Batteries play a crucial role in powering contemporary devices and systems, ranging from smartphones and electric vehicles to renewable energy storage. With the increasing demand for more efficient and reliable battery technologies, the need for accurate monitoring and assessment of battery condition and performance has also grown. Online estimators, that continuously analyse battery conditions in real-time, have emerged as valuable tools to meet these goals. This thesis focuses on constructing model-based online state estimators for real-time estimation of a battery's State of Health (SOH).

These estimators, necessitate a state space model for a lithium-ion cell. In the initial part of the thesis, a physics-based reduced-order model (ROM) of a lithium-ion cell is developed. This model accounts for major aging mechanisms such as Solid Electrolyte Interphase (SEI) layer formation, Loss of Active Material (LAM), and Lithium Plating (LIP). To incorporate temperature effects on cell parameters, a simplified lumped thermal model is integrated into the battery model. The model is subsequently transformed into a state space model using the Discrete Realization Algorithm (DRA) process.

Building upon the noisy outputs from the ROM models, a set of five estimators is formulated: State of Charge (SOC), Voltage, SEI loss, LAM loss, and LIP loss estimators. These estimators are constructed based on Kalman filters and collectively contribute to real-time prediction of a battery's SOH. Given their reliance on the model, the ROM model's output is employed as a reference to gauge the precision of the estimators.

To address the real life scenarios and to check the robustness of the estimators, a series of sub-questions were analysed:
Sub question1: How to estimate the SOH of a cell in real-time using adaptive control techniques ?
Sub question2: How fast can the estimator react to changing initial states of the cell?
Sub question3: Can the estimators be adapted to concurrently estimate both the states and the time varying cell parameters in case of an old cell? How fast can this be
achieved in real-time ?

Overall, this research contributes to the development of model-based online estimators, which are poised to have a significant impact on enhancing battery performance, prolonging lifespan, and facilitating the transition towards a more sustainable energy future.