🔬 applied physics

Model-Free Detection and Accommodation of Sensor Faults for a PEM Electrolyzer

This paper proposes a novel model-free approach based on ultra-local models to detect and accommodate sensor faults in a renewable energy-powered PEM electrolyzer system, thereby ensuring closed-loop stability and performance without relying on prior system models.

Original authors: Meziane Ait Ziane, Michel Zasadzinski, Cédric Join, Michel Fliess

Published 2026-07-14

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CC BY 4.0

Original authors: Meziane Ait Ziane, Michel Zasadzinski, Cédric Join, Michel Fliess

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to bake the perfect loaf of bread (that's your hydrogen fuel) using a very finicky, high-tech oven (the PEM electrolyzer). This oven is powered by a solar panel that acts like a fickle friend: sometimes it's bright and sunny (high voltage), and sometimes it's cloudy (low voltage). To keep the oven running smoothly, you use a special dimmer switch (a DC/DC converter) to adjust the power.

Now, here's the problem: You have a thermometer (a sensor) that tells you how hot the oven is. But what if that thermometer starts lying? Maybe it gets stuck saying "300 degrees" when the oven is actually freezing, or maybe it just starts buzzing with static noise. If your oven's brain trusts this lying thermometer, it will try to bake the bread at the wrong temperature, and your hydrogen production will go haywire.

For a long time, scientists tried to fix this by building a massive, complex mathematical map of exactly how the oven works inside and out. They thought, "If we know every single wire and chemical reaction, we can predict when the thermometer is lying." But this paper says: Nope, that's too complicated.

Instead, the authors propose a "model-free" approach. Think of it like this: Instead of studying the entire blueprint of the oven, your control system just listens to the current behavior. It uses a clever trick called an "ultra-local model." Imagine a smart assistant who doesn't need to know how the oven was built; they just watch what happens when you turn the knob and what the thermometer says right now.

Here is how their "smart assistant" works in three simple steps:

The Guess: The assistant predicts what the thermometer should be saying based on the last few seconds of data.
The Check: It compares the prediction to the actual reading. If they match, everything is fine. If they don't match, the assistant shouts, "Hey! Something is wrong!" This difference is called a residual.
The Fix: Once the assistant spots the lie (the sensor fault), it doesn't panic. It calculates exactly how much the thermometer is lying. Then, it adjusts the oven's brain to ignore the lie and focus on the real goal.

The authors tested this idea using computer simulations (not a real physical oven in a lab yet, but a very detailed digital twin). They set up a scenario where the solar power fluctuates between 25 V and 55 V. They also introduced a "lie" where the sensor suddenly reported a current that was 2 Amps too high (or 4 Amps too low) at specific times.

The results were promising. In the simulations, when the sensor started lying, the system detected the error almost instantly. Without the fix, the oven would have tried to follow the fake reading. But with their new "model-free" strategy, the system realized, "Ah, the sensor is broken," and corrected itself. The actual current flowing through the system stayed perfectly on track, hitting the desired target even while the sensor was screaming lies and the solar power was dancing up and down.

The paper explicitly argues against relying on complex, pre-built mathematical models of the system for this specific job. They show that you don't need to know every single resistor and capacitor value (like the 100.06 Ω or 901.43 F components mentioned in their technical notes) to fix the sensor. You just need the ultra-local model.

So, what's the bottom line? The authors suggest that this method is a strong candidate for real-life use because it's fast and doesn't need a heavy computer to do the math. They haven't built the physical robot yet, but in their digital world, it worked like a charm, keeping the hydrogen production steady despite the chaos. It's a bit like teaching a car to drive itself by just watching the road, rather than memorizing the entire map of the city first.

Technical Summary: Model-Free Detection and Accommodation of Sensor Faults for a PEM Electrolyzer

Problem Statement
Proton Exchange Membrane Water Electrolyzers (PEMWE) coupled with DC/DC converters are critical for producing green hydrogen using renewable energy sources (RES). However, these systems are susceptible to various faults, including sensor failures. While Active Fault-Tolerant Control (AFTC) strategies exist for component faults (e.g., gate faults in converters), the literature lacks specific approaches for accommodating sensor faults in PEMWE systems operating under variable RES voltages. Without compensation, a sensor fault ( $f$ ) causes the control loop to regulate the faulty measurement ( $y_m$ ) rather than the actual system output ( $y$ ), leading to a deviation from the desired hydrogen production setpoint. The challenge is to detect, estimate, and accommodate these sensor faults in a closed-loop system subject to input voltage variations without relying on complex mathematical models of the electrolyzer.

Methodology
The authors propose a model-free approach based on the concept of an ultra-local model, a technique increasingly used in control engineering. The methodology consists of three main components:

Ultra-Local Modeling and Control:
Instead of using the high-order analytical model of the PEMWE (derived from Electrochemical Impedance Spectroscopy), the system is represented by the ultra-local model: $\dot{y}_m = F + \alpha u$ . Here, $F$ represents the unknown dynamics and disturbances, $\alpha$ is a constant coefficient, and $u$ is the control input. An "intelligent proportional" (iP) controller is used to estimate $F$ and generate the control law: $u = -(\hat{F} - \dot{y}^* + K_p e)/\alpha$ .
Residual Generation and Fault Detection:
To detect faults, a residual signal $r(t)$ is generated by comparing the measured output $y_m$ with a reconstructed output $\hat{y}_m$ derived from the ultra-local model integration.
$r(t) = y_m(t) - \beta(t)\hat{y}_m(t)$
The parameter $\beta(t)$ is dynamically adjusted based on the steady-state relationship between the control input and the RES voltage ( $V_{RES}$ ), acknowledging that the system is not Linear Time-Invariant (LTI) due to $V_{RES}$ variations. A threshold $\rho(t)$ is established based on noise levels and the minimum detectable fault magnitude. If $|r(t)| > \rho(t)$ , a fault is declared.
Fault Estimation and Accommodation:
Once a fault is detected, its magnitude $\hat{f}$ is estimated directly from the residual:
$\hat{f}(t) = \frac{r(t)}{1 - \beta(t)}$
The accommodation strategy involves modifying the tracking error definition in the iP controller. Instead of using the raw measurement, the controller uses the compensated error:
$e(t) = y_m(t) - y^*(t) - \hat{f}(t)$
This allows the controller to drive the actual output $y$ to the reference $y^*$ despite the sensor fault.

Key Contributions

First Application to PEMWE Sensor Faults: The paper claims to be the first work to address Active Fault-Tolerant Control specifically for sensor faults in PEMWE systems coupled with DC/DC converters.
Model-Free Architecture: The detection and accommodation mechanisms do not rely on the analytical mathematical model of the PEMWE or the converter. This avoids the complexities of modeling degradation, non-linearities, and parameter uncertainties.
Handling Variable Inputs: The proposed method explicitly accounts for variations in the renewable energy source voltage ( $V_{RES}$ ), ensuring the fault detection threshold and estimation remain valid during both transient and steady-state operations.

Simulation Results
The approach was validated using numerical simulations of a PEMWE system coupled with a Stacked Interleaved Buck Converter (SIBC). Two scenarios were tested:

Constant $V_{RES}$ (40 V): A sensor fault of +2 A was introduced at $t=30$ s.
Variable $V_{RES}$ : The input voltage varied between 25 V and 55 V, with a sensor fault of -4 A introduced at $t=60$ s.

In both cases, the results demonstrated:

Detection: The residual $r(t)$ exceeded the threshold $\rho(t)$ almost immediately upon fault occurrence.
Estimation: The estimated fault $\hat{f}$ accurately tracked the actual fault magnitude.
Accommodation: Without AFTC, the regulated output $y$ deviated from the setpoint $y^*$ following the fault. With AFTC enabled, the system successfully compensated for the fault, ensuring the actual current $y$ converged to the desired setpoint $y^*$ despite the sensor error and input voltage variations.
Transient Behavior: The AFTC logic was designed to remain inactive during transient phases to prevent false triggering, activating only once steady-state conditions were re-established.

Significance and Claims
The authors assert that their model-free approach offers a robust solution for maintaining system stability and performance in the presence of sensor faults. By leveraging the ultra-local model, the method achieves fault accommodation without the computational burden or modeling inaccuracies associated with analytical approaches. The paper concludes that this technique is a strong candidate for real-time implementation on test benches due to its low computational requirements. Future work is identified as the physical implementation of this method on a real test bench.

Technical Summary: Model-Free Detection and Accommodation of Sensor Faults for a PEM Electrolyzer

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