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arxiv: 2604.11433 · v1 · submitted 2026-04-13 · 📡 eess.SY · cs.SY· physics.app-ph

Air supply control for proton exchange membrane fuel cells without explicit modeling

M\'eziane Ait Ziane , Michel Zasadzinski , C\'edric Join , Michel Fliess This is my paper

Pith reviewed 2026-05-10 15:30 UTC · model grok-4.3

classification 📡 eess.SY cs.SYphysics.app-ph
keywords model-free controlproton exchange membrane fuel cellair supply systemoxygen stoichiometryrobustnessnumerical simulationreal-time adaptation
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The pith

A model-free control law regulates oxygen stoichiometry in PEM fuel cell air supply systems solely through real-time adaptation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates applying a model-free control approach to manage the air supply in proton exchange membrane fuel cells, focusing on oxygen stoichiometry without deriving or using an explicit dynamic model. This strategy adapts directly from measured signals to follow desired setpoints while operating under changing load conditions. Simulations with constant and variable stoichiometry references across two current profiles demonstrate that the law maintains tracking performance. The same tests confirm that the approach tolerates large changes in system parameters without retuning.

Core claim

Numerical simulations for two scenarios with constant and variable oxygen stoichiometry and two current profiles reveal satisfactory performance of the model-free control law. The robustness is addressed by considering significant variations in the parameters of the proton exchange membrane air supply system.

What carries the argument

The model-free control law that tracks operating points through real-time adaptation without any explicit model of the air supply dynamics.

If this is right

  • The control requires only low computational effort and therefore fits industrial hardware constraints.
  • No detailed system modeling or parameter identification step is needed before deployment.
  • The same law handles both fixed and changing oxygen stoichiometry targets under different current demands.
  • Performance holds when key parameters such as those of the compressor or manifold change substantially.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Design effort for new fuel cell installations could decrease because the controller does not depend on accurate first-principles models.
  • The approach may transfer to other energy conversion systems where actuator and sensor data are available but full dynamics remain uncertain.
  • Implementation on embedded processors becomes simpler since no online model update or observer is required.

Load-bearing premise

Real-time adaptation alone suffices to deliver both setpoint tracking and robustness to large parameter changes when applied to the air supply system.

What would settle it

Hardware tests on a physical PEM fuel cell stack in which the control law loses oxygen stoichiometry tracking when parameters vary by the amounts used in the simulations would falsify the result.

Figures

Figures reproduced from arXiv: 2604.11433 by C\'edric Join, M\'eziane Ait Ziane, Michel Fliess, Michel Zasadzinski.

Figure 2
Figure 2. Figure 2: 2 nd current profile • some physical parameters of PEMFC system in (3) given in table 2 in [8] are modified and given in Table II for uncertain case. TABLE II: Parameters uncertainties Symbol Parameter Value f Motor friction +20% kt Motor constant −5% ηcp Compressor efficiency −10% ηcm Motor mechanical efficiency −20% kca,out Cathode outlet constant +10% Tatm Atmospheric temperature +10% Vca Cathode volume… view at source ↗
Figure 1
Figure 1. Figure 1: 1 st current profile In order to analyze the robustness of the iP controller, two cases are considered: • the physical parameters of PEMFC system in (3) given in table 2 in [8] are considered for nominal case, 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time [s] 100 150 200 250 300 350 400 Current [A] [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Constant desired oxygen stoichiometry λ ⋆ O2 with and without uncertainties: 1 st current profile 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time [s] 0.5 1 1.5 2 2.5 3 3.5 (a) Constant λO2 for 2 nd current profile 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time [s] 0 0.5 1 1.5 2 2.5 3 3.5 4 Current [A] (b) u for 2 nd current profile 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 T… view at source ↗
Figure 4
Figure 4. Figure 4: Constant desired oxygen stoichiometry λ ⋆ O2 with and without uncertainties: 2 nd current profile PEMFC air supply system by intelligent PID methods,” Sustainability, vol. 15, p. ID 8500, 2023. [26] Y. Wang and Y. Wang, “Pressure and oxygen excess ratio control of PEMFC air management system based on neural network and prescribed performance,” Engineering Applications of Artificial Intel￾ligence, vol. 121,… view at source ↗
Figure 5
Figure 5. Figure 5: Variable desired oxygen stoichiometry λ ⋆ O2 with and without uncertainties: 1 st current profile 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time [s] 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 (a) Variable λO2 for 2 nd current profile 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time [s] 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 Current [A] (b) u for 2 nd current profile 0 10 20 30 40 50 60 70 80 90 100… view at source ↗
Figure 6
Figure 6. Figure 6: Variable desired oxygen stoichiometry λ ⋆ O2 with and without uncertainties: 2 nd current profile Syst. Techn., vol. 15, pp. 465–473, 2007. [34] S. Laghrouche, J. Liu, F. Ahmed, M. Harmouche, and M. Wack, “Adaptive second-order sliding mode observer-based fault reconstruc￾tion for PEM fuel cell air-feed system,” IEEE Trans. Control Syst. Techn., vol. 23, pp. 1098–1109, 2015. [35] M. Ait Ziane, M. P´era, C.… view at source ↗
read the original abstract

Our objective is to study the performance and robustness of the model-free strategy for controlling the oxygen stoichiometry of a fuel cell air supply system with a proton exchange membrane. After reviewing the literature on modeling and control of this process, the model-free approach appears to be a good candidate because, on the one hand, it allows straightforward real-time adaptation to track operating points and, on the other hand, it requires a low computational burden, which is attractive for industrial applications. Numerical simulations for two scenarios (constant and variable oxygen stoichiometry) with two current profiles reveal satisfactory performance of the model-free control law. The robustness is addressed by considering significant variations in the parameters of the proton exchange membrane air supply system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a model-free control strategy for regulating oxygen stoichiometry in the air supply system of proton exchange membrane fuel cells (PEMFCs). Following a literature review on modeling and control approaches, the authors advocate for a model-free method relying on real-time adaptation due to its simplicity and low computational cost. They evaluate the approach via numerical simulations across two scenarios (constant and variable oxygen stoichiometry) under two current profiles, reporting satisfactory performance, and assess robustness through significant variations in air supply system parameters.

Significance. A validated model-free controller could reduce reliance on detailed plant models that are often difficult to maintain for PEMFC systems, offering practical benefits for industrial deployment through real-time adaptation and modest computational demands. The simulation-based evidence for tracking and robustness to parameter changes provides a starting point, but the absence of quantitative benchmarks limits assessment of its potential contribution relative to established model-based methods in the systems and control literature.

major comments (2)
  1. [Numerical simulations] Numerical simulations section: The central claims of 'satisfactory performance' and robustness rest on qualitative descriptions without reported quantitative metrics (e.g., RMS tracking error, settling time, or overshoot) for oxygen stoichiometry regulation, nor any comparison against baseline controllers such as PID or model-based alternatives. This omission makes it impossible to verify whether the real-time adaptation achieves the claimed level of tracking under the tested current profiles.
  2. [Robustness tests] Robustness analysis: Parameter variations are introduced to test robustness, yet the plant responses are generated from an underlying (undisclosed) mathematical model. Without explicit tests for unmodeled dynamics such as sensor noise, transport delays, or compressor nonlinearities, the simulations do not fully demonstrate that the algebraic estimator and feedback law compensate solely through adaptation, as required by the model-free claim.
minor comments (2)
  1. [Abstract] The abstract states that simulations 'reveal satisfactory performance' but provides no numerical indicators; adding at least one key metric would improve clarity.
  2. [Control law description] Notation for the model-free law and estimator parameters should be defined consistently when first introduced to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which helps improve the clarity and rigor of our simulation results. We agree that quantitative metrics and enhanced robustness tests will better support our claims and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Numerical simulations] Numerical simulations section: The central claims of 'satisfactory performance' and robustness rest on qualitative descriptions without reported quantitative metrics (e.g., RMS tracking error, settling time, or overshoot) for oxygen stoichiometry regulation, nor any comparison against baseline controllers such as PID or model-based alternatives. This omission makes it impossible to verify whether the real-time adaptation achieves the claimed level of tracking under the tested current profiles.

    Authors: We agree that the current presentation relies too heavily on qualitative descriptions. In the revised version, we will add quantitative metrics including RMS tracking errors, settling times, and overshoot values for oxygen stoichiometry under both constant and variable scenarios with the tested current profiles. We will also include a comparison against a standard PID controller (tuned for the nominal system) to provide a baseline and better contextualize the performance of the model-free approach. revision: yes

  2. Referee: [Robustness tests] Robustness analysis: Parameter variations are introduced to test robustness, yet the plant responses are generated from an underlying (undisclosed) mathematical model. Without explicit tests for unmodeled dynamics such as sensor noise, transport delays, or compressor nonlinearities, the simulations do not fully demonstrate that the algebraic estimator and feedback law compensate solely through adaptation, as required by the model-free claim.

    Authors: The simulations use a mathematical model only to generate plant responses for validation, which is standard practice for control design studies. The control law and algebraic estimator remain model-free and do not use this model. We will disclose the full set of model equations in an appendix of the revised manuscript. To strengthen the demonstration of adaptation, we will add new simulation cases that include sensor noise and transport delays, confirming that performance is maintained through real-time adaptation alone. revision: yes

Circularity Check

0 steps flagged

No circularity: model-free control law applied and validated via independent simulations

full rationale

The paper applies a pre-existing model-free control approach (referenced from prior literature) to PEMFC air supply without deriving new equations or parameters within this work. Performance and robustness claims rest on numerical simulations across scenarios and parameter sweeps, which constitute external testing rather than any reduction of outputs to inputs by construction, fitted parameters renamed as predictions, or load-bearing self-citations. The central result does not equate to its own assumptions or prior citations; simulations serve as falsifiable evidence independent of the controller's algebraic estimator.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the domain assumption that model-free control can be applied directly to this process. No new free parameters, axioms beyond standard control theory, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption A model-free control strategy can regulate the air supply system to desired oxygen stoichiometry levels using only real-time measurements and adaptation, without an explicit dynamic model.
    This is the central premise stated in the objective and motivation sections of the abstract.

pith-pipeline@v0.9.0 · 5428 in / 1317 out tokens · 52580 ms · 2026-05-10T15:30:29.875801+00:00 · methodology

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Reference graph

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