Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 26, No. 11 (November 2013) 1357-1368   

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  SYSTEMATIC APPROACH TO DESIGN A FINITE TIME CONVERGENT DIFFERENTIATOR IN SECOND ORDER SLIDING MODE CONTROLLER
 
S. M. Rakhtala, A. Ranjbar and R. Ghaderi
 
( Received: November 30, 2012 – Accepted: April 18, 2013 )
 
 

Abstract    This paper presents a systematic approach to design a Lyapunov based super twisting differentiator. The differentiator will be shown convergent in a finite time whilst the relevant time is accurately estimated. This differentiator is the main part to establish the sliding surface in higher order sliding mode. The differentiator is used in the prescribed control structure to regulate pressures of hydrogen and oxygen of a nonlinear Polymer Electrolyte Membrane Fuel Cells (PEMFCs) to prolong the stack life. The aim of the control strategy is to minimize and keep the deviation between the pressures of hydrogen and oxygen. The deviation forms a sliding surface, where its appropriate differentiation is required in the control law. It is why to reconstruct finite time derivatives in a closed-loop control. Finally, simulation result and a comparative study verify the performance of the proposed differentiator and the control structure to provide convergent estimator in finite time.

 

Keywords    PEM fuel cell dynamic model, Second order sliding mode control, Step by step differentiator, Pressure regulation.

 

چکیده    در این مقاله روش سیستمی برای طراحی مشتق­گیر با الگوریتم سوپرتویستینگ بر مبنای تابع لیاپانف ارائه شده است. نشان داده شد که مشتق­گیر در زمان محدود همگرا شده، که زمان مربوطه دقیقا تخمین زده شده است. این مشتق­گیر بعنوان قسمت اصلی از کنترل مد لغزشی مرتبه بالا است. این مشتق­گیر در ساختار کنترلی پیشنهادی برای تثبیت فشار هیدروژن و اکسیژن در سیستم غیر خطی پیل سوختی PEM با هدف طولانی کردن طول عمر پشته بکار گرفته شده است. هدف از استراتژی کنترلی، حفظ اختلاف فشار بین هیدروژن و اکسیژن، بمیزان حداقل ممکن است. مشتقات مطلوبی از سطح لغزش در قانون کنترلی مورد نیاز است که این امر دلیلی، برای بازسازی مشتقات زمان محدود در کنترل حلقه بسته می باشد. سرانجام نتایج شبیه سازی و مطالعات، تاییدی بر کارایی مشتق­گیر و ساختار کنترلی پیشنهادی در همگرایی تخمین در زمان محدود است.

References   

 

1.        Larminie, J., Dicks, A., "Fuel cell systems explained", 2nd ed. New York, USA, Wiley & Sons, (2003).

2.        Chiu, L.Y., Diong, B. andGemmen, R.S., "An Improved Small Signal Model of the Dynamic Behavior of PEM Fuel Cells", IEEE Transactions on Industry Application, Vol. 40, (2004), 970-977.

3.        Peng, H. and Pukrushpan, J.,"Control of Fuel Cell Power Systems: Principle, Modeling, Analysis and Feedback Design", Berlin, Germany Springers-Verlag, (2004).

4.        Pukrushpan, J., Peng, H. and Stefanopoulou, A., "Simulation and analysis of transient fuel cell system Performance based on a dynamic reactant flow model",  In: Proceedings of IMECE’02 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, USA, (2002), 1-12.

5.        Pukrushpan,J., Stefanopoulou, A. and Peng, H.,"Control of  Fuel Cell Breathing", Control Systems Magazine, Vol. 24, (2004), 30-46.

6.        Na,W. K., Gou,B. and Diong, B.,"Nonlinear Control of PEM Fuel Cells by Exact Linearization", IEEE Transactions on Industry Application, Vol. 43, (2007), 1426-1433.

7.        Na,W.K., Gou,B., "Feedback-Linearization-Based Nonlinear Control for PEM Fuel Cells", IEEE Transactions on Energy Conversion, Vol. 23, (2008), 179-190.

8.        Li, Q., Chen, W., Wang, Y., Jia, J. and Han, M., "Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization", Journal of Power Sources, Vol. 194, (2009), 338-348.

9.        Garcia-Gabin, W., Dorado, F. and Bordons, C., "Real-time implementation of a sliding mode controller for air supply on a PEM fuel cell", Journal of Process Control, Vol. 20, (2010), 325-336.

10.     Talj, R.J., Hissel, D., Ortega, R., Becherif, M. and Hilairet, M., "Experimental Validation of a PEM Fuel Cell Reduced Order Model and a Moto-Compressor Higher Order Sliding Mode Control", IEEE Transactions on Industrial Electronics, Vol. 57,(2010), 1906-1913.

11.     Talj, R.J., Hissel, D., Ortega, R., Becherif, M. and Hilairet, M.,"Reduced-Order Model and a Higher-Order Sliding-Mode Control of the Air Supply System  of a Proton-Exchange-Membrane Fuel Cell with Experimental Validation", In: 8th IEEE International Conference of Advanced Electromechanical Motion Systems & Electric Drives, Lille, (2009) 1-6.

12.     Kunusch, C., Puleston, P.F., Mayosky, M.A. and Riera J., "Sliding Mode Strategy for PEM Fuel Cells Stacks Breathing Control Using a Super-Twisting Algorithm", IEEE Transactions on Control Systems Technology, Vol. 17, (2009), 167-174.

13.     Kunusch, C., Puleston, P.F., Mayosky, M.A. and Serra M., "Advances in HOSM control design and implementation for PEM fuel cell systems," In: 14th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2009), 709-716.

14.     Matraji, I., Laghrouche, S. and Wack, M.,"Second order sliding mode control for PEM Fuel Cells", In: 49th IEEE Conference on Decision and Control (CDC), (2010), 2765-2770.

15.     Matraji, I., Laghrouche, S. and Wack, M.,"Pressure control in a PEM fuel cell via second order sliding mode", International Journal of Hydrogen Energy, Vol. 37, (2012), 16104-16116.

16.     Levent, A., "Robust exact differentiation via sliding mode technique," Automatica, Vol. 34, 379-384, 1998.

17.     Levant, A., "Higher-order sliding modes, differentiation and output-feedback control", International Journal of Control, Vol. 76, (2003), 924-941.

18.     Cannas, B., Cincotti, S. and Usai, E., "Chaos Synchronization via Sliding Modes", In: AIP Conference of 4th International  Conference Computing Anticipatory System, CASYS 2000, New York,(2001), 229 - 241.

19.     Pisano, A. and Usai, E., "Sliding mode control: A survey with applications in math", Mathematics and Computers in Simulation, Vol. 81, (2011), 954-979.

20.     Pisano,A.,"Second Order Sliding Modes: Theory and Applications", PhD, Dipartimento di Ingegneria Elettrica ed Elettronica (DIEE) Universit´a degli Studi di Cagliari, Cagliari,Italia, (2000).

21.     Levant, A.,"Principles of 2-sliding mode design," Automatica, Vol. 43, (2007), 576-586.

22.     Levant, A.,"Sliding order and sliding accuracy in sliding mode control," International Journal of Control, Vol. 58, (1993), 1247-1263.

23.     Bartolini, G., Ferrara, A., Pisano, A. and Usai, E., "On the convergence properties of a 2-sliding control algorithm for non-linear uncertain systems", International Journal of Control, Vol.74, (2001), 718-731.

24.     Bartolini, G., Pisano, A., Punta, E. and Usai, E.,"A survey of applications of second-order sliding mode control to mechanical systems", International Journal of Control, Vol. 76, (2003), 875-892.

25.     Moreno, J.,"A linear framework for the robust stability analysis of a generalized super-twisting algorithm", In: 6th International Conference Electrical Engineering, Computing Science and Automatic Control, Toluca, (2009), 12-17.

26.     Cruz-Zavala, E., Moreno, J. and Fridman, L., "Uniform Second-Order Sliding Mode Observer for Mechanical Systems", In: 11th International Conference Variable Structure Systems, Mexico City, Mexico, (2010), 14-15.

 

 

 

 

 

 

 

 

 

1.        Larminie, J., Dicks, A., "Fuel cell systems explained", 2nd ed. New York, USA, Wiley & Sons, (2003).

2.        Chiu, L.Y., Diong, B. andGemmen, R.S., "An Improved Small Signal Model of the Dynamic Behavior of PEM Fuel Cells", IEEE Transactions on Industry Application, Vol. 40, (2004), 970-977.

3.        Peng, H. and Pukrushpan, J.,"Control of Fuel Cell Power Systems: Principle, Modeling, Analysis and Feedback Design", Berlin, Germany Springers-Verlag, (2004).

4.        Pukrushpan, J., Peng, H. and Stefanopoulou, A., "Simulation and analysis of transient fuel cell system Performance based on a dynamic reactant flow model",  In: Proceedings of IMECE’02 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, USA, (2002), 1-12.

5.        Pukrushpan,J., Stefanopoulou, A. and Peng, H.,"Control of  Fuel Cell Breathing", Control Systems Magazine, Vol. 24, (2004), 30-46.

6.        Na,W. K., Gou,B. and Diong, B.,"Nonlinear Control of PEM Fuel Cells by Exact Linearization", IEEE Transactions on Industry Application, Vol. 43, (2007), 1426-1433.

7.        Na,W.K., Gou,B., "Feedback-Linearization-Based Nonlinear Control for PEM Fuel Cells", IEEE Transactions on Energy Conversion, Vol. 23, (2008), 179-190.

8.        Li, Q., Chen, W., Wang, Y., Jia, J. and Han, M., "Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization", Journal of Power Sources, Vol. 194, (2009), 338-348.

9.        Garcia-Gabin, W., Dorado, F. and Bordons, C., "Real-time implementation of a sliding mode controller for air supply on a PEM fuel cell", Journal of Process Control, Vol. 20, (2010), 325-336.

10.     Talj, R.J., Hissel, D., Ortega, R., Becherif, M. and Hilairet, M., "Experimental Validation of a PEM Fuel Cell Reduced Order Model and a Moto-Compressor Higher Order Sliding Mode Control", IEEE Transactions on Industrial Electronics, Vol. 57,(2010), 1906-1913.

11.     Talj, R.J., Hissel, D., Ortega, R., Becherif, M. and Hilairet, M.,"Reduced-Order Model and a Higher-Order Sliding-Mode Control of the Air Supply System  of a Proton-Exchange-Membrane Fuel Cell with Experimental Validation", In: 8th IEEE International Conference of Advanced Electromechanical Motion Systems & Electric Drives, Lille, (2009) 1-6.

12.     Kunusch, C., Puleston, P.F., Mayosky, M.A. and Riera J., "Sliding Mode Strategy for PEM Fuel Cells Stacks Breathing Control Using a Super-Twisting Algorithm", IEEE Transactions on Control Systems Technology, Vol. 17, (2009), 167-174.

13.     Kunusch, C., Puleston, P.F., Mayosky, M.A. and Serra M., "Advances in HOSM control design and implementation for PEM fuel cell systems," In: 14th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2009), 709-716.

14.     Matraji, I., Laghrouche, S. and Wack, M.,"Second order sliding mode control for PEM Fuel Cells", In: 49th IEEE Conference on Decision and Control (CDC), (2010), 2765-2770.

15.     Matraji, I., Laghrouche, S. and Wack, M.,"Pressure control in a PEM fuel cell via second order sliding mode", International Journal of Hydrogen Energy, Vol. 37, (2012), 16104-16116.

16.     Levent, A., "Robust exact differentiation via sliding mode technique," Automatica, Vol. 34, 379-384, 1998.

17.     Levant, A., "Higher-order sliding modes, differentiation and output-feedback control", International Journal of Control, Vol. 76, (2003), 924-941.

18.     Cannas, B., Cincotti, S. and Usai, E., "Chaos Synchronization via Sliding Modes", In: AIP Conference of 4th International  Conference Computing Anticipatory System, CASYS 2000, New York,(2001), 229 - 241.

19.     Pisano, A. and Usai, E., "Sliding mode control: A survey with applications in math", Mathematics and Computers in Simulation, Vol. 81, (2011), 954-979.

20.     Pisano,A.,"Second Order Sliding Modes: Theory and Applications", PhD, Dipartimento di Ingegneria Elettrica ed Elettronica (DIEE) Universit´a degli Studi di Cagliari, Cagliari,Italia, (2000).

21.     Levant, A.,"Principles of 2-sliding mode design," Automatica, Vol. 43, (2007), 576-586.

22.     Levant, A.,"Sliding order and sliding accuracy in sliding mode control," International Journal of Control, Vol. 58, (1993), 1247-1263.

23.     Bartolini, G., Ferrara, A., Pisano, A. and Usai, E., "On the convergence properties of a 2-sliding control algorithm for non-linear uncertain systems", International Journal of Control, Vol.74, (2001), 718-731.

24.     Bartolini, G., Pisano, A., Punta, E. and Usai, E.,"A survey of applications of second-order sliding mode control to mechanical systems", International Journal of Control, Vol. 76, (2003), 875-892.

25.     Moreno, J.,"A linear framework for the robust stability analysis of a generalized super-twisting algorithm", In: 6th International Conference Electrical Engineering, Computing Science and Automatic Control, Toluca, (2009), 12-17.

26.     Cruz-Zavala, E., Moreno, J. and Fridman, L., "Uniform Second-Order Sliding Mode Observer for Mechanical Systems", In: 11th International Conference Variable Structure Systems, Mexico City, Mexico, (2010), 14-15.






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