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Segmented Model-Based Hydrogen Delivery Control for PEM Fuel Cells: a Port-Hamiltonian Approach

Lalitesh Kumar, Jian Chen, Chengshuai Wu, Yuzhu Chen, Arjan van der Schaft

TL;DR

The paper addresses the challenge of regulating spatially distributed pressure dynamics in the FDS of PEM fuel cells by introducing a segmented, MIMO lumped-parameter model within a port-Hamiltonian framework. It develops an extended IDA-PBC energy-shaping and output-tracking control law, augmented with a high-order sliding-mode observer to estimate unmeasurable pressures, and provides explicit stability analyses. The approach preserves interconnection feasibility through segment-passivity and delivers rigorous proofs of stability, complemented by simulations showing robust performance under disturbances. This work advances robust hydrogen delivery control in segmented PEM fuel cells, enabling improved stability and tracking with reduced modeling errors.

Abstract

This paper proposes an extended interconnection and damping assignment passivity-based control technique (IDA-PBC) to control the pressure dynamics in the fuel delivery subsystem (FDS) of proton exchange membrane fuel cells. The fuel cell stack is a distributed parameter model which can be modeled by partial differential equations PDEs). In this paper, the segmentation concept is used to approximate the PDEs model by ordinary differential equations (ODEs) model. Therefore, each segments are having multiple ODEs to obtain the lump-sum model of the segments. Subsequently, a generalized multi-input multi-output lumped parameters model is developed in port-Hamiltonian framework based on mass balance to minimize the modeling error. The modeling errors arises due to the difference between spatially distributed pressures in FDS segments, and also due to the difference between the actual stack pressure and the measured output pressure of the anode. The segments interconnection feasibilities are ensured by maintaining passivity of each segment. With consideration of re-circulation and bleeding of the anode in the modeling, an extended energy-shaping and output tracking IDA-PBC based state-feedback controller is proposed to control the spatially distributed pressure dynamics in the anode. Furthermore, a sliding mode observer of high order is designed to estimate the unmeasurable pressures in FDS with known disturbances. Performance recovery of output feedback control is accomplished with explicit stability analysis. The effectiveness of the proposed IDA-PBC approach is validated by the simulation results.

Segmented Model-Based Hydrogen Delivery Control for PEM Fuel Cells: a Port-Hamiltonian Approach

TL;DR

The paper addresses the challenge of regulating spatially distributed pressure dynamics in the FDS of PEM fuel cells by introducing a segmented, MIMO lumped-parameter model within a port-Hamiltonian framework. It develops an extended IDA-PBC energy-shaping and output-tracking control law, augmented with a high-order sliding-mode observer to estimate unmeasurable pressures, and provides explicit stability analyses. The approach preserves interconnection feasibility through segment-passivity and delivers rigorous proofs of stability, complemented by simulations showing robust performance under disturbances. This work advances robust hydrogen delivery control in segmented PEM fuel cells, enabling improved stability and tracking with reduced modeling errors.

Abstract

This paper proposes an extended interconnection and damping assignment passivity-based control technique (IDA-PBC) to control the pressure dynamics in the fuel delivery subsystem (FDS) of proton exchange membrane fuel cells. The fuel cell stack is a distributed parameter model which can be modeled by partial differential equations PDEs). In this paper, the segmentation concept is used to approximate the PDEs model by ordinary differential equations (ODEs) model. Therefore, each segments are having multiple ODEs to obtain the lump-sum model of the segments. Subsequently, a generalized multi-input multi-output lumped parameters model is developed in port-Hamiltonian framework based on mass balance to minimize the modeling error. The modeling errors arises due to the difference between spatially distributed pressures in FDS segments, and also due to the difference between the actual stack pressure and the measured output pressure of the anode. The segments interconnection feasibilities are ensured by maintaining passivity of each segment. With consideration of re-circulation and bleeding of the anode in the modeling, an extended energy-shaping and output tracking IDA-PBC based state-feedback controller is proposed to control the spatially distributed pressure dynamics in the anode. Furthermore, a sliding mode observer of high order is designed to estimate the unmeasurable pressures in FDS with known disturbances. Performance recovery of output feedback control is accomplished with explicit stability analysis. The effectiveness of the proposed IDA-PBC approach is validated by the simulation results.
Paper Structure (21 sections, 4 theorems, 62 equations, 11 figures, 2 tables)

This paper contains 21 sections, 4 theorems, 62 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Development of the Mathematical Models
  3. Modeling of Segmented Anode
  4. Membrane Gas Consumption and Crossover
  5. Supply Manifold Model
  6. Cathode and Blower Models
  7. The Integrated State-Space Model Development
  8. State-Feedback PH Control Design
  9. PH Control Design Preambles
  10. IDA-PBC Based Controller Design
  11. Stability Analysis
  12. Output Feedback Control Design
  13. Observer Design
  14. Output Feedback Control With Performance Recovery
  15. Simulation Results and Discussions
  16. ...and 6 more sections

Key Result

Lemma 1

Suppose $f_1\left(\bar{b} (x), x\right) = \frac{\partial F_1}{\partial \bar{b}}$ and $f_2\left(\bar{c} (x), x\right) = \frac{\partial F_1}{\partial \bar{c}}$. If the conditions Equilibrium_Assignment_Condition and Lyapunov_Stability_Condition are satisfied by $f_1\left(\bar{b} (x), x\right)$ and $f_

Figures (11)

  • Figure 1: PEM Fuel Cell Segmented Model.
  • Figure 2: Geometrical PH Structure of FDS
  • Figure 3: Stack Current
  • Figure 4: Control input $u_1$ to the anode
  • Figure 5: Control input $u_2$ to the anode
  • ...and 6 more figures

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Proof
  • Remark 4
  • Remark 5
  • Lemma 2
  • Proof
  • Theorem 1
  • ...and 6 more