<p style='text-indent:20px;'>In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.</p>

中文翻译：

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电化学锂离子电池模型中充电状态的跟踪问题

<p style='text-indent:20px;'>在本文中，单粒子模型用于描述锂离子电池的行为。主要目标是设计反馈输入电流，以便将充电状态 (SOC) 调节到规定的参考轨迹。为此，我们使用边界离子浓度作为输出。首先，我们直接测量它，然后我们假设存在一个适当的估计器，该估计器已在文献中使用电压测量建立。通过应用 backstepping 和 Lyapunov 工具，我们能够构建观察器并设计输出反馈控制器，从而对 SOC 跟踪问题给出肯定的答案。我们提供了收敛性证明并进行了一些数值模拟来说明我们的理论结果。</p>