Type-2 Adaptive Fuzzy Modeling and Oxygen Excess Ratio Control for PEMFC Air Supply System
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摘要: 质子交换膜燃料电池（Proton exchange membrane fuel cell，PEMFC）空气供给系统存在外部扰动和参数不确定等动态特性，难以实现精准建模和控制.本文结合精确线性化和二型模糊逻辑系统，提出一种自适应控制器实现PEMFC空气供给系统的建模与过氧比控制.该控制器不需要PEMFC空气供给系统模型结构和参数完全已知的条件，而是通过二型模糊逻辑系统在线逼近PEMFC空气供给系统中的未建模动态并从Lyapunov函数中导出自适应参数，从而保证系统收敛性与稳定性.通过稳定性分析证明了该控制器作用下系统跟踪误差的有界性，仿真实验进一步验证了该控制器的有效性与实用性.
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关键词:
- 二型模糊逻辑系统 /
- 自适应控制 /
- 精确线性化 /
- Lyapunov稳定性 /
- 过氧比
Abstract: Proton exchange membrane fuel cell (PEMFC) air supply system has the characteristics of external disturbances and uncertain parameters, which make it difficult to achieve accurate modeling and stability control. In this paper, an adaptive controller is proposed to control the oxygen excess ratio of PEMFC air supply system by using the type-2 fuzzy logic systems. The controller does not need the known conditions of PEMFC system model but approximates unmodeled dynamics in the system by the adaptive fuzzy system whose the parameter adjustment is derived based on the Lyapunov theory. The stability analysis shows that the system is stable under the control of the controller. Simulation results demonstrate the usefulness and effectiveness of our proposed control strategy.1) 本文责任编委 赵旭东 -
图 2 PEMFC系统负载电流、过氧比和输出净功率的关系
Fig. 2 Power relationship of PEMFC system load current, OER, and output net
图 7 在$T_{st}=80\, ^{\circ}{ \rm C}$时精确线性化控制器的仿真结果
Fig. 7 The simulation results of exact linearization controller when $T_{st}=80\, ^{\circ}{ \rm C}$
图 8 在$T_{st}=75\, ^\circ{ \rm C}$时精确线性化控制器和本文所建议控制器的对比仿真结果
Fig. 8 The simulation results of exact linearization controller and proposed controller when $T_{st}=75\, ^{\circ}{ \rm C}$
表 1 PEMFC空气供给系统状态变量
Table 1 State variables of PEMFC air supply system
状态变量 符号 单位 空压机转速 $x_{1}=\omega_{cp}$ rad/s 供给管道内空气压强 $x_{2}=P_{sm}$ Pa 供给管道内空气质量 $x_{3}=m_{sm}$ kg 阴极内氧气质量 $x_{4}=m_{{\rm O_{2}}}$ kg 阴极内氮气质量 $x_{5}=m_{{\rm N_{2}}}$ kg 回流管道内空气压强 $x_{6}=P_{rm}$ Pa 
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A1 原公式和修正后公式的对比
A1 Comparison of original formulas and revised formulas
物理意义 原公式 修正后公式 注入阴极氧气流量 $\begin{array}{c}W_{{\rm O_{2}}, \rm in}(x_{2}, x_{3}, x_{4})=((x_{2}-B_{32}-B_{33}-\\x_{5}B_{34}-x_{4}B_{35})\times(x_{2}-x_{2}B_{6})^{-1}+ \\(x_{2}B_{36}-B_{37}-x_{5}B_{38}-\\x_{4}B_{39}))e(x_{2})k(x_{2})\end{array}$ $\begin{array}{c}W_{{\rm O_{2}}, \rm in}(x_{2}, x_{4}, x_{5})=((x_{2}B_{32}-B_{33}-\\x_{5}B_{34}-x_{4}B_{35})\times(x_{2}-x_{2}B_{6})^{-1}+\\(x_{2}B_{36}-K_{sm, \rm out}B_{37}-x_{5}K_{sm, \rm out}B_{38}-\\x_{4}K_{sm, \rm out}B_{39}))e(x_{2})k(x_{2})\end{array}$ 流出阴极空气流量 $\begin{array}{c}W_{ca, \rm out}(x_{4}, x_{5}, x_{6})=B_{47}+x_{5}B_{48}+\\x_{4}B_{49}-x_{6}B_{46} \end{array}$ $\begin{array}{c}W_{ca, \rm out}(x_{4}, x_{5}, x_{6})=B_{20}+x_{5}B_{21}+\\ x_{4}B_{22}-x_{6}B_{19}\end{array}$ 注入阴极氮气流量 $\begin{array}{c}W_{{\rm N_{2}}, \rm in}(x_{2}, x_{3}, x_{4})=((x_{2}B_{23}-B_{24}-\\x_{5}B_{25}-x_{4}B_{26})\times(x_{2}-x_{2}B_{6})^{-1}+\\(x_{2}B_{27}-B_{28}-x_{5}B_{29}-\\x_{4}B_{30}))e(x_{2})k(x_{2})\end{array}$ $\begin{array}{c}W_{{\rm N_{2}}, \rm in}(x_{2}, x_{4}, x_{5})=((x_{2}B_{23}-B_{24}-\\x_{5}B_{25}-x_{4}B_{26})\times(x_{2}-x_{2}B_{6})^{-1}+\\(x_{2}B_{27}-K_{sm, \rm out}B_{28}-x_{5}K_{sm, \rm out}B_{29}-\\x_{4}K_{sm, \rm out}B_{30}))e(x_{2})k(x_{2})\end{array}$ 流出阴极氧气流量 $\begin{array}{c} W_{{\rm O_{2}}, \rm out}(x_{4}, x_{5}, x_{6})=-x_{4}(B_{10}-x_{5}B_{11} +\\ x_{4}B_{12}-x_{6}B_{9})\times j(x_{4}, x_{5})x_{4 }^{-1} \times\\(j(x_{4}, x_{5})B_{40}-M_{N_{2}})^{-1} \times m(x_{4}, x_{5})\end{array}$ $\begin{array}{c}W_{{\rm O_{2}}, \rm out}(x_{4}, x_{5}, x_{6})=x_{4}(B_{10}+x_{5}B_{11} +\\x_{4}B_{12}-x_{6}B_{9}) \times j(x_{4}, x_{5})x_{4 }^{-1} \times\\(j(x_{4}, x_{5})B_{40}+M_{N_{2}})^{-1} \times m(x_{4}, x_{5})\end{array}$ 空压机驱动力矩 $\begin{array}{c}\tau_{cm}(u, x_{1})=\frac{\eta_{cm}K_{t}(u-K_{v}x_{1})}{R_{cm}J_{cp}}\end{array}$ $\begin{array}{c}\tau_{cm}(u, x_{1})=\frac{\eta_{cm}K_{t}(u-K_{v}x_{1})}{R_{cm}}\end{array} $ 空压机负载力矩 $\begin{array}{c}\tau_{cp}(x_{1}, x_{2})=\frac{C_{p}T_{atm}n(x_{2})W_{cp}(x_{1}, x_{2})}{\eta_{cp}J_{cp}x_{1}}\end{array}$ $\begin{array}{c}\tau_{cp}(x_{1}, x_{2})=\frac{C_{p}T_{atm}n(x_{2})W_{cp}(x_{1}, x_{2})}{\eta_{cp}x_{1}}\end{array}$
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