质子交换膜燃料电池模型的频域分数阶子空间辨识

Frequency domain fractional subspace identification of PEMFC model

针对质子交换膜燃料电池(PEMFC)系统发电过程中的分数阶特性,本文提出了一种频域分数阶子空间辨识方法建立PEMFC的分数阶状态空间(FOSS)模型.考虑到时域分数阶的微分形式计算复杂度较大,将时域中的分数阶微分在频域中转化为乘积的形式.首先,采用随机多频正弦激励信号对时域采集的信号进行处理,得到输入输出的频率响应数据;其次,利用频率响应数据构造实、虚部矩阵;接着,通过RQ分解、SVD分解以及最小二乘法求取系统系数矩阵A,B,C,D;由于参数同元分数阶次α、辅助阶次q以及频域采样点数M未知,本文提出了一种GA–PSO算法进行优化,将PSO算法作为主线,加入GA算法中的选择、交叉和变异操作,以进一步提高个体的自适应调整搜索方向、增强全局寻优的能力.仿真结果验证了算法的有效性,频域分数阶子空间辨识方法得到的输出能够较好的跟随实测数据,且优化后的辨识结果误差更小,精确度更高,能够更准确地描述PEMFC的电特性变化过程.

In this paper,a frequency domain fractional subspace identification method is proposed to establish PEMFC’s fractional order state space(FOSS)model for the fractional order characteristics of proton exchange membrane fuel cell(PEMFC)system in power generation.Considering the computational complexity of fractional order differential in time domain,the fractional order differential is transformed into product form in frequency domain.Firstly,the random multi-frequency sinusoidal excitation signal is adopted to obtain the input and output frequency response data.Secondly,the frequency response data is employed to construct real and imaginary part matrix.Then,RQ decomposition,SVD decomposition and least square method are used to calculate system coefficient matrix A,B,C,D.Because the parameters of the same element fractional orderα,auxiliary order q and frequency domain sampling points M are unknown,a GA–PSO algorithm is employed to optimize them,in which the selection,crossover and mutation operations of GA is added to PSO process to further improve the self-adaptive search direction of individuals and enhance the ability of global optimization.The simulation results verified the effectiveness of the algorithm.The output of frequency-domain fractional subspace identification can follow the measured data more closely,and the optimized identification results have smaller error and higher accuracy,which can more accurately describe the electrical characteristics of PEMFC.