This paper investigates the state estimation of a high-fidelity spatially resolved thermalelectrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1 % in less than 200 s despite a 30 % error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.

This paper investigates the identifiability and estimation of the parameters of the single particle model (SPM) for lithium-ion battery simulation. Identifiability is addressed both in principle and in practice. The approach begins by grouping parameters and partially non-dimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that, excluding open circuit voltage, there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearised SPM is unique. It is found that the model is unique provided that the electrode open circuit voltage functions have a known non-zero gradient, the parameters are ordered, and the electrode kinetics are lumped into a single charge transfer resistance parameter. We then demonstrate the practical estimation of model parameters from measured frequency-domain experimental electrochemical impedance spectroscopy (EIS) data, and show additionally that the parametrised model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between model and experiment over a 10 minute dynamic discharge. NOMENCLATURE Roman A Electrode surface area, m 2 a i Specific active surface area, m −1 c e Electrolyte lithium concentration, mol m −3 c i Lithium concentration (active material), mol m −3 c 0 i Initial lithium concentration, mol m −3 c max i Maximum lithium concentration, mol m −3 c s iSurface lithium concentration, mol m −3 D i Electrode active material diffusivity, m 2 s −1 F Faraday's constant, C mol −1 H 0 SPM transfer function, Ω H d i Diffusion model transfer function, A −1 I Applied current, A i 0,i Exchange current density, A m −2 j i Reaction rate, mol m −2 s −1 k i Reaction rate constant, m 2.5 mol −0.5 s −1 L j Single DoD loss function, Ω 2 L Combined DoDs loss function, Ω 2 N ω Number of data points per EIS measurement N DoD Number of EIS datasets at different DoDs J-H Kim is with the Energy Lab,

Metal forming processes operate in conditions of uncertainty due to parameter variation and imperfect understanding. This uncertainty leads to a degradation of product properties from customer specifications, which can be reduced by the use of closed-loop control. A framework of analysis is presented for understanding closed-loop control in metal forming, allowing an assessment of current and future developments in actuators, sensors and models. This leads to a survey of current and emerging applications across a broad spectrum of metal forming processes, and a discussion of likely developments

This brief investigates the observability of one of the most commonly used equivalent circuit models (ECMs) for lithium-ion batteries and presents a method to estimate the state of charge (SOC) in the presence of sensor biases, highlighting the importance of observability analysis for choosing appropriate state estimation algorithms. Using a differential geometric approach, necessary and sufficient conditions for the nonlinear ECM to be observable are derived and are shown to be different from the conditions for the observability of the linearised model. It is then demonstrated that biases in the measurements, due to sensor ageing or calibration errors, can be estimated by applying a nonlinear Kalman filter to an augmented model where the biases are incorporated into the state vector. Experiments are carried out on a lithium-ion pouch cell and three types of nonlinear filters, the first-order extended Kalman filter (EKF), the secondorder EKF and the unscented Kalman filter (UKF) are applied using experimental data. The different performances of the filters are explained from the point of view of observability.