Contributions to Adaptative Higher Order Sliding Mode Observers : Application to Fuel Cell an Power Converters

Automotive PEM Fuel Cell systems rely upon a set of auxiliary systems for proper operation, such as humidifier, air-feed compressor, power converter etc. The internal physical states of the latter are often unmeasurable, yet required for their precise control. Observers provide a means of obtaining the unmeasured states of these auxiliary systems for feedback control, optimal energy consumption and Fault Diagnosis and Isolation (FDI). This thesis is based on higher order sliding mode observer design studies for two major PEMFC auxiliary systems found in modern automobiles, the air-feed system and the power electronics system.The first part is focused on robust observation and FDI of the PEMFC air-feed systems. Sliding mode observer design and their applications to FDI have been studied in detail for this purpose and the key observation problems in this system have been identified. Based on this study, two solutions are proposed, a sliding mode algebraic observer for oxygen and nitrogen partial pressures and a novel robust adaptive-gain Second Order Sliding Mode (SOSM) observer based FDI for simultaneous state observation, parameter identification, health monitoring and fault reconstruction of the PEMFC air-feed system. The performance of the proposed observers has been validated on an instrumented Hardware-In-Loop (HIL) test bench.The observation and output feedback control problems of different power electronic converters, commonly found in fuel cell vehicles, are addressed in the next part. Robust output feedback SOSM control for three phase AC/DC converters have been presented. A robust SOSM observer for multi-cell converters has also been designed. The performance of all these designs has been demonstrated through a multi-rate simulation approach. The results highlight the robustness of the observers and controllers against parametric uncertainty, measurement noise and external disturbance.

[1]  Daniel E. Quevedo,et al.  Model Predictive Control of an Asymmetric Flying Capacitor Converter , 2009, IEEE Transactions on Industrial Electronics.

[2]  Pascal Maussion,et al.  Multicell converters: active control and observation of flying-capacitor voltages , 2002, IEEE Trans. Ind. Electron..

[3]  G. Moschopoulos,et al.  A Nonlinear Optimal Control Approach Based on the Control-Lyapunov Function for an AC/DC Converter Used in Electric Vehicles , 2012, IEEE Transactions on Industrial Informatics.

[4]  M. Fadel,et al.  Flying capacitor voltages estimation in three-cell converters using a discrete-time Kalman filter at one third switching period , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[5]  M. Staroswiecki,et al.  Fault estimation in nonlinear uncertain systems using robust/sliding-mode observers , 2004 .

[6]  W. Dayawansa,et al.  Global stabilization by output feedback: examples and counterexamples , 1994 .

[7]  Antonio Loría,et al.  Uniform exponential stability of linear time-varying systems: revisited , 2002, Syst. Control. Lett..

[8]  Hamid Gualous,et al.  DC/DC Converter Design for Supercapacitor and Battery Power Management in Hybrid Vehicle Applications—Polynomial Control Strategy , 2010, IEEE Transactions on Industrial Electronics.

[9]  T. Holmgaard,et al.  Active three-phase rectifier with only one current sensor in the DC-link , 1999, Proceedings of the IEEE 1999 International Conference on Power Electronics and Drive Systems. PEDS'99 (Cat. No.99TH8475).

[10]  Ralph E. White,et al.  A water and heat management model for proton-exchange-membrane fuel cells , 1993 .

[11]  Phatiphat Thounthong,et al.  Control Strategy of Fuel Cell and Supercapacitors Association for a Distributed Generation System , 2007, IEEE Transactions on Industrial Electronics.

[12]  Denise A. McKay,et al.  Measurement of Liquid Water Accumulation in a PEMFC with Dead-Ended Anode , 2008 .

[13]  Maxime Wack,et al.  Robust control of the PEM fuel cell air-feed system via sub-optimal second order sliding mode , 2013 .

[14]  Michael Defoort,et al.  Robust finite time observer design for multicellular converters , 2011, Int. J. Syst. Sci..

[15]  Gildas Besançon,et al.  High-gain observation with disturbance attenuation and application to robust fault detection , 2003, Autom..

[16]  James Larminie,et al.  Fuel Cell Systems Explained , 2000 .

[17]  M. Ghanes,et al.  On sliding mode and adaptive observers design for multicell converter , 2009, 2009 American Control Conference.

[18]  M. I. Castellanos,et al.  Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs , 2007, Int. J. Syst. Sci..

[19]  Alain Glumineau,et al.  An Adaptive Interconnected Observer for Sensorless Control of PM Synchronous Motors With Online Parameter Identification , 2013, IEEE Transactions on Industrial Electronics.

[20]  Jong-Woo Ahn,et al.  Dynamic Simulator for a PEM Fuel Cell System With a PWM DC/DC Converter , 2008, IEEE Transactions on Energy Conversion.

[21]  Yiguang Hong,et al.  Stabilization of uncertain chained form systems within finite settling time , 2005, IEEE Transactions on Automatic Control.

[22]  Christopher Edwards,et al.  Sliding mode observers for robust detection and reconstruction of actuator and sensor faults , 2003 .

[23]  Carlos Andrés Ramos-Paja,et al.  Switching and linear power stages evaluation for PEM fuel cell emulation , 2011, Int. J. Circuit Theory Appl..

[24]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[25]  Christopher Edwards,et al.  Sensor fault tolerant control using sliding mode observers , 2006 .

[26]  T. Floquet,et al.  On Sliding Mode Observers for Systems with Unknown Inputs , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[27]  Guillaume Gateau,et al.  Digital Sliding-Mode Observer Implementation Using FPGA , 2007, IEEE Transactions on Industrial Electronics.

[28]  Romeo Ortega,et al.  An adaptive passivity-based controller for a unity power factor rectifier , 2001, IEEE Trans. Control. Syst. Technol..

[29]  Daniel Hissel,et al.  Energy-Management Strategy for Embedded Fuel-Cell Systems Using Fuzzy Logic , 2007, IEEE Transactions on Industrial Electronics.

[30]  Frede Blaabjerg,et al.  A direct power conversion topology for grid integrations of hybrid AC/DC resources , 2012, Proceedings of The 7th International Power Electronics and Motion Control Conference.

[31]  Ali Emadi,et al.  Classification and Review of Control Strategies for Plug-In Hybrid Electric Vehicles , 2011, IEEE Transactions on Vehicular Technology.

[32]  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.

[33]  Mehrdad Saif,et al.  Nonlinear adaptive observer design for fault detection , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[34]  Ali Emadi,et al.  Advanced Integrated Bidirectional AC/DC and DC/DC Converter for Plug-In Hybrid Electric Vehicles , 2009, IEEE Transactions on Vehicular Technology.

[35]  Guowu Yang,et al.  Global finite-time stabilization: from state feedback to output feedback , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[36]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[37]  Miguel Angel Mayosky,et al.  Sliding Mode Strategy for PEM Fuel Cells Stacks Breathing Control Using a Super-Twisting Algorithm , 2009, IEEE Transactions on Control Systems Technology.

[38]  Daniel Hissel,et al.  A New Modeling Approach of Embedded Fuel-Cell Power Generators Based on Artificial Neural Network , 2008, IEEE Transactions on Industrial Electronics.

[39]  Halim Alwi,et al.  Fault Detection and Fault-Tolerant Control of a Civil Aircraft Using a Sliding-Mode-Based Scheme , 2008, IEEE Transactions on Control Systems Technology.

[40]  Anna G. Stefanopoulou,et al.  Control of Fuel Cell Breathing : Initial Results on the Oxygen Starvation Problem , 2003 .

[41]  Maurice Fadel,et al.  Sliding Mode Observer for Multicell Converters , 2001 .

[42]  Jaime A. Moreno,et al.  Lyapunov function for Levant's Second Order Differentiator , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[43]  Maurice Fadel,et al.  A Predictive Control With Flying Capacitor Balancing of a Multicell Active Power Filter , 2008, IEEE Transactions on Industrial Electronics.

[44]  Boon-Teck Ooi,et al.  Indirect current control of a unity power factor sinusoidal current boost type three-phase rectifier , 1988 .

[45]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[46]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[47]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[48]  Tzann-Shin Lee,et al.  Input-output linearization and zero-dynamics control of three-phase AC/DC voltage-source converters , 2003 .

[49]  Abdellatif Miraoui,et al.  Design and Optimization of a Switched Reluctance Motor Driving a Compressor for a PEM Fuel-Cell System for Automotive Applications , 2010, IEEE Transactions on Industrial Electronics.

[50]  H. Khalil,et al.  Discrete-time implementation of high-gain observers for numerical differentiation , 1999 .

[51]  Malek Ghanes,et al.  Observability and observer design for hybrid multicell choppers , 2010, Int. J. Control.

[52]  Raymond A. DeCarlo,et al.  MPC of Switching in a Boost Converter Using a Hybrid State Model With a Sliding Mode Observer , 2009, IEEE Transactions on Industrial Electronics.

[53]  M. Hou,et al.  Design of observers for linear systems with unknown inputs , 1992 .

[54]  Sarah K. Spurgeon,et al.  Sliding mode observers: a survey , 2008, Int. J. Syst. Sci..

[55]  Eung-Seok Kim Observer Based Nonlinear State Feedback Control of PEM Fuel Cell Systems , 2012 .

[56]  Dong-Choon Lee,et al.  AC voltage and current sensorless control of three-phase PWM rectifiers , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[57]  Jamal Daafouz,et al.  On the algebraic characterization of invariant sets of switched linear systems , 2010, Autom..

[58]  Salim Ibrir,et al.  Online exact differentiation and notion of asymptotic algebraic observers , 2003, IEEE Trans. Autom. Control..

[59]  D. Luenberger Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

[60]  S. Shankar Sastry,et al.  Observability of Linear Hybrid Systems , 2003, HSCC.

[61]  Jie Chen,et al.  Robust Residual Generation Using Unknown Input Observers , 1999 .

[62]  Hong Wang,et al.  On the use of adaptive updating rules for actuator and sensor fault diagnosis , 1997, Autom..

[63]  Leonid M. Fridman,et al.  Variable Gain Super-Twisting Sliding Mode Control , 2012, IEEE Transactions on Automatic Control.

[64]  Murat Arcak,et al.  An algorithm for estimation of membrane water content in PEM fuel cells , 2006 .

[65]  Yuri B. Shtessel,et al.  Unity Power Factor Control in Three-Phase AC/DC Boost Converter Using Sliding Modes , 2008, IEEE Transactions on Industrial Electronics.

[66]  Marios M. Polycarpou,et al.  Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation , 2010, Autom..

[67]  Jessy W. Grizzle,et al.  Interpolation and numerical differentiation for observer design , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[68]  Henk Nijmeijer,et al.  Time scaling for observer design with linearizable error dynamics , 2004, Autom..

[69]  Salah Laghrouche,et al.  Finite time observer design for a class of nonlinear systems with unknown inputs , 2013, 2013 American Control Conference.

[70]  M. Baja,et al.  Hybrid control of a three-level three-cell dc-dc converter , 2007, 2007 American Control Conference.

[71]  Ali Emadi,et al.  A new battery/ultra-capacitor hybrid energy storage system for electric, hybrid and plug-in hybrid electric vehicles , 2009, 2009 IEEE Vehicle Power and Propulsion Conference.

[72]  Wilfrid Perruquetti,et al.  Observer-based second order sliding mode control laws for stepper motors , 2008 .

[73]  Avrie Levent,et al.  Robust exact differentiation via sliding mode technique , 1998, Autom..

[74]  Romeo Ortega,et al.  Experimental Validation of a PEM Fuel-Cell Reduced-Order Model and a Moto-Compressor Higher Order Sliding-Mode Control , 2010, IEEE Transactions on Industrial Electronics.

[75]  Bin Wu,et al.  Recent Advances and Industrial Applications of Multilevel Converters , 2010, IEEE Transactions on Industrial Electronics.

[76]  Serge Pierfederici,et al.  Flatness-Based Control of Three-Phase Inverter With Output $LC$ Filter , 2012, IEEE Transactions on Industrial Electronics.

[77]  Christopher Edwards,et al.  Sliding mode observers for detection and reconstruction of sensor faults , 2002, Autom..

[78]  Jaime A. Moreno,et al.  A Lyapunov approach to second-order sliding mode controllers and observers , 2008, 2008 47th IEEE Conference on Decision and Control.

[79]  P. K. Jain,et al.  A New Control Approach Based on the Differential Flatness Theory for an AC/DC Converter Used in Electric Vehicles , 2012, IEEE Transactions on Power Electronics.

[80]  S. Bacha,et al.  On nonlinear observers applied to three-phase voltage source converters , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[81]  R. Ortega,et al.  A saturated output feedback controller for the three phase voltage sourced reversible boost type rectifier , 1998, IECON '98. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.98CH36200).

[82]  Jie Chen,et al.  Design of unknown input observers and robust fault detection filters , 1996 .

[83]  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.

[84]  Alessandro Pisano,et al.  Observer-based output feedback control of a PEM fuel cell system by high-order sliding mode technique , 2013, 2013 European Control Conference (ECC).

[85]  M. Ghanes,et al.  Direct control based on sliding mode techniques for multicell serial chopper , 2011, Proceedings of the 2011 American Control Conference.

[86]  C. K. Michael Tse,et al.  A Fast-Response Sliding-Mode Controller for Boost-Type Converters With a Wide Range of Operating Conditions , 2007, IEEE Transactions on Industrial Electronics.

[87]  Phatiphat Thounthong,et al.  Control of a Three-Level Boost Converter Based on a Differential Flatness Approach for Fuel Cell Vehicle Applications , 2012, IEEE Transactions on Vehicular Technology.

[88]  Mehrdad Saif,et al.  A new approach to robust fault detection and identification , 1993 .

[89]  Vicenç Puig,et al.  LPV observer design for PEM fuel cell system: Application to fault detection , 2011 .

[90]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[91]  A. Isidori Nonlinear Control Systems , 1985 .

[92]  Jaime A. Moreno,et al.  Identification and observation in the anode line of PEM fuel cell stacks , 2013, 52nd IEEE Conference on Decision and Control.

[93]  Wei Kang,et al.  On the Observability of Nonlinear and Switched Systems , 2009 .

[94]  Fang Zheng Peng,et al.  Multilevel inverters: a survey of topologies, controls, and applications , 2002, IEEE Trans. Ind. Electron..

[95]  Vicenç Puig,et al.  Model-based fault diagnosis in PEM fuel cell systems , 2009 .

[96]  Leonid M. Fridman,et al.  Lyapunov-Designed Super-Twisting Sliding Mode Control for Wind Energy Conversion Optimization , 2013, IEEE Transactions on Industrial Electronics.

[97]  Carlos Andrés Ramos-Paja,et al.  Fuel cell emulator for oxygen excess ratio estimation on power electronics applications , 2012, Comput. Electr. Eng..

[98]  R. Rajamani Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[99]  Hao-Chi Chang,et al.  Sliding mode control on electro-mechanical systems , 1999 .

[100]  Sheldon S. Williamson,et al.  Power-Electronics-Based Solutions for Plug-in Hybrid Electric Vehicle Energy Storage and Management Systems , 2010, IEEE Transactions on Industrial Electronics.

[101]  Ahmed Al-Durra,et al.  Study of nonlinear control schemes for an automotive traction PEM fuel cell system , 2010 .

[102]  Cassiano Rech,et al.  Hybrid Multilevel Converters: Unified Analysis and Design Considerations , 2007, IEEE Transactions on Industrial Electronics.

[103]  Kyung Won Suh,et al.  Modeling, analysis and control of fuel cell hybrid power systems , 2006 .

[104]  Arie Levant,et al.  Principles of 2-sliding mode design , 2007, Autom..

[105]  Murat Arcak,et al.  A nonlinear observer design for fuel cell hydrogen estimation , 2004, IEEE Transactions on Control Systems Technology.

[106]  Alberto Isidori,et al.  A Geometric Approach to Nonlinear Fault Detection and Isolation , 2000 .

[107]  Bimal K. Bose,et al.  Modern Power Electronics and AC Drives , 2001 .

[108]  A. Levant Sliding order and sliding accuracy in sliding mode control , 1993 .

[109]  M. Fadel,et al.  Floating voltages estimation in three-cell converters using a discrete-time Kalman filter , 2001, 2001 IEEE 32nd Annual Power Electronics Specialists Conference (IEEE Cat. No.01CH37230).

[110]  D.G. Holmes,et al.  Analytical Modelling of Voltage Balance Dynamics for a Flying Capacitor Multilevel Converter , 2008, IEEE Transactions on Power Electronics.

[111]  Chanin Panjapornpon Estimation of Water Content in PEM Fuel Cell , 2008 .

[112]  Dong-Seok Hyun,et al.  Comparison of single-sensor current control in the DC link for three-phase voltage-source PWM converters , 2001, IEEE Trans. Ind. Electron..

[113]  Youmin Zhang,et al.  Bibliographical review on reconfigurable fault-tolerant control systems , 2003, Annu. Rev. Control..

[114]  Diego Feroldi,et al.  Design and Analysis of Fuel-Cell Hybrid Systems Oriented to Automotive Applications , 2009, IEEE Transactions on Vehicular Technology.

[115]  Asif Sabanovic,et al.  Variable structure systems : from Principles to Implementation , 2004 .

[116]  A.G. Stefanopoulou,et al.  Model based detection of hydrogen leaks in a fuel cell stack , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[117]  Hai Lin,et al.  Design and analysis of continuous hybrid differentiator , 2011, ArXiv.

[118]  Christopher Edwards,et al.  Adaptive Sliding-Mode-Observer-Based Fault Reconstruction for Nonlinear Systems With Parametric Uncertainties , 2008, IEEE Transactions on Industrial Electronics.

[119]  Eung-Seok Kim,et al.  Nonlinear observer Design for PEM fuel cell systems , 2007, 2007 International Conference on Electrical Machines and Systems (ICEMS).

[120]  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.

[121]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[122]  Steven X. Ding,et al.  Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis , 1994, Autom..

[123]  Janos Gertler,et al.  Robust FDI systems and H/sub /spl infin//-optimization-disturbances and tall fault case , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[124]  Alessandro Pisano,et al.  Globally convergent real-time differentiation via second order sliding modes , 2007, Int. J. Syst. Sci..

[125]  Christopher Edwards,et al.  On the Development and Application of Sliding Mode Observers , 2002 .

[126]  Hasan Komurcugil,et al.  Lyapunov-based control for three-phase PWM AC/DC voltage-source converters , 1998 .

[127]  J. C. Amphlett,et al.  Performance modeling of the Ballard Mark IV solid polymer electrolyte fuel cell. II: Empirical model development , 1995 .

[128]  Mehrdad Saif,et al.  Sliding Mode Observers and Their Application in Fault Diagnosis , 2003 .

[129]  T.A. Meynard,et al.  Multi-level conversion: high voltage choppers and voltage-source inverters , 1992, PESC '92 Record. 23rd Annual IEEE Power Electronics Specialists Conference.

[130]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[131]  John G. Hayes,et al.  Power-Factor-Corrected Single-Stage Inductive Charger for Electric Vehicle Batteries , 2007, IEEE Transactions on Industrial Electronics.

[132]  Anna G. Stefanopoulou,et al.  Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design , 2004 .

[133]  Anna G. Stefanopoulou,et al.  Control-Oriented Modeling and Analysis for Automotive Fuel Cell , 2004 .

[134]  Marco Liserre,et al.  Implementation issues of a fuzzy-logic-based three-phase active rectifier employing only Voltage sensors , 2005, IEEE Transactions on Industrial Electronics.

[135]  Christopher Edwards,et al.  Nonlinear robust fault reconstruction and estimation using a sliding mode observer , 2007, Autom..

[136]  Wei-Mon Yan,et al.  Effective schemes to control the dynamic behavior of the water transport in the membrane of PEM fuel cell , 2005 .

[137]  Michael Defoort,et al.  High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction , 2014, J. Frankl. Inst..

[138]  Fei Gao,et al.  PEM Fuel Cell Stack Modeling for Real-Time Emulation in Hardware-in-the-Loop Applications , 2011, IEEE Transactions on Energy Conversion.

[139]  J. Slotine,et al.  On Sliding Observers for Nonlinear Systems , 1986, 1986 American Control Conference.

[140]  Gildas Besancon,et al.  Nonlinear observers and applications , 2007 .

[141]  S. Żak,et al.  Comparative study of non-linear state-observation techniques , 1987 .

[142]  J. Fernando A. da Silva,et al.  Sliding-mode control of boost-type unity-power-factor PWM rectifiers , 1999, IEEE Trans. Ind. Electron..

[143]  George J. Pappas,et al.  Observability of Switched Linear Systems in Continuous Time , 2005, HSCC.

[144]  Dong-Choon Lee,et al.  DC-bus voltage control of three-phase AC/DC PWM converters using feedback linearization , 2000 .

[145]  Thierry Meynard,et al.  Modeling of multilevel converters , 1997, IEEE Trans. Ind. Electron..

[146]  M. Tadjine,et al.  Sliding mode and fault tolerant control for multicell converter four quadrants , 2013 .

[147]  Anna G. Stefanopoulou,et al.  Current Management in a Hybrid Fuel Cell Power System: A Model-Predictive Control Approach , 2006, IEEE Transactions on Control Systems Technology.

[148]  C. Pan,et al.  Modeling and Analysis of Three Phase PWM AC-DC Converter without Current Sensor , 1993 .

[149]  Mohamed Djemai,et al.  High-order sliding mode control of a DC motor drive via a switched controlled multi-cellular converter , 2011, Int. J. Syst. Sci..

[150]  Chee Pin Tan,et al.  Sliding mode observers for fault detection and isolation , 2002 .

[151]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[152]  Alon Kuperman,et al.  Battery Charger for Electric Vehicle Traction Battery Switch Station , 2013, IEEE Transactions on Industrial Electronics.

[153]  Patrick Wheeler,et al.  High-voltage multicellular converters applied to ac/ac conversion , 2003 .

[154]  Carlos Bordons,et al.  Nonlinear MPC for the airflow in a PEM fuel cell using a Volterra series model , 2012 .