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Exploiting Monotonicity to Design an Adaptive PI Passivity-Based Controller for a Fuel-Cell System

Carlo A. Beltran, Rafael Cisneros, Diego Langarica-Cordoba, Romeo Ortega, Luis H. Diaz-Saldierna

Abstract

We present a controller for a power electronic system composed of a fuel cell (FC) connected to a boost converter which feeds a resistive load. The controller aims to regulate the output voltage of the converter regardless of the uncertainty of the load. Leveraging the monotonicity feature of the fuel cell polarization curve we prove that the nonlinear system can be controlled by means of a passivity-based proportional-integral approach. We afterward extend the result to an adaptive version, allowing the controller to deal with parameter uncertainties, such as inductor parasitic resistance, load, and FC polarization curve parameters. This adaptive design is based on an indirect control approach with online parameter identification performed by a ``hybrid'' estimator which combines two techniques: the gradient-descent and immersion-and-invariance algorithms. The overall system is proved to be stable with the output voltage regulated to its reference. Experimental results validate our proposal under two real-life scenarios: pulsating load and output voltage reference changes.

Exploiting Monotonicity to Design an Adaptive PI Passivity-Based Controller for a Fuel-Cell System

Abstract

We present a controller for a power electronic system composed of a fuel cell (FC) connected to a boost converter which feeds a resistive load. The controller aims to regulate the output voltage of the converter regardless of the uncertainty of the load. Leveraging the monotonicity feature of the fuel cell polarization curve we prove that the nonlinear system can be controlled by means of a passivity-based proportional-integral approach. We afterward extend the result to an adaptive version, allowing the controller to deal with parameter uncertainties, such as inductor parasitic resistance, load, and FC polarization curve parameters. This adaptive design is based on an indirect control approach with online parameter identification performed by a ``hybrid'' estimator which combines two techniques: the gradient-descent and immersion-and-invariance algorithms. The overall system is proved to be stable with the output voltage regulated to its reference. Experimental results validate our proposal under two real-life scenarios: pulsating load and output voltage reference changes.
Paper Structure (11 sections, 6 theorems, 54 equations, 8 figures, 1 table)

This paper contains 11 sections, 6 theorems, 54 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. System description and control
  3. Assignable equilibrium points
  4. The full-information PI Passivity-based control
  5. Main result
  6. Estimation of $\theta$
  7. The proposed adaptive PI-PBC
  8. Experimental results
  9. Pulsating voltage reference changes
  10. Pulsating load changes
  11. Conclusions

Key Result

Lemma 1

The assignable equilibrium points of Phmodel and the associated constant input are those values in the set where

Figures (8)

  • Figure 1: FC System under consideration.
  • Figure 2: Experimental testbench for the FC System with the Nexa® $$ PEMFC power stack.
  • Figure 3: Implementation diagram of the API-PBC
  • Figure 4: Experimental results of the online estimation of the parasitic resistance of the inductor and the load conductance through I&I.
  • Figure 5: Experimental results of the output voltage regulation under pulsating voltage reference changes at 1 Hz. The resulting equilibria are $x^\star=($33.32 V, 7.11 A, 48.0 V$)$ and $x^\star=($35.75 V, 4.05 A, 38.0 V$)$.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 1: Parameter estimator
  • Lemma 4
  • Proposition 2: Adaptive PI-PBC