适用于质子交换膜燃料电池系统的高阶滑模观测器

doi:10.13229/j.cnki.jdxbgxb20220394

Abstract

Abstract:

To address the problem that the internal state variables of the Proton Exchange Membrane Fuel Cell （PEMFC） system are difficult to be measured directly by sensors， which makes it impossible to troubleshoot the PEMFC system and design a model-based controller， the High Order Sliding Mode （HOSM） observer was designed. Firstly， an 11th-order anode dead-end PEMFC system model suitable for observation was built. Then，on the basis of this model， the HOSM observer was designed by adjusting the errors between the measured sensor values （stack voltage， compressor outlet flow rate and stack temperature） and the estimated values by the HOSM algorithm. Finally, the performance of the designed HOSM observer was compared with the performance of the traditional sliding mode observer. The comparison results of the observation effect and the squared error integral show that the designed observer can accurately observe each state quantity and has better observation performance.

Key words: vehicle engineering, proton exchange membrane fuel cell（PEMFC）, observer, high order sliding mode, modeling and simulation

CLC Number:

TM911.4

Cheng LI,Hao JING,Guang-di HU,Xiao-dong LIU,Biao FENG. High⁃order sliding mode observer for proton exchange membrane fuel cell system[J].Journal of Jilin University(Engineering and Technology Edition), 2022, 52(9): 2203-2212.

Figures/Tables 8

Fig.1

Table 1

Main parameters of the stack"

参数	取值	参数	取值
燃料电池节数N	3.16	经验参数B	0.003 255 6
燃料电池活化面积A/cm²	260	最大电流密度i_max/（A·cm^-2）	2.2
阳极容积V_an/m³	0.002 35	氢气比热容 $C p, H 2$ /［J·（g·K）^-1］	14.03
阴极容积V_ca/m³	0.004 5	氧气比热容 $C p, O 2$ /［J·（g·K）^-1］	0.917
供应歧管容积V_sm/m³	0.005	氮气比热容 $C p, N 2$ /［J·（g·K）^-1］	1.039
电压经验参数 $ξ 1$	1.050 2	水蒸气比热容 $C p, v$ /［J·（g·K）^-1］	1.87
电压经验参数 $ξ 2$	-0.002 294 9	电堆质量比热乘 $m s t C p, s t$ /（kJ·K^-1）	490
电压经验参数 $ξ 3$	-9.518×10^-5	法拉第常数F	96 485
电压经验参数 $ξ 4$	0.000 148 05	空气气体常数 $R a$ /［J·（kg·K）^-1］	286.9
电压经验参数 $ξ 5$	0.000 249 24	氢气气体常 $R H 2$ /［J·（kg·K）^-1］	4124
电压经验参 $ξ 6$	-6.872×10^-7	氧气气体常 $R O 2$ /［J·（kg·K）^-1］	259.8
电压经验参数 $ξ 7$	3.26×10^-7	氮气气体常 $R N 2$ /［J·（kg·K）^-1］	296.8
MAP图拟合参数 $P 00$	288.2	水蒸气常数 $R v$ /［J·（kg·K）^-1］	461.5
MAP图拟合参 $P 01$	-0.000 463 1	热比系数 $γ$	1.4
MAP图拟合参数 $P 10$	-336.9	转动惯量J_cp/（ $k g ? m 2$ ）	-5.28×10^-5
MAP图拟合参数 $P 20$	-74.51	供应歧管容积V_s/m³	0.005
MAP图拟合参 $P 02$	-4.166×10^-8	环境压力P_atm/10⁶ Pa	1.013 25
MAP图拟合参数 $P 11$	0.006 191	环境温度T_atm/K	298.15

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Table 2

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观测对象	观测器
观测对象	HOSM	SMO
阳极氢气分压/Pa	6 289	82 520
阳极水蒸气分压/Pa	216.7	194.3
阴极氧气分压/Pa	4 854	28 260
阴极氮气分压/Pa	4 464	122 700
空压机电机转速/（rad·s^-1）	821.4	45 070
供应管气压/Pa	9 038	98 250
供应管气体质量/kg	3.996×10^-7	1.563×10^-6
阴极出气管压力/Pa	551.6	575.9
电堆阴极温度/K	0.344 1	0.876 5
电堆阳极温度/K	4.84	0.779 8
电堆温度/K	3.693×10^-8	5.354×10^-13
电堆输出电压/Pa	6.348	154.8
空压机输出流量/（kg·s^-1）	2.163×10^-7	1.78×10^-6

High⁃order sliding mode observer for proton exchange membrane fuel cell system

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