Data-driven Discrete-time Identification of Continuous-time Nonlinear Systems and Nonlinear Modelling of Li-Ion Batteries

Nowadays, due to the environmental concerns, increasing demand for cleaner energy and energy ecient systems, lithium-ion batteries are used in many systems due to their high specic energy and energy density. Hence, the emphasis of this presented work is towards the development of a mathematical model for lithium-ion batteries. System identication is the process of deriving these mathematical models from measured data or observations systematically. The dynamical response of lithium-ion battery evolves continuously in time but discrete-time models are very convenient to simulate a dynamical system on a computer. Therefore both linear and nonlinear discrete-time models are often used to approximate such kind of dynamical systems. In this thesis, a measurement methodology is proposed to acquire data in order to develop such discrete-time representation. Furthermore, theoretical foundations are laid out to control the errors of such kind of approximated discrete-time representation for continuous time systems. The presented work also proposes a data-driven methodology for characterising the battery's short term electrical response at varying operating conditions in terms of its linear and nonlinear behaviour. A decision can be made by the battery modeller at this stage to develop either a linear or nonlinear model based on the information and knowledge gained from the chracterisation step. Based on the choice made, this work proposes a novel data-driven methodology to estimate either a discrete-time best linear approximation of the nonlinear battery response at dierent operating conditions, or to develop a exible discrete-time nonlinear model (Polynomial nonlinear state-space model (PNLSS)), which is valid for the complete operating range, starting from the data acquired at multiple operating conditions with varying levels of noise and nonlinear distortions. The developed models are especially suited for operating points lying in the nonlinear regime of the battery's electrical operation of almost depleted battery in terms of state of charge (SoC) at a low temperature.