the classical manual sliding resistive load since the programmable device cloud provides considerable advantages such as generating a list of resistance waveform sequence with speed, accurate values and high resolution in real-time.
2.2. Control Design
- Modeling the power converter and determining its state-space model.
- Obtaining the discrete time state-space model that allows the prediction of the future behavior.
- Defining the cost function J that represents the desired behavior of the system.
- Determining the MPC control law that minimizes the cost function J.
- The first one is to evaluate the cost function at each step (sampling time). For instance, by taking the example presented in Figure 6 where the performed switching actions are indicated with the bold black line; at first, when the sampling time is , the controller has to choose between and , where the choice is based on the most preferred switching condition that leads to minimizing the cost function J. Since is selected in this example, it means that the predicted controlled variable that corresponds to is the closest to the desired reference . Following the same criterion for the two-step horizon at which the sampling time is , the controller will decide between and . Since is selected, then, the cost function is performed and considered as the cost function of the previous step at the sampling time . However, despite the simplicity of this strategy, it may fall in a local lower cost function since the cost functions and that, respectively, correspond to the switching states and , were not evaluated.
- The second strategy is to evaluate the cost functions of all the sets of switching states given in Equation (15), and finally, the lowest cost function is performed. The performed switching actions using this method are indicated with the bold blue line. The main feature of this method is its capability to calculate the global lower cost function for the two-step horizon. Therefore, a new cost function for the two-step prediction horizon is defined in Equation (16). The latter is composed of the error at the sampling time plus the error at the sampling time .
2.3. Performance Metrics Used
3. Results
Performance Metrics Comparison
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Abbreviations
PEM | polymer electrolyte membrane |
PEMFC | polymer electrolyte membrane fuel cell |
MPC | model predictive control |
PI | proportional-integral |
PD | proportional derivative |
PID | proportional integral derivative |
FOPID | fractional order PID |
FSBB | four-switch buck-boost |
TZTP | two-zero/three-pole |
PID-SSA | PID based slap swarm algorithm |
IRA | incremental resistance algorithm |
MBA | mine-blast algorithm |
GWM | grey wolf optimizer |
P&O | perturb and observe |
FLC | fuzzy logic control |
FLC-PSO | FLC based on particle swarm optimization |
ANFIS | adaptive neuro-fuzzy inference system |
NNA | neural network algorithm |
GA | genetic algorithm |
IC | incremental conductance |
PSO | particle swarm optimization |
ACO | ant colony optimization |
DE | differential evolution |
SMC | sliding mode control |
IFTSMC | integral fast terminal sliding mode control |
BSMC | back-stepping sliding mode control |
TA | twisting algorithm |
STA | super-twisting algorithm |
PCL | prescribed convergence law |
QC | quasi-continuous algorithm |
MPPT | maximum power point tracking |
EKF | extended Kalman filter |
PWM | pulse width modulation |
IAE | integral of the absolute error |
RMSE | root mean square error |
RRMSE | relative root mean square error |
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Reference | Year | Controller | Converter | Features | Drawbacks |
---|---|---|---|---|---|
Ref. [8] Ref. [9] Ref. [10] | 2017 2014 2020 | PI PD PID | Boost converter - Buck-boost converter | - Less energy consumption. - Simplicity of implementation - Frequently used in the industry. - Low computational requirements. | - Sensitive against large load variation. - Inappropriate control parameters leads to the system instability. - Not proper for non-linear systems. - Parameters setting is difficult. |
Ref. [11] | 2020 | FOPID | FSBB | - High robustness in comparison with PID. - Less energy consumption. | - Complex implementation. - Abundant parameters are required to be adjusted. |
Ref. [12] | 2021 | SSA-PID | Boost converter | - Reasonable execution time. - Good convergence acceleration. - Few parameters tuning. | - Suffers from premature convergence. - Unsuccessful to achieve the near-global solution. |
Ref. [13] | 2017 | FLC | Boost converter | - Uses simple mathematics. - Simplicity of rules modifications. - Simplicity of implementation. | - Stability is not guaranteed. - The accuracy is not guaranteed since the outputs are perceived as a guess. - Necessity of human expertise. |
Ref. [14] | 2019 | FLC-PSO | Boost converter | - Easy to implement. - Few parameters to adjust. | - High implementation cost. - complex calculation. - Needs memory to update velocity. |
Ref. [15] | 2019 | ANFIS | Boost converter | - Capability of adaptation. - Expert knowledge is not required. - High convergence speed and tracking accuracy in comparison with FLC. | - Requires large data for training and learning. - Abundant parameters are required to be adjusted. - High computational cost. |
Ref. [16] Ref. [17] | 2018 2018 | NNA | Interleaved boost Boost converter | - Similar to human reasoning. - No exact model is required - Possibility application for feed forward control. | - Needs an expert for a good initialization. - Stability is not guaranteed. - Abundant parameters are required to be adjusted. |
Ref. [18] | 2018 | GA | Boost converter | - Easy to understand. - Effective for noisy environments. - Works well for mixed discrete/continuous problem. - Supports multi-objective optimization. | - Sometimes inappropriate for real-time applications. - Needs an expert for the implementation. - The objective function is hard to design. - Computationally expensive. |
Ref. [19] | 2019 | ACO PSO DE | Boost converter | - High convergence speed. - High tracking accuracy. - High efficiency. | - Complex calculation. - High implementation cost. - Optimization process is lengthy. |
Ref. [3] Ref. [20] Ref. [21] | 2017 2019 2019 | SMC | Boost converter | - High robustness. - Simple structure. - Easy parameter tuning. - Wide operation range. | - Excessive chattering effect. - Considerable energy consumption. - Lack of robustness during the reaching phase. |
Ref. [22] | 2021 | IFTSMC | Boost converter | - Robust to parameter uncertainties and disturbances. - Finite time convergence. - Capable of reducing the chattering. - High convergence speed. | - Requires the knowledge of the system boundary uncertainties. - Problem of intrinsic singularity. - Convergence problem may occur when the states are away from the equilibrium. |
Ref. [23] | 2018 | BSMC | Boost converter | - Stability is guaranteed. - Popular technique for high-order systems. - Uncertainties could be handled. | - Complex design. - Requires an exact mathematical model. - Sensitive to parameter variation. - Requires the measures of all the states. |
Ref. [24] Ref. [21] Ref. [25] Ref. [26] | 2020 2019 2020 2020 | TA STA PCL QC | Boost converter | - Capability of chattering reduction. - Robust to uncertainties and disturbances. - Finite time convergence. | - Complex design. - Complex stability demonstration. - Accuracy is not guaranteed. - Unable to use for first-order systems. |
Ref. [27] Ref. [28,29] Ref. [30] Ref. [31] Ref. [32] | 2019 2019 2020 2020 2020 | MPC | Buck converter 3-phase inverter Two-level inverter Boost converter High-gain converter | - Offers multiple variables control. - Prediction on upcoming disturbance. -Upcoming control actions prediction. - Peak load shifting capability. - Enhanced energy saving. - Enhanced transient response: peak, rise and settling time reduction. | - Plant model is required. - Requires specific background knowledge of the method. |
PEMFC Features | Electrical Features | ||
---|---|---|---|
Type | Heliocentris FC50 | Operating Voltage | 2.5–10 V |
Cooling | fans | Operating Current | 0–10 A |
Fuel | Rated power | 40 W | |
Dimensions | 1210.313.5 cm | Maximum power | 50 W |
Weight | 1150 g | Open-circuit voltage | 9 V |
Hydrogen Flowmeter | Hydrogen 15 bar Kit | ||
Precision | 0.8% of the the quantified value | Inlet pressure | 1–15 bar |
Measuring range | 10–1000 sml/min | Outlet pressure | 0.6 ∓ 0.2 bar |
Thermal | Hydrogen 200 bar kit | ||
Operating temperature | 15–50 ºC | inlet pressure | 200 bar |
Max. start temperature | 45 ºC | outlet pressure | 1–15 bar |
Fuel characteristics | Hydrogen Detector | ||
Recommended purity | 5.0 (99.999%) | Type of sensor | 4% |
Hydrogen input pressure | 0.4–8 bar (5.8–11.6 psig) | Measuring principle | 3 electrode sensor |
Hydrogen consumption | Max. 700 sml/min (at 0 ºC, 1013 bar) | Range | 0–4% |
Parameter | Range | Accuracy | Resolution |
---|---|---|---|
CR Mode Regulation Inputcurrent≥FS10% Input Voltage≥FS10% | 0.1–10 | ∓ (1% + 0.3% FS) | 0.001 |
10–99 | ∓ (1% + 0.3% FS) | 0.01 | |
100–999 | ∓ (1% + 0.3% FS) | 0.1 | |
1 k–4 k | ∓ (1% + 0.8% FS) | 1 | |
CV Mode Regulation | 0.1–18 V | ∓ (0.05% + 0.02% FS) | 1 mV |
0.1–120 V | ∓ (0.05% + 0.025% FS) | 10 mV | |
CC Mode Regulation | 0–3 A | ∓ (0.1% + 0.1% FS) | 0.1 mA |
0–30 A | ∓ (0.2% + 0.15% FS) | 1 mA | |
Current Measurement | 0–3 A | ∓ (0.1% + 0.1% FS) | 0.1 mA |
0–30 A | ∓ (0.2% + 0.15% FS) | 1 mA | |
Voltage Measurement | 0–18 V | ∓ (0.02% + 0.02% FS) | 1 mV |
0–120 V | ∓ (0.05% + 0.025% FS) | 10 mV |
IAE | RMSE | RRMSE (%) | |||
---|---|---|---|---|---|
MPC | PI | MPC | PI | MPC | PI |
2.0607 | 9.2310 | 0.2068 | 0.5085 | 5.1705 | 12.7115 |
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Derbeli, M.; Charaabi, A.; Barambones, O.; Napole, C. High-Performance Tracking for Proton Exchange Membrane Fuel Cell System PEMFC Using Model Predictive Control. Mathematics 2021, 9, 1158. https://doi.org/10.3390/math9111158
Derbeli M, Charaabi A, Barambones O, Napole C. High-Performance Tracking for Proton Exchange Membrane Fuel Cell System PEMFC Using Model Predictive Control. Mathematics. 2021; 9(11):1158. https://doi.org/10.3390/math9111158
Chicago/Turabian StyleDerbeli, Mohamed, Asma Charaabi, Oscar Barambones, and Cristian Napole. 2021. "High-Performance Tracking for Proton Exchange Membrane Fuel Cell System PEMFC Using Model Predictive Control" Mathematics 9, no. 11: 1158. https://doi.org/10.3390/math9111158
APA StyleDerbeli, M., Charaabi, A., Barambones, O., & Napole, C. (2021). High-Performance Tracking for Proton Exchange Membrane Fuel Cell System PEMFC Using Model Predictive Control. Mathematics, 9(11), 1158. https://doi.org/10.3390/math9111158