The underlying models of lithium-ion batteries are spatiotemporal and, therefore, consist of partial differential equations (PDEs), as they have to capture spatiotemporal electrochemical mechanisms. As parametric uncertainty increases, often PDE models become inadequate as modeling errors due to parameter uncertainty are much larger than those due to model reduction to ordinary differential equations (ODEs). In this paper, we focus on a linear ODE model derived from the PDE combined with algebraic nonlinearities to carry out parameter identification. The ODE model captures the diffusion dynamics while the nonlinearities capture the overpotential and open-circuit potential aspects. The parameter identification method consists of a matrix-regressor adaptive observer, whose regressors are composed using both the states of the linear dynamic model and suitably constructed basis functions of the algebraic nonlinearities. Under conditions of persistent excitation, the parameter and state estimation errors are shown to converge to zero if the overpotential is known, and to a compact set if the overpotential is unknown. A PDE-based single-particle model is used as the truth model to evaluate the accuracy of the proposed adaptive observer. It is shown that the adaptive observer is able to carry out fast estimation of internal states for a battery management system, such as the state of charge and state of health, under a range of operating conditions.

中文翻译：

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用于电池管理系统的快速自适应观察器

锂离子电池的基本模型是时空的，因此由偏微分方程（PDE）组成，因为它们必须捕获时空的电化学机理。随着参数不确定性的增加，由于参数不确定性导致的建模误差远大于因将模型简化为常微分方程（ODE）而导致的建模误差，PDE模型通常变得不够用。在本文中，我们集中于从PDE导出的线性ODE模型并结合代数非线性来进行参数识别。ODE模型捕获扩散动力学，而非线性则捕获过电势和开路电势。参数识别方法由矩阵回归自适应观测器组成，其回归变量是使用线性动力学模型的状态和代数非线性的适当构造的基函数组成的。在持续励磁的条件下，如果已知过电势，则参数和状态估计误差将收敛为零；如果未知电势，则参数和状态估计误差将收敛为紧集。基于PDE的单粒子模型用作真实模型，以评估所提出的自适应观测器的准确性。结果表明，自适应观察者能够在一定范围的工作条件下快速估算电池管理系统的内部状态，例如充电状态和健康状态。如果已知过电势，则参数和状态估计误差将收敛为零；如果未知电势，则将参数和状态估计误差收敛为紧集。基于PDE的单粒子模型用作真实模型，以评估所提出的自适应观测器的准确性。结果表明，自适应观察者能够在一定范围的工作条件下快速估算电池管理系统的内部状态，例如充电状态和健康状态。如果已知过电势，则参数和状态估计误差将收敛为零；如果未知电势，则将参数和状态估计误差收敛为紧集。基于PDE的单粒子模型用作真实模型，以评估所提出的自适应观测器的准确性。结果表明，自适应观察者能够在一定范围的工作条件下快速估算电池管理系统的内部状态，例如充电状态和健康状态。