Ditherless Extremum Seeking for Hydrogen Minimization in PEM Fuel Cells

This paper presents a nonsmooth adaptive extremum seeker that minimizes the hydrogen consumption in a fuel-cell system. The extremum seeker operates by estimating the gradient of the objective function but, unlike other seekers, it does not require a dither signal to produce such estimate. The absence of a dither signal simplifies the choice of parameter values for the seeker, and more importantly, it allows it to converge to the optimal value exactly, not only to a small neighborhood. The proper functioning of the proposed scheme is proved using nonsmooth Lyapunov analysis. The strategy is tested on the input-output map of a real polymer electrolyte fuel cell.

[1]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[2]  Dragan Nešić,et al.  Extremum seeking control: Convergence analysis , 2009, 2009 European Control Conference (ECC).

[3]  Salah Laghrouche,et al.  Extremum seeking control for net power output maximization of a PEM fuel cell using second order sliding mode , 2012, 2012 12th International Workshop on Variable Structure Systems.

[4]  Fernando Castaños,et al.  Extremum seeking algorithms for minimal hydrogen consumption in PEM fuel cells , 2013, 2013 American Control Conference.

[5]  B. Wittenmark,et al.  Adaptive extremal control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[6]  Fernando Castaños,et al.  On the implementation of an adaptive extremum seeking algorithm for hydrogen minimization in PEM fuel cell based systems , 2013, 2013 European Control Conference (ECC).

[7]  M. A. Mayosky,et al.  Control-Oriented Modeling and Experimental Validation of a PEMFC Generation System , 2011, IEEE Transactions on Energy Conversion.

[8]  K. Agbossou,et al.  Online System Identification and Adaptive Control for PEM Fuel Cell Maximum Efficiency Tracking , 2012, IEEE Transactions on Energy Conversion.

[9]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[10]  Miguel Angel Mayosky,et al.  Sliding-Mode Control of PEM Fuel Cells , 2012 .

[11]  Scott J. Moura,et al.  Air flow control in fuel cell systems: An extremum seeking approach , 2009, 2009 American Control Conference.

[12]  Carlos Bordons,et al.  Real-Time Implementation of a Constrained MPC for Efficient Airflow Control in a PEM Fuel Cell , 2010, IEEE Transactions on Industrial Electronics.

[13]  Fabrizio Marignetti,et al.  Assessment of Fuel Cell Performance Under Different Air Stoichiometries and Fuel Composition , 2011, IEEE Transactions on Industrial Electronics.

[14]  Miroslav Krstic,et al.  Stability of extremum seeking feedback for general nonlinear dynamic systems , 2000, Autom..

[15]  Carlos Andrés Ramos-Paja,et al.  A PEM Fuel-Cell Model Featuring Oxygen-Excess-Ratio Estimation and Power-Electronics Interaction , 2010, IEEE Transactions on Industrial Electronics.

[16]  Carlos Ocampo-Martinez,et al.  A Gain-Scheduled LPV Control for Oxygen Stoichiometry Regulation in PEM Fuel Cell Systems , 2014, IEEE Transactions on Control Systems Technology.

[17]  I. Mareels,et al.  Extremum seeking from 1922 to 2010 , 2010, Proceedings of the 29th Chinese Control Conference.

[18]  Michael C. Georgiadis,et al.  On-line nonlinear model predictive control of a PEM fuel cell system , 2013 .

[19]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[20]  Anna G. Stefanopoulou,et al.  Control of Fuel Cell Power Systems , 2004 .

[21]  Miroslav Krstic,et al.  Performance improvement and limitations in extremum seeking control , 2000 .

[22]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[23]  Tine Konjedic,et al.  Simplified Mathematical Model for Calculating the Oxygen Excess Ratio of a PEM Fuel Cell System in Real-Time Applications , 2014, IEEE Transactions on Industrial Electronics.

[24]  Miguel Angel Mayosky,et al.  Experimental results applying second order sliding mode control to a PEM fuel cell based system , 2013 .

[25]  Dragan Nec,et al.  Extremum Seeking Control: Convergence Analysis ∗ , 2009 .

[26]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .