Battery internal temperature estimation via a semilinear thermal PDE model

Accurate Lithium-ion (Li-ion) battery internal temperature information enables high-fidelity monitoring and safe operation in battery management systems, thus prevents thermal faults that could cause catastrophic failures. This paper proposes an online temperature estimation scheme for cylindrical Li-ion batteries based on a one-dimensional semilinear parabolic partial differential equation (PDE) model subject to in-domain and output uncertainties, using temperature measurements at the battery surface only. The thermal state observer design exploits PDE backstepping method, with a mild assumption on the Lipschitz continuity of the nonlinear heat generation rate. A sufficient condition on the Lipschitz constant to achieve exponential convergence is derived. Furthermore, when the thermal system uncertainties are present, an analytic bound on the temperature estimation error is formulated in the sense of spatial L₂ norm, in terms of Lipschitz constant, design parameters, and bounds on system uncertainties. Simulation studies on various practical current profiles are demonstrated to illustrate the effectiveness of the proposed thermal estimation framework on a commercial cylindrical Li-ion battery cell.