** Embedded P.E.M. Fuel Cell Stack Nonlinear Observer**

** by means of a Takagi-Sugeno Approach**

**Severus Constantin OLTEANU ^{1}, Abdel AITOUCHE^{1}, Lotfi BELKOURA^{1},**

Adnan JOUNI^{2}

^{1}Laboratoire CRIStAL (Research Center in Informatics, Signal and

Automatic control in Lille), University of Lille 1, Cité Scientifique,

Av. Paul Langevin, 59655, Villeneuve D’Ascq Cedex, France

severus.olteanu@gmail.com, lotfi.belkoura@univ-lille1.fr, abdel.aitouche@hei.fr

^{2}Lebanese University of Beirut,

Baabda, Beirut, Lebanon

adnan_jouni@yahoo.fr

**Abstract: **This paper deals with the design of a nonlinear state observer for parameters within the gas transfer part of a fuel cell stack and its implementation on a small-scale embedded system. The fuel cell stack is of a proton exchange membrane type, with parameters specific to vehicle applications. The observer is afterwards applied on a small scale embedded board. In order to validate the embedded observer, a real time hardware in the loop testing is done using a co-simulation between the embedded observer and the professional simulation software AMESim, linked with Simulink on a Windows platform. To act upon the nonlinear character of the system, a Takagi-Sugeno approach is implemented, where the premise variables are unmeasurable. The procedure applies Lyapunov stability theory and by demanding bounded stability instead of asymptotic one, the algorithm manages to eliminate the need for Lipschitz constants.

**Keywords: **nonlinear state estimation, PEM fuel cell, Takagi Sugeno, unmeasurable premise variables, embedded observer, hardware in the loop validation.

**>Full text**

**CITE THIS PAPER AS**:

Severus Constantin OLTEANU, Abdel AITOUCHE, Lotfi BELKOURA, Adnan JOUNI, **Embedded P.E.M. Fuel Cell Stack Nonlinear Observer by means of a Takagi-Sugeno Approach**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 24 (1), pp. 61-70, 2015.

**Introduction**

The Hydrogen Fuel Cell systems have spurred interest in the last decade, despite the still high production cost, because of their elevated efficiency, reduced pollution level and the targeted independence from fossil fuels. Amongst different types of Fuel Cells (FC) like solid oxide or alkaline ones [1], the proton exchange membrane (P.E.M.) type [2] stands out, because of its low working temperature, and proves to be best suited for vehicle applications. In electrical vehicles, the energy storage plays one of the most important roles [3], so the research on Fuel Cells will boost the acceptance of electrical vehicles as well. Therefore, it directly competes with batteries which have been developing continuously for many years, yet prove inferior in some aspects to hydrogen technology as shown in [4], both as weight per storage capacity and energy density; these represent two important factors, that add to the slow recharge rate of a battery.

The Fuel Cells are small scaled devices therefore the development of virtual sensors would reduce the price. Also, a state observer may be used for diagnostics [5]. The majority of the papers that take into account the dynamics and not only the static models of FCs, focus only upon the electrical part of the fuel cell ignoring the auxiliary components [6] or treating just the compressor separately [7]. Nevertheless, papers such as [8], have to be mentioned as a thorough review upon all the components used so far. Indeed, for the more general case of system diagnosis, we find also many alternative approaches to model based techniques (for which a good review is [9]): experimental (ex: impedance spectroscopy [10], neuro-fuzzy techniques). As there is still no standardization in different existing types of FCs, a functional model would be easier to adapt to any particular case instead of experimental approaches that require extensive training data. Also model based approaches [11], [12] have the potential to give fast response to time variations, therefore being very efficient for on-line diagnosis [13] as well as control [14]. Of course one has to mention the greatest inconvenient of model based techniques that is the difficulty in parameter estimation. The state observer acts as a virtual sensors and it is designed to estimate cathode and anode pressures and mass flows of oxygen and hydrogen which are generally not measured. The mass flow rates of reactant gases play a pivotal role in the reliable and efficient operation of FCS.

For the design of the nonlinear observer, a Takagi-Sugeno (TS) representation has been chosen [15],[16]. This method can be found in literature, acting upon different types of industrial processes [17]. This approach has an advantage over other nonlinear ones in that there is no need for many assumptions regarding the form of the state space model, it has a structured form, it is easy to implement numerically and it also allows a parallel to linear techniques to be drawn. The construction of state observers based on TS representation has been in a continuous augmentation in the last period. Although many papers consider the premise variables measurable [19], this case in many practical applications is unfortunately unattainable. Among those who have tackled the issue of unmeasurable premise variables, one can cite [18].

It is useful to adopt the use of simulation software to replace the real system in the first hardware in the loop testing stage. For this, AMESim has been chosen [20]. Also, in the last years, small scaled embedded systems have become more and more accessible.

We can distinguish three classes:

*Microcontroller (based boards)*as Arduino boards;*FPGA*which are good for parallel computing;*Processor based:*as Raspberry PI, Beagle board, that act like small computers.

Each of them has certain advantages and disadvantages. In this article the authors have adopted the use of an Arduino Due board, and the development procedure with the hardware in the loop testing being described in [21].

The paper is organized as follows. Second section develops upon the Fuel Cell model. It is followed by a description of the TS representation and nonlinear observer design in the section III. Afterwards, in the fourth section, the embedded platform is described as well as the hardware in the loop (HIL) validation mechanism. The paper ends with results in section V respectively conclusions in section VI.

**REFERENCES**

- KIRUBAKARAN, A., S. JAIN, R. K. NEMA,
**A Review on Fuel Cell Technologies and Power Electronic Interface**, Renewable and Sustainable Energy Reviews, vol. 13, no. 9, December 2009, pp. 2430-2440. - BARBIR, F.,
**PEM Fuel Cells Theory and Practice**. Second edition, Ed. Elsevier Inc., 2013. - LUKIC, S. M., J. CAO, R. C. BANSAL, F. RODRIGUEZ, A. EMADI,
**Energy Storage Systems for Automotive Applications**, IEEE Transactions on Industrial Electronics, vol. 55, no. 6, June 2008, pp. 2258-2267. - THOMAS, C. E.,
**Fuel Cell and Battery Electric Vehicles Compared**, International Journal of Hydrogen Energy, vol. 34, Jan 2009, pp. 6005-6020. - ZHANG, J., H. ZHANG, J. WU, J. ZHANG,
**Techniques for PEM Fuel Cell Testing and Diagnosis,**PEM Fuel Cell Testing and Diagnosis, Elsevier, 2011, pp. 81-119. - KIM, J., J. LEE, B. H. CHO,
**Equivalent Circuit Modeling of PEM Fuel Cell Degradation Combined with a LFRC**, IEEE Transactions on Industrial Electronics, vol. 60, no. 11, November 2013, pp. 5075-5085. - MATRAJI, I., S. LAGHROUCHE, M. WACK,
**Cascade Control of the Moto-Compressor of a PEM Fuel Cell via Second Order Sliding Mode**, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference, December 2011, pp.633-638. - PUKRUSHPAN, J. T., A. G. STEFANOPOULOU, H. PENG,
**Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design**. Ed. Springer, 2004. - PETRONE, R., Z. ZHENG, D. HISSEL, M. C. PERA, C. PIANESE, M. SORRENTINO, M. BECHERIF, N. Y. STEINER,
**A Review on Model-based Diagnosis Methodologies for PEMFCs**, International Journal of Hydrogen Energy, vol. 38, no. 17, 2013, pp. 7077-7091. - STEINER, N. Y., D. HISSEL, P. MOÇOTÉGUY, D. CANDUSSO,
**Non Intrusive Diagnosis of Polymer Electrolyte Fuel Cells by Wavelet Packet Transform**, International Journal of Hydrogen Energy, vol. 36, no. 1, 2011, pp. 740-746. - HOSSEINI, M., A. H. SHAMEKHI, A. YAZDANI,
**Modeling and Simulation of a PEM Fuel Cell (PEMFC) Used in Vehicles**, SAE 2012 World Congress & Exhibition 2012, 2012-01-1233. - AITOUCHE, A., Q. YANG, B. OULD BOUAMAMA,
**Fault Detection and Isolation of PEM Fuel Cell System based on Nonlinear Analytic Redundancy. An Application Via Parity Space Approach**, The European Physical Journal of Applied Physics, vol. 54, January 2011. - HAFAIFA, A., F. LAAOUAD, K. LAROUSSI,
**Fuzzy Approach Applied in Fault Detection and Isolation to the Compression System Control**, Studies in Informatics and Control, ISSN 1220-1766, vol. 19, no. 1, 2010, pp. 17-26. - KIM, E. S.,
**Observer Based Nonlinear State Feedback Control of PEM Fuel Cell Systems**, Journal of Electrical Engineering and Electronic Technology vol. 7, no. 6, 2012, pp. 891-897. - TANAKA, K., T. IKEDA, H. WANG,
**Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-based Designs**, IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, 1998, pp. 250-265. - JAMEL, W., A. KHEDHER, N. BOUGUILA, K. B. OTHMAN,
**State Estimation via Observers with Unknown Inputs: Application to a Particular Class of Uncertain Takagi-Sugeno Systems**, Studies in Informatics and Control, ISSN 1220-1766, vol. 19, no. 3, 2010, pp. 219-228. - GEORG, S., M. MULLER, H. SCHULTE,
**Wind Turbine Model and Observer in Takagi-Sugeno Model Structure**, Journal of Physics: Conference Series, vol. 555, no 1, 2014. - YACINE, Z., D. ICHALAL, N. AIT OUFROUKH, S. DJENNOUNE,
**Nonlinear Vehicle Lateral Dynamics Estimation with Unmeasurable Premise Variable Takagi-Sugeno Approach**, 20^{th}Mediterranean Conference on Control & Automation (MED), Barcelona, Spain, July 2012, pp. 1117-1122. - LENDEK, Z., T. M. GUERRA, R. BABUSKA, B. de SCHUTTER,
**Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models**, Studies in Fuzziness and Soft Computing, Ed. Springer, 2010. - BOURDON, T., L. SAUSSOL, B. VAROQUIÉ,
**Integration of Physical AMESim® Engine Model in Hardware in the Loop Environment, Dedicated to Engine Control Unit Testing**,*SAE Technical Paper,*January 2007. - OLTEANU, S. C., A. AITOUCHE, L. BELKOURA,
**Advanced Embedded Nonlinear Observer Design and HIL Validation Using a Takagi-Sugeno Approach with Unmeasurable Premise Variables**, Journal of Physics: Conference Series, vol 570, no. 2, 2014. - OLTEANU, S. C., A. AITOUCHE, L. BELKOURA,
**Advances in P.E.M. Fuel Cell Stack Observer Design Using Takagi-Sugeno Approach with Unmeasurable Premise Variables**, ICREGA 2014 Renewable Energy: Generation and Applications, Springer Proceedings in Energy, Chapter 10, 2014, pp. 117-130. - GHORBEL, H., A. El HAJJAJI, M. SOUISSI, M. CHAABANE,
**Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System**, Journal of Dynamic Systems, Measurement, and Control, vol. 136, no. 4, 2014. - SONTAG, E. D.,
**On the Input-to-State Stability Property**, Journal Systems & Control Letters, vol. 24, 1995, pp. 351-359.