Offset-free Explicit Model Predictive Control and Its Application on the Net Output Power Tracking of PEMFC System

doi:10.3901/JME.2024.14.282

Abstract

Abstract: Considering the optimal tracking issue of the net output power for the proton exchange membrane fuel cell(PEMFC), an explicit model predictive control(EMPC) based offset-free optimal control strategy is proposed, which aims at achieving the robust steady state offset-free tracking of desired net output power, in terms of system’s operating constraints and model mismatching, and is for the purpose of optimizing the system efficiency, by regulating the PEMFC’s operating points at around the optimal (sub-optimal) operating curve. Firstly, a control-oriented linear model is proposed by linearizing the PEMFC system. Then, a state observer is designed to estimate the state variables and model mismatching. A target calculator is designed to track the optimal net output power and to constrain the operating boundary of the air compressor. An EMPC controller is designed to relax the air compressor boundary constraints and achieve a reachable explicit solution, and consequently an offset-free EMPC strategy is proposed involves the above three parts. Finally, a hardware in loop test bench is set up, and a simulation is performed based on a standard vehicular fuel cell stack test cycle， in comparing with the conventional MPC and EMPC strategy. The results demonstrate that the off-set free EMPC control strategy is able to improve the system efficiency from 41% up to 47.6%, and to reduce the absolute average error of the output power tracking from 0.26 kW down to 0.17 kW, and the single step average time cost is reduced from 22.2 ms down to 2.1 ms, respectively.

Key words: proton exchange membrane fuel cell, net output power tracking, robust optimization, offset-free explicit model predictive control

CLC Number:

TG156

LI Hao, BIN Yang, HU Jie, YUE Xiao, JIN Tingan, ZHANG Kai. Offset-free Explicit Model Predictive Control and Its Application on the Net Output Power Tracking of PEMFC System[J]. Journal of Mechanical Engineering, 2024, 60(14): 282-297.

References

[1] DAS V，PADMANABAN S,VENKITUSAMY K，et al. Recent advances and challenges of fuel cell based power system architectures and control–A review[J]. Renewable and Sustainable Energy Reviews，2017，73：10-18.
[2] CHEN J，LIU Z，WANG F，et al. Optimal oxygen excess ratio control for PEM fuel cells[J]. IEEE Transactions on Control Systems Technology，2017，26(5)：1711-1721.
[3] PUKRUSHPAN J T，STEFANOPOULOU A G，PENG H. Control of fuel cell power systems：Principles，modeling，analysis and feedback design[M]. Berlin：Springer Science & Business Media，2004.
[4] KIM B，CHA D，KIM Y. The effects of air stoichiometry and air excess ratio on the transient response of a PEMFC under load change conditions[J]. Applied Energy，2015，138：143-149.
[5] Suh K W. Modeling，analysis and control of fuel cell hybrid power systems[D]. Ann Arbor：University of Michigan，2006.
[6] TALJ R J，HISSEL D，ORTEGA R，et al. Experimental validation of a PEM fuel-cell reduced-order model and a moto-compressor higher order sliding-mode control[J]. IEEE Transactions on Industrial Electronics，2010，57(6)：1906-1913.
[7] WANG F，OUYANG Q，CHEN J，et al. Feedback linearization control of the air supply system of PEM fuel cells[C]// 2015 10th Asian Control Conference (ASCC). IEEE，2015：1-6.
[8] BIN Y，RAJASHEKARA K，LI Y. Nonlinear tracking control of output power for PEMFC systems[C]// 2016 American Control Conference (ACC). IEEE，2016：6809-6814.
[9] ARCE A，PANOS C，BORDONS C，et al. Design and experimental validation of an explicit MPC controller for regulating temperature in PEM fuel cell systems[J]. IFAC Proceedings Volumes，2011，44(1)：2476-2481.
[10] ARCE A，ALEJANDRO J，BORDONS C，et al. Real-time implementation of a constrained MPC for efficient airflow control in a PEM fuel cell[J]. IEEE Transactions on Industrial Electronics，2009，57(6)：1892-1905.
[11] BAROUD Z，BENMILOUD M，BENALIA A，et al. Novel hybrid fuzzy-PID control scheme for air supply in PEM fuel-cell-based systems[J]. International Journal of Hydrogen Energy，2017，42(15)：10435-10447.
[12] BEIRAMI H，SHABESTARI A Z，ZERAFAT M. Optimal PID plus fuzzy controller design for a PEM fuel cell air feed system using the self-adaptive differential evolution algorithm[J]. International Journal of Hydrogen Energy，2015，40(30)：9422-9434.
[13] ABBASPOUR A，KHALILNEJAD A，CHEN Z. Robust adaptive neural network control for PEM fuel cell[J]. International Journal of Hydrogen Energy，2016，41(44)：20385-20395.
[14] MATRAJI I，AHMED F，LAGHROUCHE S，et al. Comparison of robust and adaptive second order sliding mode control in PEMFC air-feed systems[J]. International Journal of Hydrogen Energy，2015，40(30)：9491-9504.
[15] PILLONI A，PISANO A，USAI E. Observer-based air excess ratio control of a PEM fuel cell system via high-order sliding mode[J]. IEEE Transactions on Industrial Electronics，2015，62(8)：5236-5246.
[16] GRUBER J，BORDONS C，OLIVA A. Nonlinear MPC for the airflow in a PEM fuel cell using a Volterra series model[J]. Control Engineering Practice，2012，20(2)：205-217.
[17] ZIOGOU C，VOUTETAKIS S，GEORGIADIS M，et al. Model predictive control strategies for PEM fuel cell systems–A comparative experimental demonstration[J]. Chemical Engineering Research and Design，2018，131：656-670.
[18] CANO M，MOUSLI M，KELOUWANI S，et al. Improving a free air breathing proton exchange membrane fuel cell through the maximum efficiency point tracking method[J]. Journal of Power Sources，2017，345：264-274.
[19] SAAD N，EL-SATTAR A，MANSOUR A. Adaptive neural controller for maximum power point tracking of ten parameter fuel cell model[J]. Journal of Electrical Engineering & Technology，2013，13(3)：233-239.
[20] PANNOCCHIA G，RAWLINGS J B. Disturbance models for offset-free model predictive control[J]. AIChE Journal，2003，49(2)：426-437.
[21] MUSKE K，BADGWELL T. Disturbance modeling for offset-free linear model predictive control[J]. Journal of Process Control，2002，12(5)：617-632.
[22] MAEDER U，BORRELLI F，MORARI M. Linear offset-free model predictive control[J]. Automatica，2009，45(10)：2214-2222.
[23] PANNOCCHIA G，BEMPORAD A. Combined design of disturbance model and observer for offset-free model predictive control[J]. IEEE Transactions on Automatic Control，2007，52(6)：1048-1053.
[24] PANNOCCHIA G. Offset-free tracking MPC：A tutorial review and comparison of different formulations[C]//2015 European Control Conference (ECC). IEEE，2015：527-532.
[25] VILLA-TAMAYO M，CAICEDO M，RIVADENEIRA P. Offset-free MPC strategy for nonzero regulation of linear impulsive systems[J]. ISA Transactions，2020，101：91-101.
[26] Manzoor T，Xia Y，Zhai D H，et al. Trajectory tracking control of a VTOL unmanned aerial vehicle using offset-free tracking MPC[J]. Chinese Journal of Aeronautics，2020，33(7)：2024-2042.
[27] HÄHNEL C，CLOPPENBORG A，HORN J. Offset-free nonlinear model predictive control of electrical power of a PEM fuel cell system using an Extended Kalman Filter[C]// 201624th Mediterranean Conference on Control and Automation (MED). IEEE，2016：106-111.
[28] AYDIN B，VAN OVERLOOP P，RUTTEN M，et al. Offset-free model predictive control of an open water channel based on moving horizon estimation[J]. Journal of Irrigation and Drainage Engineering，2017，143(3)：B4016005.
[29] PUKRUSHPAN J. Modeling and control of fuel cell systems and fuel processors[D]. Michigan：University of Michigan，2003.
[30] VAHIDI A，KOLMANOVSKY I，STEFANOPOULOU A. Constraint handling in a fuel cell system：A fast reference governor approach[J]. IEEE Transactions on Control Systems Technology，2007，15(1)：86-98.
[31] SONTAG E D. Mathematical control theory：Deterministic finite dimensional systems[M]. Berlin：Springer Science & Business Media，2013.
[32] 张宇鑫，武建华，郑林锋，等. 基于数字孪生的锂离子电池管理系统设计分析[J]. 电气工程学报，2022，17(4)：103-112. ZHANG Yuxin，WU Jianhua，ZHENG Linfeng，et al. Design and analysis of lithium-ion battery management system based on digital twin[J]. Journal of Electrical Engineering，2022，17(4)：103-112.
[33] HERCEG M，KVASNICA M，JONES C，et al. Multi-parametric toolbox 3.0[C]// 2013 European Control Conference (ECC). IEEE，2013：502-505.
[34] 李维聪，穆浩，沈恒龙，等. 固态锂电池在载运工具中的应用前景分析[J]. 电气工程学报，2022，17(4)：88-102. LI Weicong，MU Hao，SHEN Henglong，et al. Application prospect analysis of solid-state lithium battery in vehicle[J]. Journal of Electrical Engineering，2022，17(4)：88-102.
[35] 徐茂舒，沈旖，王晟，等. 先进感知技术在电池状态估计中的应用与启示[J]. 电气工程学报，2022，17(3)：40-57. XU Maoshu，SHEN Yi，WANG Sheng，et al. Application and enlightenment of advanced sensing technology in battery state estimation[J]. Journal of Electrical Engineering，2022，17(3)：40-57.